14 Chemical Kinetics. Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that

14 Chemical Kinetics

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings

CHAPTER OBJECTIVES

• To understand the factors that affect the rate of chemical reactions

• To be able to determine a reaction rate

• To understand the meaning of a rate law

• To be able to determine the concentration dependence of the rate of a chemical reaction

• To be able to predict the individual steps of a simple reaction

• To begin to understand why chemical reactions occur


Chemistry: Principles, Patterns, and Applications, 1e

14.1 Factors That Affect Reaction Rates


14.1 Factors That Affect Reaction Rates

• Chemical kinetics – Study of reaction rates, or the changes in the concentrations of

reactants and products with time

– By studying kinetics, insights are gained into how to control reaction conditions to achieve a desired outcome

• Chemical kinetics of a reaction depend on various factors

1. Reactant concentrations

2. Temperature

3. Physical states and surface areas of reactants

4. Solvent and catalyst properties


Concentration Effects

• Two substances cannot react with each other unless their constituent particles come into contact; if there is no contact, the rate of reaction will be zero.

• The more reactant particles that collide per unit time, the more often a reaction between them can occur.

• The rate of reaction usually increases as the concentration of the reactants increases.


Temperature Effects

• Increasing the temperature of a system increases the average kinetic energy of its constituent particles.

• As the average kinetic energy increases, the particles move faster, so they collide more frequently per unit time and possess greater energy when they collide, causing increases in the rate of the reaction.

• Rate of all reactions increases with increasing temperature and decreases with decreasing temperature.


Phase and Surface Area Effects

• If reactants are uniformly dispersed in a single homogeneous solution, the number of collisions per unit time depends on concentration and temperature.

• If the reaction is heterogeneous, the reactants are in two different phases, and collisions between the reactants canoccur only at interfaces between phases; therefore, the number of collisions between the reactants per unit time is reduced, as is the reaction rate. The rate of a heterogeneous reaction depends on the surface area of the more condensed phase.


Solvent Effects

• The nature of the solvent can affect the reaction rates of solute particles.

• Solvent viscosity is also important in determining reaction rates.

1. In highly viscous solvents, dissolved particles diffuse much more slowly than in less viscous solvents and collide less frequently per unit time.

2. Rates of most reactions decrease rapidly with increasing solvent viscosity.


Catalyst Effects

• Catalyst is a substance that participates in a chemical reaction and increases the rate of the reaction without undergoing a net chemical change itself.

• Catalysts are highly selective and often determine the product of a reaction by accelerating only one of several possible reactions that could occur.



14.2 Reaction Rates and Rate Laws


Reaction Rates

• Reaction rates

– Expressed as the concentration of reactant consumed or the concentration of product formed per unit time

– Units are moles per liter per unit time (M/s, M/min or M/h)

– To measure reaction rates 1. initiate the reaction;

2. measure the concentration of the reactant or product at different times as the reaction progresses;

3. plot the concentration as a function of time on a graph;

4. calculate the change in the concentration per unit time.


Reaction Rates• Reaction Rates

– The change in the concentration of either the reactant or the product over a period of time.

– For a simple reaction (A B), rate = [B] = – [A] t t

– Square brackets indicate concentration; and means “change in.”

– Concentration of A decreases with time; and the concentration of B increases with time.


Reaction Rates

• Determining the rate of hydrolysis of aspirin

– One can calculate the average reaction rate for a given time interval from the concentrations of either the reactant or one of the products at the beginning of the interval (time = t0) and at the end of the interval (tf).

– Using salicylic acid, one can find the rate of the reaction for the interval between t = 0 and t = 2h; one can also calculate the rate of the reaction from the concentrations of aspirin at the beginning and the end of the same interval.


Reaction Rates• Calculating the Rate of Fermentation of Sucrose

– A reaction in which coefficients are not all the same

–The coefficients show that the reaction produces four molecules of ethanol and four molecules of carbon dioxide for every one molecule of sucrose that is consumed

–The coefficients in the balanced equation show that the rate at which ethanol is formed is four times faster than the rate at which sucrose is consumed: [ethanol] = – 4[sucrose]

t t

This can also be expressed in terms of the reactant or product with the smallest coefficient in the balanced equation

rate = – [sucrose] / t = ¼([ethanol] /t).


Reaction Rates

• Instantaneous rate of reaction

– The rate at any given point in time

– As the period of time used to calculate an average rate of a reaction becomes shorter and shorter, the average rate approaches the instantaneous rate

– In chemical kinetics, focus is on one particular instantaneous rate, t = 0, which is the initial rate of the reaction; initial rates are determined by measuring the rate of the reaction at various times and then extrapolating a plot of rate versus time to t = 0


Rate Laws

• Describes the relationships between reactant rates and reactant concentrations

• May be written from either of two different, but related, perspectives:

1. Differential rate law – Expresses the rate of a reaction in terms of changes in the

concentration of one or more reactants, [R], over a specific time interval, t

– Describes what is occurring on a molecular level during a reaction


Rate Laws

2. Integrated rate law

– Describes the rate of a reaction in terms of the initial concentration, [R]0, and the measured concentration of one or more reactants, [R], after a given amount of time, t

– Used for determining the reaction order and the value of the rate constant from experimental measurements

• Rate law must give the proper units for the rate, M/s

• Rate law must be determined experimentally


Rate Laws

• Reaction orders

– For a reaction with the general equation

aA + bB cC + dD,

the experimentally determined rate law has the form

rate = k[A]m [B]n.

– The proportionality constant, k, is called the rate constant. 1. Value is characteristic of the reaction and reaction conditions

2. A given reaction has a particular value of the rate constant under a given set of conditions, such as

temperature, pressure, and solvent


Rate Laws

– Rate of a reaction depends on the rate constant for the given set of reaction conditions and on the concentration of each reactant, raised to the powers m and n

– Values of m and n are derived from experimental measurements of the changes in reactant concentrations over time and indicate the reaction order, the degree to which the rate of the reaction depends on the concentration of each reactant

– m and n are not related to the stoichiometric coefficients a and b in the balanced chemical equation but must be determined experimentally

– Overall reaction order is the sum of all the exponents in the rate law, or m + n



14.3 Methods of Determining Reaction

Orders


• Zeroth-order reaction – Reaction whose rate is independent of concentration

– Its differential rate law is rate = k

– One can write their rate in a form such that the exponent of the reactant in the rate law is 0

rate = – [A] = k[reactant]0 = k(1) = k t

– Since rate is independent of reactant concentration, a graph of the concentration of any reactant as a function of time is a straight line with a slope of –k (concentration decreases with time); a graph of the concentration of any product as a function of time is a straight line with a slope of +k

Zeroth-Order Reactions


– Integrated rate law for a zeroth-order reaction produces a straight line and has the general formula

[A] = [A]0 – kt, where [A]0 is the initial concentration of reactant A; the rate

constant must have the same units as the rate of the reaction, M/s, in a zeroth-order reaction

– Equation has the form of the equation for a straight line (y = mx + b); y = [A], mx = – kt, and b = [A]0

– Occur most often when the reaction rate is determined by available surface area

Zeroth-Order Reactions


• First-order reaction – Reaction rate is directly proportional to the concentration of

one of the reactants

– Have the general form A products

– Differential rate for a first-order reaction is rate = – [A] = k[A] t

– If the concentration of A is doubled, the rate of the reaction doubles; if the concentration of A is increased by a factor of 10, the rate increases by a factor of 10

– Units of a first-order rate constant are inverse seconds, s–1

– First-order reactions are very common

First-Order Reactions


– Integrated rate law for a first-order reaction can be written in two different ways, one using exponentials and one using logarithms

1. Exponential form, [A] = [A]0e–kt, where [A]0 is the initial concentration of reactant A at t = 0; k is the rate constant, and e is the base of the natural logarithms, which has the value 2.718. Concentration of A will decrease in a smooth exponential curve over time

2. The logarithmic expression of the relationship between the concentration of A and t is obtained by taking the natural logarithm of each side of the preceding equation and rearranging: ln[A] = ln[A]0 – kt; the equation has the form of the equation for a straight line; y = ln[A] and b = ln[A]0; and a plot of ln[A] vs. t for a first-order reaction gives a straight line with a slope of –k and an intercept of ln[A]0

First-Order Reactions


• Two kinds of second-order reactions

1. The simplest kind of second-order reaction is one whose rate is proportional to the square of the concentration of the reactant and has the form 2A products.

– Differential rate law is rate = – [A] = k[A]2

2t

– Doubling the concentration of A quadruples the rate of the reaction

– Units of rate constant is M–1s–1 or L/mols

– Concentration of the reactant at a given time is described by the following integrated rate law: 1/ [A] =

1/ [A]0 + kt, which has the form of an equation of a straight line; y = 1/ [A], b = 1/ [A]0; and a plot of 1/ [A] vs t is a straight line with a slope of k and an intercept of 1/[A]0

Second-Order Reactions


2. The second kind has a rate that is proportional to the product of the concentrations of two reactants and has the form A + B products.

– Reaction is first order in A and first order in B

– Differential rate law for the reaction is rate = – [A] = – [B] = k[A] [B] t t

– Reaction is first order both in A and in B and has an overall reaction order of 2

Second-Order Reactions


• Understanding reaction mechanisms (sets of steps in a reaction) simplifies chemical reactions.

• The first step in discovering the mechanism of a reaction is to determine the reaction’s rate law, which can be done by designing experiments that measure the concentration(s) of one or more of the reactants or products as a function of time.

• For the reaction A + B products, one needs to determine the value of k and the exponents m and n in the equation

rate = k[A]m [B]n.

• Rate data is given in the following table:

Determining the Rate Law of a Reaction


• One can determine values of k and exponents m and n in several ways:

1. Keep the initial concentration of B constant while varying the initial concentration of A and calculating the initial rate of the reaction and then deducing the order of the reaction with respect to A

2. Determine the order of reaction with respect to B by studying the reaction rates when the initial concentration of A is kept constant while the concentration of B is varied

3. Determine order of reaction with respect to a given reactant by comparing the different rates obtained when only the concentration of the reactant in question was changed

4. Determine reaction orders by taking the quotient of the rate laws for two different experiments

Determining the Rate Law of a Reaction


5. Obtain the value of m and n directly by finding the ratio of the rate laws for two experiments in which the concentration of one of the reactants is the same such as Experiments 1 and 3 in the table 14.4.

rate1 = k[A1]m [B1]n

rate3 = k[A3]m [B3]n

6. By selecting two experiments in which the concentration of B is the same, one can solve for the value of m; by selecting two experiments in which the concentration of A is the same, one can solve for n

7. Calculate the rate constant by inserting data from any line from the table into the experimentally determined rate law and solve for k

Determinin the Rate Law of a Reaction



14.4 Using Graphs to Determine Rate Laws, Rate

Constants, and Reaction Orders


14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders

• For a zeroth-order reaction, a plot of the concentration of any reactant versus time is a straight line with a slope of – k.

• For a first-order reaction, a plot of the logarithm of the concentration of a reactant versus time is a straight line with a slope of – k.

• For a second-order reaction, a plot of the inverse of the concentration of a reactant versus time is a straight line with a slope of k.

• Properties of reactions that obey zeroth-, first-, and second-order rate laws are summarized in the following table.


14.4 Using Graphs to Determine Rate Laws, Rate Constants, and Reaction Orders



14.5 Half-Lives and Radioactive Decay

Kinetics


Half-Lives

• Another approach to describe reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value.

• The period of time is called the half-life of the reaction, written as t½ .

• The half-life of a reaction is the time required for the reactant concentration to decrease from [A]0 to [A]0 /2.

• If two reactions have the same order, the faster reaction will have a shorter half-life and the slower reaction will have a longer half-life.


Half-Lives

• The half-life of a first-order reaction under a given set of reaction conditions is a constant; this is not true for zeroth- or second-order reactions.

• The half-life of a first-order reaction is independent of the concentration of the reactants.

• Rearranging the integrated rate law for a first-order reaction produces the equation [A]0

[A]

• Substituting [A]0 /2 for [A] and t½ for t (to indicate a half-life) into the above equation gives [A]0

[A]0 /2

• Solving for t½: t½ = 0.693/k

• For a first-order reaction, each successive half-life is the same length of time and is independent of [A].

= ktln

ln = ln 2 = kt½


Radioactive Decay Rates

• Radioactivity, or radioactive decay, is the emission of a particle or a photon that results from the spontaneous decomposition of the unstable nucleus of an atom.

• The rate of radioactive decay is an intrinsic property of each radioactive isotope, independent of the chemical and physical form of the radioactive isotope.

• Rate is also independent of temperature.

• In a sample of a given radioactive substance, the number of atoms of the radioactive isotope must decrease with time as their nuclei decay to nuclei of a more stable isotope.



• Using N to represent the number of atoms of the radioactive isotope, the rate of decay of the sample (also called its activity, A) can be defined as the decrease in the number of the radioisotope’s nuclei per unit time A = – N/t

• Activity is measured in disintegrations per second (dps) or disintegrations per minute (dpm)

• Activity of a sample is directly proportional to the number of atoms of the radioactive isotope in the sample A = kN

• k is the radioactive decay constant and has units of inverse time (s–1, yr

–1) and has a characteristic value for each radioactive isotope



• Combining equations, the relationship between the number of decays per unit time and the number of atoms of the isotope in a sample is obtained

– N/t = kN

• The equation is the same as the equation for the rate of a first-order reaction; except that it uses number of atoms instead of concentrations

• Radioactive decay is a first-order process and can be described in terms of either the differential rate law as above or the integrated rate law

N = N0e–kt or ln N/N0 = – kt



• Because radioactive decay is a first-order process, the time required for half of the nuclei in any sample of a radioactive isotope to decay is a constant, called the half-life of the isotope

• Half-life tells how radioactive an isotope is (the number of decays per unit time) and is the most commonly cited property of any isotope

• Isotopes with a short half-life decay more rapidly, undergoing a greater number of radioactive decays per unit time than do isotopes with a long half-life


Radioisotope Dating Techniques

• Using the half-lives of isotopes, one can estimate the ages of geological and archaeological artifacts.

• Techniques that have been developed for this application are known as radioisotope dating techniques.

• The most common method for measuring the age of ancient objects is carbon-14 dating; carbon-14 isotope, created in the upper regions of Earth’s atmosphere, reacts with atmospheric oxygen or ozone to form 14CO2.

• The CO2 that plants use as a carbon source include a proportion of 14CO2 molecules as well as nonradioactive 12CO2 and 13CO2; animals that eat plants ingest these carbon isotopes.


Radioisotope Dating Techniques

• When the animals or plants die, the carbon-14 nuclei in its tissue decay to nitrogen-14 nuclei by a radioactive process known as beta decay, which releases low-energy electrons ( particles) that can be detected and measured: 14C 14N + – with a half-life of 5700 ± 30 yr.

• The 14C/ 12C ratio in living organisms is 1.3 x 10–12 with a decay rate of 15 dpm per gram of carbon (dpm/g carbon).

• Comparing the disintegrations per minute per gram of carbon from an archaeological sample with those from a recently living sample enables scientists to estimate the age of the artifact.



14.6 Reaction Rates—A Microscopic View



• One of the major reasons for studying chemical kinetics is to use measurements of the macroscopic properties of a system to discover the sequence of events that occur at the molecular level during a reaction.

• Molecular description is the mechanism of the reaction; it describes how individual atoms, ions, or molecules interact to form particular products.

• Stepwise changes are called the reaction mechanism, the microscopic path by which reactants are transformed into products by a complex series of reactions that take place in a stepwise fashion.



• Each step or individual reaction is called an elementary reaction, and the overall sequence of elementary reactions is the mechanism of the reaction.

• The sum of the individual steps, or elementary reactions, in the mechanism must give the balanced chemical equation for the overall reaction.


Molecularity and the Rate-Determining Step

• Species that are formed in one step and consumed in another are intermediates; and they do not appear in the balanced chemical equation for the reaction.

• Following the two-step mechanism is an example:

Step 1 NO2 + NO2 NO3 + NO Elementary reaction

Step 2 NO3 + CO NO2 + CO2 Elementary reaction

Sum NO2 + CO NO + CO2 Overall reaction

• NO3 is an intermediate in the reaction.



• Using molecularity to describe a rate law

– Each elementary step can be described in terms of its molecularity, the number of molecules that collide in that step.

– If there is only a single reactant molecule in an elementary reaction, that step is designated as unimolecular.

– If there are two reactant molecules, it is bimolecular; if there are three reactant molecules, it is termolecular.

– Order of the elementary reaction is the same as its molecularity, but the rate law for the reaction cannot be determined from the balanced equation for the overall reaction.



– The general rate law for a unimolecular elementary reaction (A products) is rate = k[A].

– For bimolecular reactions, the reaction rate depends on the number of collisions per unit time, which is proportional to the product of the concentrations of the reactants.

– For a bimolecular elementary reaction of the form 2A products, the general rate law is rate = k[A]2.

– Common types of elementary reactions and their rate laws are summarized in the following table:



• Identifying the rate-determining step

– The balanced chemical equation does not necessarily reveal the individual elementary reactions by which the reaction occurs.

– One cannot obtain the rate law for a reaction from the overall balanced equation alone.

– The rate law for the overall reaction is the same as the rate law for the slowest step in the reaction mechanism, the rate-determining step, because any process that occurs through a sequence of steps can take place no faster than the slowest step in the sequence.


Chain Reactions

• Many reaction mechanisms consist of long series of elementary reactions called chain reactions, in which one or more elementary reactions that contain a highly reactive species repeat again and again during the reaction process.

• Chain reactions have three stages:

1. initiation, a step that produces one or more reactive intermediates; often these intermediates are radicals, species that have an unpaired valence electron;

2. propagation, reactive intermediates are continuously consumed and regenerated while products are formed;

3. termination, intermediates are also consumed, usually by forming stable products.



14.7 The Collision Model of Chemical Kinetics


14.7 The Collision Model of Chemical Kinetics

• A useful tool for understanding the behavior of reacting chemical species

• The collision model explains the following:

– A chemical reaction can occur only when the reactant molecules, atoms, or ions collide with more than a certain amount of kinetic energy and in the proper orientation

– Explains why most collisions between molecules do not result in a chemical reaction, because in most collisions, the molecules simply bounce off one another without reacting

– Why such chemical reactions occur more rapidly at higher temperatures


Activation Energy• A minimum energy (activation energy, Ea) is required for a collision

between molecules to result in a chemical reaction.

• Reacting molecules must have enough energy to overcome electrostatic repulsion and a minimum amount of energy to break chemical bonds so that new ones may be formed.

• Molecules that collide with less than the activation energy bounce off one another chemically unchanged, with only their direction of travel and their speed altered by the collision.

• Molecules that are able to overcome the energy barrier react and form an arrangement of atoms called the activation complex or the transition state.


Graphing the Energy Changes during a Reaction

• One can graph the energy of a reaction by plotting the potential energy of the system as the reaction progresses with time.

• Plots show an energy barrier that must be overcome for the reaction to occur, which means that the activation energy is always positive.

• Ea provides information about the rate of a reaction and how rapidly the rate changes with temperature.

• For two similar reactions under comparable conditions, the reaction with the smallest Ea will occur more rapidly.


Graphing the Energy Changes during a Reaction

• Even when the energy of collisions between two reactant species is greater than Ea, most collisions do not produce a reaction; the probability of a reaction occurring depends not only on the collision energy, but also on the spatial orientation of the molecules when they collide.

• The fracture of orientations that result in a reaction is called the steric factor, p, and its value can range from 0 (no orientations of molecules result in reaction) to 1 (all orientations result in reaction).


The Arrhenius Equation

• In the following figure, both the kinetic energy distributions and a potential energy diagram for a reaction are shown



•

– Shaded areas show that at the lower temperature, only a small fraction of molecules collide with kinetic energy greater than Ea; at the higher temperature, a much larger fraction of molecules collide with kinetic energy greater than Ea

– The rate of the reaction is much slower at the lower temperature because only a few molecules collide with enough energy to overcome the potential energy barrier



• For an A + B elementary reaction, all the factors that affect the reaction rate can be summarized in a single series of relationships:

rate = (collision frequency) (steric factor) (fraction of collisions with E > Ea) where rate = k[A] [B]

• Arrhenius used these relationships to arrive at an equation that relates the magnitude of the rate constant of a reaction to the temperature; the activation energy; and the constant, A, called the frequency factor, which converts concentrations to collisions per second

k = Ae–Ea /RT (Arrhenius equation)



• The Arrhenius equation summarizes the collision model of chemical kinetics, where T is the absolute temperature (in K) and R is the ideal gas constant [8.314 J/(K•mol)].

• The value of Ea indicates the sensitivity of the reaction to changes in temperature.

• The rate of a reaction with a large Ea increases rapidly with increasing temperature, and the rate of a reaction with a smaller Ea increases much more slowly with increasing temperature.



• If the rate of a reaction at various temperatures is known, the Arrhenius equation can be used to calculate the activation energy by taking the natural logarithm of both sides of the Arrhenius equation.

ln k = ln A + (–Ea /RT) = ln A + [(–Ea /R) (1/T )]

• The preceding equation is the equation for a straight line, where y = ln k and x = 1/T; a plot of ln k versus 1/T is a straight line with a slope of –Ea /R and an intercept of ln A.

• Knowing the value of Ea at one temperature predicts the rate of a reaction at other temperatures.



14.8 Catalysis


14.8 Catalysis• Catalysts

– Substances that increase the rate of a chemical reaction without being consumed in the process

– A catalyst does not appear in the overall stoichiometry of the reaction it catalyzes, but it must appear in at least one of the elementary steps in the mechanism for the catalyzed reaction

– Catalyzed pathway has a lower Ea, but the net change in energy that results from the reaction (the difference between the energy of the reactants and the energy of the products) is not affected by the presence of a catalyst

– Because of its lower Ea, the rate of a catalyzed reaction is faster than the rate of the uncatalyzed reaction at the same temperature


14.8 Catalysis


14.8 Catalysis

– A catalyst decreases the height of the energy barrier, and its presence increases the rates of both the forward and the reverse reactions by the same amount

– There are three major classes of catalysts

1. Heterogeneous catalysts 2. Homogeneous catalysts 3. Enzymes


Heterogeneous Catalysis

• In heterogeneous catalysis, the catalyst is in a different phase from the reactants.

• At least one of the reactants interacts with the solid surface (in a physical process called adsorption) in such a way that a chemical bond in the reactant becomes weak and then breaks.


Homogeneous Catalysis

• In homogeneous catalysis, the catalyst is in the same phase as the reactant(s); the number of collisions between reactants and catalyst is at a maximum because the catalyst is uniformly dispersed throughout the reaction mixture.


Enzymes

• Enzymes are catalysts that occur naturally in living organisms and are almost all protein molecules with typical molecular masses of 20,000–100,000 amu.

• Some are homogeneous catalysts that react in aqueous solution within a cellular compartment of an organism.

• Some are heterogeneous catalysts embedded within the membranes that separate cells and cellular compartments from their surroundings.

• A reactant in an enzyme-catalyzed reaction is called a substrate.

• Enzymes can increase reaction rates by enormous factors and tend to be very specific, typically producing only a single product in quantitative yield.


Enzymes

• Enzymes are expensive, and often cease functioning at temperatures higher than 37ºC, and have limited stability in solution.

• Enzyme inhibitors cause a decrease in the rate of an enzyme-catalyzed reaction by binding to a specific portion of an enzyme and thus slowing or preventing a reaction from occurring.


15Chemical Equilibrium


CHAPTER OBJECTIVES

• To understand what is meant by chemical equilibrium

• To know the relationship between the equilibrium constant and the rate constants for the forward and reverse reactions

• To be able to write an equilibrium constant expression for any reaction

• To be able to solve quantitative problems involving chemical equilibrium

• To predict the direction of reaction

• To predict the effects of stresses on a system at equilibrium

• To understand different ways to control the products of a reaction



15.1 The Concept of Chemical Equilibrium


15.1 The Concept of Chemical Equilibrium

• Chemical equilibrium – A dynamic process

– Consists of a forward reaction, in which reactants are converted to products, and a reverse reaction, in which products are converted to reactants

– At equilibrium, the forward and reverse reactions proceed at equal rates

– Double arrow (⇋) indicates that both the forward and reverse reactions are occurring simultaneously and is read “is in equilibrium with”

– At equilibrium, the composition of the system no longer changes with time

– Composition of an equilibrium mixture is independent of the direction from which equilibrium is approached



15.2 The Equilibrium Constant


15.2 The Equilibrium Constant

• Equilibrium state is achieved when the rate of the forward reaction equals the rate of the reverse reaction.

• Under a given set of conditions, there must be a relationship between the composition of the system at equilibrium and the kinetics of a reaction represented by rate constants.

• The ratio of the rate constants yields a new constant, the equilibrium constant (K), a unitless quantity and is defined as K = kf /kr.

• The fundamental relationship between chemical kinetics and chemical equilibrium states that, under a given set of conditions, the composition of the equilibrium mixture is determined by the magnitudes of the rate constants for the forward and reverse reactions.


Developing an Equilibrium Constant Expression

• In1864, Guldberg and Waage discovered that for any reversible reaction of the general form

aA + bB ⇋ cC + dD, where A and B are reactants, C and D are products, and a, b, c, and

d are the stoichiometric coefficients in the balanced equation for the reaction, the ratio of the product of the equilibrium concentrations of the products (raised to their coefficients in the balanced equation) to the product of the equilibrium concentrations of the reactants (raised to their coefficients in the balanced equation) is always a constant under a given set of conditions.

This equation is called the equilibrium equation.

• This relationship is known as the law of mass action



• Law of mass action is stated as

K = [C]c [D]d

[A]a [B]b

– K is the equilibrium constant for the reaction

– Right side of the equation is called the equilibrium constant expression

– Relationship is true for any pair of opposing reactions regardless of the mechanism of the reaction or of the number of steps in the mechanism



• Equilibrium constant (K) – Can vary over a wide range of values and is unitless

– Values of K greater than 103 indicate a strong tendency for reactants to form products, so equilibrium lies to the right, favoring the formation of products (kf >>kr)

– Values of K less than 10–3 indicate that the ratio of products to reactants at equilibrium is very small; reactants do not tend to form products readily, and equilibrium lies to the left, favoring the formation of reactants (kf<<kr)

– Values of K between 103 and 10–3 are not very large or small, so there is no strong tendency to form either products or reactants; at equilibrium, there are significant amounts of both products and reactants (kf kr)




Variations in the Form of the Equilibrium Constant Expression

• Equilibrium can be approached from either direction in a chemical reaction, so the equilibrium constant expression and the magnitude of the equilibrium constant depend on the form in which the chemical reaction is written.

• When a reaction is written in the reverse direction,

cC + dD ⇋ aA + bB K and the equilibrium constant expression are inverted: K´= [A]a [B]b

[C]c [D]d

so K´ = 1/K


Equilibrium Constant Expressions for Systems that Contain Gases

• For reactions that involve nongaseous substances, the concentrations used in equilibrium calculations are expressed in moles/liter.

• For gases, the concentrations are expressed in terms of partial pressures where the standard state is 1 atm of pressure.

• Symbol Kp is used to denote equilibrium constants calculated from partial pressures.

• For the general reaction aA + bB ⇋ cC + dD in which all the components are gases, the equilibrium constant is the ratio of the partial pressures of the products and reactants, each raised to its coefficient in the chemical equation.

Kp =

(PA)c (PC)d

(PB)a (PD)b


Equilibrium Constant Expressions for Systems that Contain Gases

• Kp is unitless.

• Partial pressures are expressed in atmospheres or mmHg, so the molar concentration of a gas and its partial pressure do not have the same numerical value but are related by the ideal gas constant R and the temperature

Kp = K(RT)n

where K is the equilibrium constant expressed in units of concentration and n is the difference between the number of moles of gaseous products and gaseous reactants; temperature is expressed in kelvins.

• If n = 0, Kp = K


Homogeneous and Heterogeneous Equilibria

• Homogeneous equilibrium – When the products and reactants of an equilibrium reaction form

a single phase, whether gas or liquid

– Concentrations of the reactants and products can vary over a wide range

• Heterogeneous equilibrium – A system whose reactants, products, or both are in more than

one phase

– An example is the reaction of a gas with a solid or liquid

• Molar concentrations of pure liquids and solids do not vary with temperature, so they are treated as constants, this simplifies their equilibrium constant expressions


Equilibrium Constant Expressions for the Sums of Reactions

• When a reaction can be expressed as the sum of two or more reactions, its equilibrium constant is equal to the product of the equilibrium constants for the individual reactions.

• H for the sum of two or more reactions is the sum of the H values for the individual reactions.



15.3 Solving Equilibrium Problems


• Two fundamental kinds of equilibrium problems 1. Those in which the concentrations of the reactants and

products at equilibrium are given and the equilibrium constant for the reaction needs to be calculated

2. Those in which the equilibrium constant and the initial concentrations of reactants are known and the concentration of one or more substances at equilibrium needs to be calculated

15.3 Solving Equilibrium Problems


Calculating an Equilibrium Constant from Equilibrium Concentrations

• An equilibrium constant can be calculated when equilibrium concentrations, molar concentrations, or partial pressures are substituted into the equilibrium constant expression for the reaction.

• Sometimes the concentrations of all the substances are not given or the equilibrium concentrations of all the relevant substances for a particular system are not measured. In these cases, the equilibrium concentrations can be obtained from the initial concentrations of the reactants and the balanced equation for the reaction, as long as the equilibrium concentration of one of the substances is known.


Calculating Equilibrium Concentrations from the Equilibrium Constant

• Equilibrium constants can be used to calculate the equilibrium concentrations of reactants and products by using the quantities or concentrations of the reactants, the stoichiometry of the balanced equation for the reaction, and a tabular format to obtain the final concentrations of all species at equilibrium.



15.4 Nonequilibrium Conditions


15.4 Nonequilibrium Conditions

• One must often decide whether a system has reached equilibrium or the composition of the mixture will continue to change with time

• To make this determination, one needs to know how to analyze the composition of a reaction mixture quantitatively


The Reaction Quotient (Q)• Reaction quotient (Q)

– A quantity used to determine whether a system has reached equilibrium

– Expression for the reaction quotient has the same form as the equilibrium constant expression

– Q may be derived from a set of values measured at any time during the reaction of any mixture of the reactants and products, regardless of whether the system is at equilibrium

– For the general reaction aA + bB ⇋ cC + dD, reaction quotient is defined as Q = [C]c [D]d

[A]a [B]b

– Qp can be written for any reaction that involves gases by using the partial pressures of the components


The Reaction Quotient (Q)

• Comparing the magnitudes of Q and K allows the determination of whether a reaction mixture is already at equilibrium and, if it is not, how to predict whether its composition will change with time (whether the reaction will proceed to the right or to the left)

1. If Q = K, the system is at equilibrium, no further change in the composition of the system will occur unless the conditions are changed

2. If Q < K, then the ratio of the concentrations of products to the concentration of reactants is less than the ratio at equilibrium; reaction will proceed to the right, forming products at the expense of reactants

3. If Q > K, then the ratio of the concentrations of products to the concentrations of reactants is greater than at equilibrium; reaction will proceed to the left, forming reactants at the expense of products


The Reaction Quotient (Q)


Predicting the Direction of Reaction Using a Graph

• Graphs derived by plotting a few equilibrium concentrations for a system at a given temperature and pressure can be used to predict the direction in which a reaction will proceed

• Points that do not lie on the line represent nonequilibrium states and the system will adjust to achieve equilibrium



15.5 Factors That Affect Equilibrium


15.5 Factors That Affect Equilibrium

• Strategies are used to increase the yield of the desired products of reactions

• Reaction conditions are controlled to obtain the maximum amount of the desired product

• Changes in reaction conditions affect the equilibrium composition of a system


• When a system at equilibrium is perturbed in some way, the effects of the perturbation can be predicted qualitatively using Le Châtelier’s principle.

• This principle states that if a stress is applied to a system at equilibrium, the composition of the system will change to relieve the applied stress.

• Stress occurs when any change in the system affects the magnitude of Q or K.

Le Châtelier’s Principle


• Three types of stresses can change the composition of an equilibrium mixture

1. A change in the concentrations (or partial pressures) of the components by the addition or removal of reactants or products

2. A change in the total pressure or volume

3. A change in the temperature of the system

Le Châtelier’s Principle


• An equilibrium is disturbed by adding or removing a reactant or product

1. Stress of an added reactant or product is relieved by reaction in the direction that consumes the added substance

a. Add reactant—reaction shifts right toward product b. Add product—reaction shifts left toward reactant

2. Stress of removing reactant or product is relieved by reaction in the direction that replenishes the removed substance

a. Remove reactant—reaction shifts left

b. Remove product—reaction shifts right

Changes in Concentration


• Changes that occur due to changes in the value of Qc

1. Add reactant—denominator in Qc expression becomes larger

A. Qc < Kc

B. To return to equilibrium, Qc must increase

I. Numerator of Qc expression must increase and

the denominator must decrease

II. Implies net conversion of reactants to

products; reaction shifts right



2. Remove reactant—denominator in Qc expression becomes

smaller

A. Qc > Kc

B. To return to equilibrium, Qc must decrease

I. Numerator of Qc expression must decrease and

the denominator must increase

II. Implies net conversion of products to reactants;

reaction shifts left



Changes in Total Pressure or Volume

• If a balanced reaction contains different numbers of gaseous reactant and product molecules, the equilibrium will be sensitive to changes in volume or pressure; change in pressure (due to changing volume) changes the composition of the equilibrium mixture

• Increase in pressure (due to decrease in volume) results in a reaction in the direction of a fewer number of moles of gas

• Decrease in pressure (due to increase in volume) results in a reaction in the direction of a greater number of moles of gas



• Changes occur due to changes in the value of Qc

1. Decrease volume—molarity increases

2. If reactant side has more moles of gas a. Increase in denominator is greater than increase in numerator

and Qc < Kc

b. To return to equilibrium, Qc must increase; the numerator of the Qc expression must increase and denominator must decrease—it shifts toward fewer moles of gas (reactants to products)



3. If product side has more moles of gas a. Increase in numerator is greater than increase in denominator and

Qc > Kc

b. To return to equilibrium, Qc must decrease; the denominator of the Qc expression must decrease and the numerator must increase—it shifts toward fewer moles of gas (products to reactants)

• If the reaction involves no change in the number of moles of gas, there is no effect on the composition of the equilibrium mixture

• Effect of pressure changes on solids and liquids can be ignored


• Changes in temperature can change the value of the equilibrium constant without affecting the reaction quotient (Q K)

• System is no longer at equilibrium, and the composition of the system will change until Q equals K at the new temperature

• To predict how an equilibrium system will respond to a change in temperature, one must know the enthalpy change of the reaction, Hrxn

1. Exothermic (heat is released, H < 0): reactants ⇋ products + heat

2. Endothermic (heat is absorbed, H > 0): reactants + heat ⇋ products

Changes in Temperature


• Heat is a product in an exothermic reaction and a reactant in an endothermic reaction; increasing the temperature of a system corresponds to adding heat

• Le Châtelier’s principle predicts 1. that an exothermic reaction will shift to the left (toward

reactants) if the temperature of the system is increased (heat is added);

2. that an endothermic reaction will shift to the right (toward the products) if the temperature of the system is increased;

3. that if Hrxn = 0, then a change in temperature will not affect the equilibrium composition.



• Value of Kc

1. Increasing the temperature increases the magnitude of

the equilibrium constant for an endothermic reaction

2. Increasing the temperature decreases the equilibrium constant for an exothermic reaction

3. Increasing the temperature has no effect on the equilibrium constant for a thermally neutral reaction




15.6 Controlling the Products of Reactions


15.6 Controlling the Products of Reactions

• One of the primary goals of modern chemistry is to control the identity and quantity of the products of chemical reactions.

• Two approaches 1. To get a high yield of a desired compound, make the rate of the

desired reaction much faster than the rate of any of the other possible reactions that might occur in the system; altering reaction conditions to control reaction rates, thereby obtaining a single product or set of products is called kinetic control.

2. Thermodynamic control—consists of adjusting conditions so that at equilibrium only the desired products are present in significant quantities.


16Aqueous Acid-Base Equilibria


CHAPTER OBJECTIVES

• To understand the autoionization reaction of liquid water

• To know the relationship among pH, pOH, and pKw

• To understand the concept of conjugate acid-base pairs

• To know the relationship between acid or base strength and the magnitude of Ka, Kb, pKa, and pKb

• To understand the leveling effect

• To be able to predict whether reactants or products are favored in an acid-base equilibrium

• To understand how molecular structure determines acid and base strengths

• To be able to use Ka and Kb values to calculate the percent ionization and pH of a solution of an acid or a base


CHAPTER OBJECTIVES• To be able to calculate the pH at any point in an acid-base titration

• To understand how the addition of a common ion affects the position of an acid-base equilibrium

• To understand how a buffer works and how to use the Henderson-Hasselbalch equation to calculate the pH of a buffer



16.1 The Autoionization of Water



• Acids and bases can be defined in different ways: 1. Arrhenius definition: An acid is a substance that dissociates in

water to produce H+ ions (protons), and a base is a substance that dissociates in water to produce OH– ions (hydroxide); an acid-base reaction involves the reaction of a proton with the hydroxide ion to form water

2. Brønsted–Lowry definition: An acid is any substance that can donate a proton, and a base is any substance that can accept a proton; acid-base reactions involve two conjugate acid-base pairs and the transfer of a proton from one substance (the acid) to another (the base)

3. Lewis definition: A Lewis acid is an electron-pair acceptor, and a Lewis base is an electron-pair donor




Acid-Base Properties of Water

• Water is amphiprotic: it can act as an acid by donating a proton to a base to form the hydroxide ion, or as a base by accepting a proton from an acid to form the hydronium ion, H3O+

• Structure of the water molecule

1. Polar O–H bonds and two lone pairs of electrons on the oxygen atom

2. Liquid water has a highly polar structure


The Ion-Product Constant of Liquid Water

• Because water is amphiprotic, one water molecule can react with another to form an OH– ion and an H3O+ ion in an autoionization process:

2H2O(l)⇋H3O+ (aq) + OH–

(aq)

• Equilibrium constant K for this reaction can be written as

K = [H3O+] [OH–]

[H2O]2

• When pure liquid water is in equilibrium with hydronium and hydroxide ions at 25ºC, the concentrations of hydronium ion and hydroxide ion are equal: [H3O+] = [OH–] = 1.003 x 10–7 M

• At 25ºC, the density of liquid water is 0.0997 g/mL



• The concentration of liquid water at 25ºC is

[H2O] = mol/L = (0.997 g/mL) (1 mol/18.02 g) (1000 mL/L) = 55.3 M

• Because the number of dissociated water molecules is very small, the equilibrium of the autoionization reaction lies far to the left, so the concentration of water is unchanged by the autoionization reaction and can be treated as a constant

• By treating [H2O] as a constant, a new equilibrium constant, the ion-product constant of liquid water (Kw), can be defined:

K[H2O]2 = [H3O+] [OH–] or Kw = [H3O+] [OH–]

• Substituting the values for [H3O+] and [OH–] at 25ºC givesKw = (1.003 x 10–7) (1.003 x 10–7) = 1.006 x 10–14



• Kw varies with temperature, ranging from 1.15 x 10–15 at 0ºC to 4.99 x 10–13 at 100ºC

• In pure water, the concentrations of the hydronium ion and the hydroxide ion are the same, so the solution is neutral

• If [H3O+] > [OH–], the solution is acidic

• If [H3O+] < [OH–], the solution is basic


The Relationship among pH, pOH, and pKw

• The pH scale is a concise way of describing the H3O+ concentration and the acidity or basicity of a solution

• pH and H+ concentration are related as follows:

pH = –log10[H+] or [H+] = 10–pH

• pH of a neutral solution ([H3O+] = 1.00 x 10–7 M) is 7.00

• pH of an acidic solution is < 7, corresponding to [H3O+] > 1.00 x 10–7

• pH of a basic solution is > 7, corresponding to [H3O+] < 1.00 x 10–7

• The pH scale is logarithmic, so a pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydronium ion concentrations


The Relationship among pH, pOH, and pKw

• There is an analogous pOH scale to describe the hydroxide ion concentration of a solution; pOH and [OH–] are related as follows:

pH = –log10[OH–] or [OH–] = 10–pOH

• A neutral solution has [OH–] = 1.00 x 10–7, so the pOH of a neutral solution is 7.00

• The sum of the pH and the pOH for a neutral solution at 25ºC is 7.00 + 7.00 = 14.00

pKw = –log Kw = –log([H3O+] [OH–]) =

(–log[H3O+]) + (–log[OH–]) = pH + pOH

• At any temperature, pH + pOH = pKw, and at 25ºC, where Kw = 1.01 x 10–14, pH + pOH = 14.00; pH of any neutral solution is just half the value of pKw at that temperature



16.2 A Qualitative Description of Acid-Base

Equilibria


Conjugate Acid-Base Pairs

• Two species that differ by only a proton constitute a conjugate acid-base pair.

1. Conjugate base has one less proton than its acid; A– is the conjugate base of HA

2. Conjugate acid has one more proton than its base; BH+ is the conjugate acid of B

• In the reaction of HCl with water, HCl, the parent acid, donates a proton to a water molecule, the parent base, forming Cl–; HCl and Cl– constitute a conjugate acid-base pair.

• In the reverse reaction, the Cl– ion in solution acts as a base to accept a proton from H3O+, forming H2O and HCl; H3O+ and H2O constitute a second conjugate acid-base pair.


Conjugate Acid-Base Pairs

• Any acid-base reaction must contain two conjugate acid-base pairs, which in this example are HCl/Cl– and H3O+/H2O

• HCl (aq) + H2O (l) H3O+ (aq) + Cl– (aq) parent acid parent base conjugate acid conjugate base


Acid-Base Equilibrium Constants: Ka, Kb, pKa, and pKb

• The magnitude of the equilibrium constant for an ionization reaction can be used to determine the relative strengths of acids and bases

• The general equation for the ionization of a weak acid in water, where HA is the parent acid and A– is its conjugate base, is

HA(aq) + H2O(l) ⇋ H3O+(aq) + A–(aq)

• The equilibrium constant for this dissociation is

K = [H3O+] [A–]

[H2O] [HA]

• The concentration of water is constant for all reactions in aqueous solution, so [H2O] can be incorporated into a new quantity, the acid ionization constant (Ka):

Ka = K[H2O] = [H3O+] [A–] [HA]



• Numerical values of K and Ka differ by the concentration of water (55.3 M); the larger the value Ka, the stronger the acid and the higher the H+ concentration at equilibrium

• Weak bases react with water to produce the hydroxide ion, B(aq) +

H2O(l) ⇋ BH+(aq) + OH–(aq), where B is the parent base and BH+ is its conjugate acid

• Equilibrium constant for this reaction is the base ionization constant (Kb); concentration of water is constant and does not appear in the equilibrium constant expression but is included in the value of Kb

• The larger the value of Kb, the stronger the base and the higher the OH– concentration at equilibrium



• The sum of the reactions described by Ka and Kb is the equation for the autoionization of water, and the product of the two equilibrium constants is Kw

• For any conjugate acid-base pair, KaKb = Kw

• pKa = –log10Ka and pKb = –log10Kb

• Smaller values of pKa correspond to larger acid ionization constants and stronger acids

• Smaller values of pKb correspond to larger base ionization constants and stronger bases

• At 25ºC, pKa + pKb = 14.00



• There is an inverse relationship between the strength of the parent acid and the strength of the conjugate base; the conjugate base of a strong acid is a weak base, and the conjugate base of a weak acid is a strong base

• One can use the relative strengths of acids and bases to predict the direction of an acid-base reaction by following a simple rule: An acid-base equilibrium always favors the side with the weaker acid and base

stronger acid + stronger base weaker acid + weaker base

• In an acid-base reaction, the proton always reacts with the stronger base


Solutions of Strong Acids and Bases: The Leveling Effect

• No acid stronger than H3O+ and no base stronger than OH– can exist in aqueous solution, leading to the phenomenon known as the leveling effect.

• Any species that is a stronger acid than the conjugate acid of water (H3O+) is leveled to the strength of H3O+ in aqueous solution because H3O+ is the strongest acid that can exist in equilibrium with water.

• In aqueous solution, any base stronger than OH– is leveled to the strength of OH– because OH– is the strongest base that can exist in equilibrium with water

• Any substance whose anion is the conjugate base of a compound that is a weaker acid than water is a strong base that reacts quantitatively with water to form hydroxide ion


Polyprotic Acids and Bases

• Polyprotic acids contain more than one ionizable proton, and the protons are lost in a stepwise manner.

• The fully protonated species is always the strongest acid because it is easier to remove a proton from a neutral molecule than from a negatively charged ion; the fully deprotonated species is the strongest base.

• Acid strength decreases with the loss of subsequent protons, and the pKa increases.

• The strengths of the conjugate acids and bases are related by pKa + pKb = pKw, and equilibrium favors formation of the weaker acid-base pair.


Acid-Base Properties of Solutions of Salts

• A salt can dissolve in water to produce a neutral, basic, or acidic solution, depending on whether it contains the conjugate base of a weak acid as the anion (A–) or the conjugate acid of a weak base as the cation (BH+), or both.

• Salts that contain small, highly charged metal ions produce acidic solutions in water.

• The most important parameter for predicting the effect of a metal ion on the acidity of coordinated water molecules is the charge-to-radius ratio of the metal ion.

• The reaction of a salt with water to produce an acidic or basic solution is called a hydrolysis reaction, which is just an acid-base

reaction in which the acid is a cation or the base is an anion.



16.3 Molecular Structure and Acid-Base Strength


• The acid-base strength of a molecule depends strongly on its structure.

• The stronger the A–H or B–H+ bond, the less likely the bond is to break to form H+ ions, and thus the less acidic the substance.

• The larger the atom to which H is bonded, the weaker the bond.

• Acid strengths of binary hydrides increase as we go down a column of the periodic table.

Bond Strengths


• The conjugate base (A– or B) contains one more lone pair of electrons than the parent acid (AH or BH+).

• Any factor that stabilizes the lone pair on the conjugate base favors dissociation of H+ and makes the parent acid a stronger acid.

• Acid strengths of binary hydrides increase as we go from left to right across a row of the periodic table.

Stability of the Conjugate Base


• Atoms or groups in a molecule other than those to which H is bonded can induce a change in the distribution of electrons within the molecule, called an inductive effect; this can have a major effect on the acidity or basicity of the molecule.

• Inductive effect can weaken an O–H bond and allow hydrogen to be more easily lost as H+ ions.

Inductive Effects



16.4 Quantitative Aspects of Acid-Base

Equilibria


Determining Ka and Kb

• The ionization constants Ka and Kb are equilibrium constants that are calculated from experimentally measured concentrations.

• What does the concentration of an aqueous solution of a weak acid or base exactly mean?

– A 1 M solution is prepared by dissolving 1 mol of acid or base in water and adding enough water to give a final volume of exactly 1 L.

– If the actual concentrations of all species present in the solution were listed, it would be determined that none of the values is exactly 1 M because a weak acid or a weak base always reacts with water to some extent.



– The extent of the reaction depends on the value of Ka or Kb, the concentration of the acid or base, and the temperature.

– Only the total concentration of both the ionized and unionized species is equal to 1 M.

– The analytical concentration (C) is defined as the total concentration of all forms of an acid or base that are present in solution, regardless of their state of protonation.

– Thus; a 1 M solution has an analytical concentration of 1 M, which is the sum of the actual concentrations of unionized acid or base and the ionized form.



– In addition to the analytical concentration of the acid or base, one must be able to measure the concentration of a least one of the species in the equilibrium constant expression in order to determine the value of Ka or Kb.

– Two common ways to obtain the concentrations

1. By measuring the electrical conductivity of the solution, which is related to the total concentration of ions present

2. By measuring the pH of the solution, which gives [H+] or [OH–]



• Procedure for determining Ka for a weak acid and Kb for a weak base

1. The analytical concentration of the acid or base is the initial concentration

2. The stoichiometry of the reaction with water determines the change in concentrations

3. The final concentrations of all species are calculated from the initial concentrations and the changes in the concentrations

4. Inserting the final concentration into the equilibrium constant expression enables the value of Ka or Kb to be calculated


Calculating Percent Ionization from Ka or Kb

• Need to know the concentrations of all species in solution

• The reactivity of a weak acid or a weak base is very different from the reactivity of its conjugate base or acid; need to know the percent ionization of a solution of an acid or base in order to understand a chemical reaction

• Percent ionization is defined as

percent ionization of acid = [H+]

CHA

percent ionization of base = [OH–] CB

x 100

x 100



• To determine the concentrations of species in solutions of weak acids and bases, use a tabular method 1. Make a table that lists the following values for each of the

species involved in the reaction a. Initial concentration b. The change in concentration on preceding to equilibrium

(–x or +x) c. The final concentration—sum of the initial concentration and

the change in concentration d. In constructing the table, define x as the concentration of the

acid that dissociates

2. Solve for x by substituting the final concentrations from the table into the equilibrium constant expression



3. Calculate the concentrations of the species present in the solution by inserting the value of x into the expressions in the last line of the table (final concentration)

4. Calculate the pH = –log[H3O+]

5. Use the concentrations to calculate the fraction of the original acid that is ionized (the concentration of the acid that is ionized divided by the analytical or initial concentration of the acid times 100%



• Strong acids and bases ionize essentially completely in water; the percent ionization is always approximately 100%, regardless of the concentration

• The percent ionization in solutions of weak acids and bases is small and depends on the analytical concentration of the weak acid or base; percent ionization of a weak acid or a weak base actually increases as its analytical concentration decreases and percent ionization increases as the magnitude of the ionization constants Ka and Kb increases


Determining Keq from Ka and Kb

• The value of the equilibrium constant for the reaction of a weak acid with a weak base can be calculated from Ka

(or pKa), Kb (or pKb), and Kw

• One can quantitatively determine the direction and extent of reaction for a weak acid and a weak base by calculating the value of K for the reaction

• The equilibrium constant for the reaction of a weak acid with a weak base is the product of the ionization constants of the acid and the base divided by Kw


Determining Keq from Ka and Kb

• Calculations 1. Write the dissociation reactions for a weak acid and a weak base and

then sum them:

Acid HA ⇋ H+ + A– Ka

Base B + H2O ⇋ HB+ + OH– Kb

Sum HA + B + H2O ⇋ H+ + A– + HB+ + OH– Ksum = KaKb

2. Obtain an equation that includes only the acid-base reaction by simply adding the equation for the reverse of the autoionization of water

(H+ + OH– ⇋ H2O), for which K = 1/Kw, to the overall reaction and canceling

HA + B + H2O ⇋ H+ + A– + HB+ + OH– Ksum = KaKb

H+ + OH– ⇋ H2O 1/Kw

HA + B ⇋ A– + HB+ K = (KaKb)/Kw



16.5 Acid-Base Titrations


16.5 Acid-Base Titrations

• In acid-base titrations, a buret is used to deliver measured volumes of an acid or base solution of known titration (the titrant) to a flask that contains a solution of a base or an acid, respectively, of unknown concentration (the unknown).

• If the concentration of the titrant is known, then the concentration of the unknown can be determined.

• Plotting the pH changes that occur during an acid-base titration against the amount of acid or base added produces a titration curve; the shape of the curve provides important information about what is occurring in solution during the titration.


Titrations of Strong Acids and Bases

• Before addition of any strong base, the initial [H3O+] equals the concentration of the strong acid.

• Addition of strong base before the equivalence point, the point at which the number of moles of base (or acid) added equals the number of moles of acid (or base) originally present in the solution, decreases the [H3O+] because added base neutralizes some of the H3O+

present.

• Addition of strong base at the equivalence point neutralizes all the acid initially present and pH = 7.00; the solution contains water and a salt derived from a strong base and a strong acid.



• Addition of a strong base after the equivalence causes an excess of OH– and produces a rapid increase in pH.

• A pH titration curve shows a sharp increase in pH in the region near the equivalence point and produces an S-shaped curve; the shape depends only on the concentration of the acid and base, not on their identity.



• For the titration of a monoprotic strong acid with a monobasic strong base, the volume of base needed to reach the equivalence point can be calculated from the following relationship:

moles of base = moles of acid

(volume)b (molarity)b = (volume)a (molarity)a

VbMb = VaaMMaa


Titrations of Weak Acids and Bases

• The shape of the titration curve for a weak acid or a weak base depends dramatically on the identity of the acid or base and the corresponding value of Ka or Kb.



• The pH changes much more gradually around the equivalence point in the titration of a weak acid or a weak base.

• [H+] of a solution of a weak acid (HA) is not equal to the concentration of the acid but depends on both its pKa and its concentration.

• Only a fraction of a weak acid dissociates, so [H+] is less than [HA]; therefore, the pH of a solution of a weak acid is higher than the pH of a solution of a strong acid of the same concentration.



• Comparing the titration curve of a strong acid with a strong base with the titration curve of a weak acid and a strong base

1. Below the equivalence point, the two curves are very different; before any base is added, the pH of the weak acid is higher than the pH of the strong acid

2. pH changes more rapidly during the first part of the titration in a weak acid and strong base titration

3. Due to the higher starting pH, the pH of the weak acid at the equivalence point is greater than 7.00, so solution is basic



4. Change in pH for the weak acid/strong base titration around the equivalence point is about half as large as for the strong acid titration; the magnitude of the change at the equivalence point depends on the pKa of the acid being titrated

5. Above the equivalence point, the two curves are identical; once acid has been neutralized, the pH of the solution is controlled only by the amount of excess of OH– present, regardless ofwhether the acid is weak or strong



• Calculating the pH of a solution of a

weak acid or base

– If Ka or Kb and the initial concentration of a weak acid or base are known, one can calculate the pH of a solution of a weak acid or base by setting up a table of initial concentrations, changes in concentrations, and final concentrations

– Define x as [H+] due to the dissociation of the acid

– Insert values for final concentrations into the equilibrium equation and solve for x and then pH (pH = –log[H+])



• Calculating the pH during titration of a

weak acid or base

– Solved in two steps: a stoichiometric calculation followed by an equilibrium calculation

1. Use stoichiometry of the neutralization reaction to calculate the amounts of acid and conjugate base present in solution after the neutralization reaction has occurred

2. Use the equilibrium equation K = [H3O+] [A–] / [H2O] [HA] to determine [H+] of the resulting solution



• Identity of the weak acid or base being titrated strongly affects the shape of the titration curve.

• The shape of titration curves as a function of the pKa or pKb shows that as the acid or base being titrated becomes weaker (its pKa or pKb becomes larger), the pH change around the equivalence point decreases significantly.



• The midpoint of a titration is defined as the point at which exactly enough acid (or base) has been added to neutralize one-half of the acid (or base) originally present and occurs halfway to the equivalence point.

• At the midpoint of the titration of an acid, [HA] = [A–].

• The pH at the midpoint of the titration of a weak acid is equal to the pKa of the weak acid.


Titrations of Polyprotic Acids or Bases

• When a strong base is added to a solution of a polyprotic acid, the neutralization reaction occurs in stages.

1. The most acidic group is titrated first, followed by the next most acidic, and so forth

2. If the pKa values are separated by at least three pKa units, then the overall titration curve shows well-resolved “steps” corresponding to the titration of each proton


Titrations of Polyprotic Acids or Bases


Indicators

• Most acid-base titrations are not monitored by recording the pH as a function of the amount of the strong acid or base solution used as a titrant

• Instead, an acid-base indicator is used, and they are compounds that change color at a particular pH and if carefully selected, undergo a dramatic color change at the pH corresponding to the equivalence point of the titration

• Acid-base indicators are typically weak acids or bases whose changes in color correspond to deprotonation or protonation of the indicator itself


Indicators


Indicators

• The chemistry of indicators are described by the general

equation Hn(aq) ⇋ H+ (aq) + n–

(aq), where the protonated form is designated by Hn and the conjugate base by n–

• The ionization constant for the deprotonation of indicator Hn is Kin = [H+] [n–] / [Hn]

• The value of pKin determines the pH at which the indicator changes color


Indicators

• A good indicator must have the following properties: 1. Color change must be easily detected 2. Color change must be rapid 3. Indicator molecule must not react with the substance being

titrated

4. The indicator should have a pKin that is within one pH unit of the expected pH at the equivalence point of the titration

• Synthetic indicators have been developed that meet the above criteria and cover the entire pH range

• An indicator does not change color abruptly at a particular pH but undergoes a pH titration like any other acid or base


Indicators

• Choosing the correct indicator for an acid-base titration

1. For titrations of strong acids and strong bases (and vice versa), any indicator with a pKin between 4 and 10 will do

2. For the titration of a weak acid, the pH at the equivalence point is greater than 7, and an indicator such as phenolphthalein or thymol blue, with pKin > 7, should be used

3. For the titration of a weak base, where the pH at the equivalence point is less than 7, an indicator such as methyl red or bromcresol blue, with pKin < 7, should be used


Indicators


Indicators

• Paper or plastic strips that contain combinations of indicators estimate the pH of a solution by simply dipping a piece of pH paper into it and comparing the resulting color with standards printed on the container



16.6 Buffers


16.6 Buffers

• Buffers are solutions that maintain a relatively constant pH when an acid or a base is added; they protect or “buffer” other molecules in solution from the effects of the added acid or base

• Buffers contain either a weak acid (HA) and its conjugate base (A–) or a weak base (B) and its conjugate acid (BH+)

• Buffers are critically important for the proper functioning of biological systems; every biological fluid is buffered to maintain its physiological pH


The Common Ion Effect

• The ionization equilibrium of a weak acid (HA) is affected by the addition of either the conjugate base of the acid (A–) or a strong acid (a source of H+); LeChâtelier’s principle is used to predict the effect on the equilibrium position of the solution

• Common-ion effect—the shift in the position of an equilibrium on addition of a substance that provides an ion in common with one of the ions already involved in the equilibrium; equilibrium is shifted in the direction that reduces the concentration of the common ion



• Buffers are characterized by the following:

1. the pH range over which they can maintain a constant pH—depends strongly on the chemical properties of the weak acid or base used to prepare the buffer (on K)

2. their buffer capacity, the amount of strong acid or base that can be absorbed before the pH changes significantly—depends solely on the concentration of the species in the buffered solution (the more concentrated the buffer solution, the greater its buffer capacity)

3. observed change in the pH of the buffer is inversely proportional to the concentration of the buffer




Calculating the pH of a Buffer

• The pH of a buffer can be calculated from the concentrations of the weak acid or the weak base used to prepare it, the concentration of the conjugate base or acid, and the pKa or pKb of the weak acid or base

• An alternative method used to calculate the pH of a buffer solution is based on a rearrangement of the equilibrium equation for the dissociation of a weak acid

• Ionization reaction is HA⇋H+ + A– and the equilibrium constant expression is

Ka = [H+] [A–] or [H+] = Ka[HA]

[HA] [A–]



• Taking the logarithm of both sides and multiplying both sides by –1 gives

–log[H+] = –logKa – log([HA]/[A–]) = – logKa + log([A–]/[HA])

• Replacing the negative logarithms gives pH = pKa + log([A–]/[HA]) or pH = pka + log([base]/[acid])

Both forms of the Henderson-Hasselbalch equation

• Henderson-Hasselbalch equation is valid for solutions whose concentrations are at least a hundred times greater than the value of their Ka’s



• Three special cases where the Henderson-Hasselbalch equation is interpreted without the need for calculations

1. [base] = [acid]. Under these conditions, [base]/[acid] = 1. Because log 1 = 0, pH = pKa, regardless of the actual concentrations of the acid and base (corresponds to the midpoint in the titration of a weak acid or base)

2. [base]/[acid] = 10. Because log 10 = 1, pH = pKa + 1

3. [base]/[acid] = 100. Because log 100 = 2, pH = pKa+ 2

• Each time the [base]/[acid] ratio is increased by 10, the pH of the solution increases by one unit; if the [base]/[acid] ratio is 0.1, then pH = pKa – 1, so each additional factor-of-10 decrease in the [base]/[acid] ratio causes the pH to decrease by one pH unit



• The Henderson-Hasselbalch equation can also be used to calculate the pH of a buffer solution after the addition of a given amount of strong acid or base

• A buffer that contains equal amounts of the weak acid (or weak base) and its conjugate base (or acid) in solution is equally effective at neutralizing either added base or added acid


The Relationship between Titrations and Buffers

• A strong correlation exists between the effectiveness of a buffer solution and the titration curves

• In a titration of a weak acid with a strong base; – the region around pKa corresponds to the midpoint of the titration,

when half the weak acid has been neutralized; this portion of the titration curve corresponds to a buffer because it exhibits the smallest change in pH per increment of added strong base (horizontal nature of the curve in this region);

– the flat portion of the curve extends only from a pH value of one unit less than the pKa to a pH value of one unit greater than the pKa ; that is why buffer solutions have a pH that is within ±1 pH units of the pKa of the acid component of the buffer;


The Relationship between Titrations and Buffers

– in the region of the titration curve at the lower left, before the midpoint, the acid-base properties of the solution are dominated by the equilibrium for dissociation of the weak acid, corresponding to Ka;

– in the region of the titration curve at the upper right, after the midpoint, the acid-base properties of the solution are dominated by the equilibrium for reaction of the conjugate base of the weak acid with water, corresponding to Kb.


Blood: A Most Important Buffer

• Metabolic processes produce large amounts of acids and bases, but organisms are able to maintain a constant internal pH because their fluids contain buffers.

• pH is not uniform throughout all cells and tissues of a mammal; even within a cell, different compartments can have very different pH values.

• Because no single buffer system can effectively maintain a constant pH value over the physiological range of 5 to 7.4, biochemical systems use a set of buffers with overlapping ranges; most important of these is the CO2/HCO3

– system, which dominates the buffering action of blood plasma.


17Solubility and Complexation Equilibria


CHAPTER OBJECTIVES

• To be able to calculate the solubility of an ionic compound from its Ksp

• To understand the factors that determine the solubility of ionic compounds

• To be able to describe complex-ion formation quantitatively

• To understand why the solubility of many compounds depends on pH

• To know how to separate metal ions by selective precipitation



17.1 Determining the Solubility of Ionic

Compounds


The Solubility Product, Ksp

• When a slightly soluble ionic compound is added to water, some of it dissolves to form a solution, establishing an equilibrium between the pure solid and a solution of its ions.

• The equilibrium constant for the dissolution of a sparingly soluble salt is the solubility product of the salt, Ksp.

• The concentration of a pure solid is a constant and does not appear in the equilibrium constant expression.

• Solubility products are determined experimentally by either directly measuring the concentration of one of the component ions or by measuring the solubility of the compound in a given amount of water.

• Ksp is defined in terms of molar concentrations of the component ions.


The Ion Product

• The ion product (Q) of a salt is the product of the concentrations of the ions in solution raised to the same powers as in the solubility product expression.

• The ion product describes concentrations that are not necessarily equilibrium concentrations, whereas Ksp

describes equilibrium concentrations.

• The process of calculating the value of the ion product and comparing it with the magnitude of the solubility product is a way to determine if a solution is unsaturated, saturated, or supersaturated and whether a precipitate will form when solutions of two soluble salts are mixed.


The Ion Product

• Three possible conditions for an aqueous solution of an ionic solid

1. Q < Ksp: the solution is unsaturated, and more of the ionic solid will dissolve

2. Q = Ksp: the solution is saturated and at equilibrium

3. Q > Ksp: the solution is supersaturated, and ionic solid will precipitate


The Common Ion Effect and Solubility

• Solubility product expression

– Equilibrium concentrations of cation and anion are inversely related

– As the concentration of the anion increases, the maximum concentration of the cation needed for precipitation to

occur decreases, and vice versa

– Ksp is constant


The Common Ion Effect and Solubility

• Common ion effect

– The solubility of an ionic compound depends on the concentrations of other salts that contain the same ions.

– This dependency is an example of the common ion effect; adding a common cation or anion shifts a solubility

equilibrium in the direction predicted by LeChâtelier’s principle.

– The solubility of any sparingly soluble salt is almost always decreased by the presence of a soluble salt that

contains a common ion.



17.2 Factors That Affect Solubility


17.2 Factors That Affect Solubility

• The solubility product of an ionic compound describes the concentrations of ions in equilibrium with a solid.

• There are four reasons that the solubility of a compound may be other than expected: 1. Ion-pair formation

2. Incomplete dissociation of molecular solutes

3. Formation of complex ions

4. Changes in pH


• An ion pair consists of a cation and anion that are in intimate contact in solution, rather than separated by solvent.

Ion-Pair Formation


• Ions in an ion pair are held together by the same attractive electrostatic forces as for ionic solids.

– Ions in an ion pair migrate as a single unit, whose net charge is the sum of the charges on the ions.

– The ion pair is a species intermediate between the ionic solid (in which each ion participates in many cation-anion interactions that hold the ions in a rigid array) and the completely dissociated ions in solution (where each is fully surrounded by water molecules and free to migrate independently).

Ion-Pair Formation


Ion-Pair Formation

• Ion pairs – A second equilibrium must be included to describe the solubility of

salts that form ion pairs.

– An ion pair is represented by the symbols of the individual ions separated by a dot, to indicate that they are associated in solution

(Ca2+ ·SO42–).

– The formation of an ion pair is a dynamic process, so a particular ion pair may exist only briefly before dissociating into the free ions, each of which may later associate briefly with other ions.

– Ion-pair formation has a major effect on the measured solubility of a salt and is most important for salts that contain M2+ and M3+ ions; it is unimportant for salts that contain monocations.


Incomplete Dissociation

• A molecular solute may be more soluble than predicted by the measured concentrations of ions in solution due to incomplete dissociation.

– Common for weak organic acids

– Weak acids do not dissociate completely into their constituent ions (H+ and A–) in water

– The molecular (undissociated) form of a weak acid (HA) is quite soluble in water

– Many carboxylic acids have a limited solubility in water


Incomplete Dissociation



17.3 Complex-Ion Formation


• Metal ions in aqueous solution are hydrated—surrounded by a shell of four to six water molecules.

• A hydrated ion is one kind of complex ion, a species formed between a central metal ion and one or more surrounding ligands, molecules or ions that contain at least one lone pair of electrons.

• A complex ion forms from a metal ion and a ligand because of a Lewis acid-base interaction.

– The positively charged metal ion acts as a Lewis acid, and the ligand, with one or more lone pairs of electrons, acts as a

Lewis base. – Small, highly charged metal ions have the greatest tendency to

act as Lewis acids and to form complex ions.

17.3 Complex-Ion Formation


• The equilibrium constant for the formation of the complex ion from the hydrated ion is called the formation constant (Kf).

• Equilibrium constant expression for Kf has the same general form as any other equilibrium constant expression.

• The larger the value of Kf, the more stable the product.

The Formation Constant


• The solubility of a sparingly soluble salt increases if a ligand that forms a stable complex ion is added to the solution.

• The formation of a complex ion by the addition of a complexing agent increases the solubility of a compound.

• Complexing agents are molecules or ions that increase the solubility of metal salts by forming soluble metal complexes.

The Effect of Complex-Ion Formation on Solubility



17.4 Solubility and pH


17.4 Solubility and pH

• Solubility of many compounds depend strongly on the pH of the solution

– The anion in many sparingly soluble salts is the conjugate base of a weak acid that may become protonated in

solution.

– The solubility of simple binary compounds such as oxides and sulfides are dependent on pH.


The Effect of Acid-Base Equilibria on the Solubility of Salts

• Examining the effect of pH on the solubility of a representative salt, M+A–, where A– is the conjugate base of the weak acid HA – When the salt dissolves in water, this reaction occurs:

M A(s) ⇋ M+(aq) + A–

(aq) Ksp = [M+] [A–] – The anion can also react with water in a hydrolysis reaction:

A–(aq) + H2O(l)⇋OH–

(aq) + HA(aq)

– If a strong acid is added to the solution, the added H+ will react essentially completely with A– to form HA, which decreases [A–] and which in turn decreases the magnitude of the ion product, Q = [M+] [A–]

– More MA will dissolve until Q = Ksp


The Effect of Acid-Base Equilibria on the Solubility of Salts

– An acidic pH dramatically increases the solubility of sparingly soluble salts whose anion is the conjugate base of a

weak acid; pH has little to no effect on the solubility of salts whose anion is the conjugate base of a strong acid

– caves and their associated pinnacles and spires of stone provide one of the most impressive examples of pH-

dependent solubility equilibria


Acidic, Basic, and Amphoteric Oxides and Hydroxides

• Oxides and hydroxides can be classified as either basic or acidic.

1. Basic oxides and hydroxides either react with water to produce a basic solution or dissolve readily in aqueous acid.

2. Acidic oxides or hydroxides either react with water to produce an acidic solution or are soluble in aqueous base.



• There is a clear correlation between the acidic or basic character of an oxide and the position of the element combined with oxygen in the periodic table.



– Oxides of metallic elements are generally basic oxides.

– Oxides of nonmetallic elements are acidic oxides.

– There is a gradual transition from basic metal oxides to acidic nonmetal oxides from the lower left to the upper right of the periodic table; a broad diagonal band of oxides of intermediate character separates the two extremes.

– Oxides of the elements in the diagonal region are soluble in both acidic and basic solutions and are called amphoteric oxides; which dissolve in acid to produce water or dissolve in base to produce a soluble complex.



• The difference in reactivity is due to the difference in bonding in the two kinds of oxides.

– Metals at the far left of the periodic table have low electronegativities; their oxides contain discrete Mn+ cations

and O2– anions. – Nonmetal oxides have high electronegativities and form oxides

that contain covalent bonds to oxygen. – Because of the high electronegativity of oxygen, the covalent

bond between oxygen and the other atom is polarized E+–O– .

– These oxides act as Lewis acids that react with water to produce an oxoacid.

– Oxides of metals in high oxidation states tend to be acidic oxides; they contain covalent bonds to oxygen.


Selective Precipitation Using pH

• Many dissolved metal ions can be separated by selective precipitation of the cations from solution under specific conditions.

• pH is used to control the concentration of the anion in solution; this in turn controls which cations precipitate.



17.5 Qualitative Analysis Using Selective

Precipitation


17.5 Qualitative Analysis Using Selective Precipitation

• The composition of relatively complex mixtures of metal ions can be determined using qualitative analysis, a procedure for discovering the identity of metal ions present in the mixture.

• The technique consists of selectively precipitating only a few kinds of metal ions at a time under given sets of conditions; consecutive precipitation steps become progressively less selective until almost all the metal ionsare precipitated.





• The traditional scheme of analysis for metal cations involves the separation of cations into five groups by selective precipitation

1. Group 1: Insoluble chlorides – Metal chloride salts are soluble in water; only Ag+, Pb2+,

and Hg22+ form

chlorides that precipitate from water – First step in qualitative analysis is to add 6 M HCl, causing

AgCl, PbCl2, and/or Hg2Cl2 to precipitate; precipitate is collected by filtration or centrifugation



2. Group 2: Acid-insoluble sulfides – Acidic solution is saturated with H2S

– Only those metal ions that form very insoluble sulfides precipitate as their sulfide

salts under these acidic conditions; all others remain in solution

– Precipitates collected by filtration or centrifugation



3. Group 3: Base-insoluble sulfides (and hydroxides)

– Ammonia or NaOH is added to the solution until it is basic, and then (NH4)2 S is added

– Treatment removes any remaining cations that form insoluble hydroxides or sulfides

4. Group 4: Insoluble carbonates or phosphates– The next metal ions to be removed are those that

form insoluble carbonates and phosphates



5. Group 5: Alkali metals– All the metal ions that form water-insoluble chlorides,

sulfides, carbonates, or phosphates have been removed

– Only common ions that remain are the alkali metals and ammonium

– Take a second sample from the original solution and add a small amount of NaOH to neutralize the ammonium ion and produce NH3; any ammonia produced can be detected by odor or by litmus paper test, and alkali metal ions, which produce characteristic colors in flame tests, allows them to be identified



• Metal ions that precipitate together are separated by various techniques, such as forming complex ions, changing the pH of the solution, or increasing the temperature to redissolve some of the solids


18Chemical Thermodynamics


CHAPTER OBJECTIVES

• To understand the connections among work, heat, and energy

• To be familiar with the concept of PV work

• To be able to calculate changes in internal energy

• To understand the relationship between internal energy and entropy

• To be able to use a thermodynamic cycle to calculate changes in entropy

• To understand the relationship between Gibbs free energy and work

• To know the difference between the information that thermodynamics and kinetics provide about a system

• To understand the importance of thermodynamics in biochemical systems


Chemical Thermodynamics

• Chemical reactions obey two fundamental laws:

1. The law of conservation of mass

– States that matter can be neither created nor destroyed

– Explains why equations must balance and is the basis for stoichiometry and equilibrium calculations

2. The law of conservation of energy – States that energy can be neither created nor destroyed

– Energy takes various forms that can be converted from one to the other


Chemical Thermodynamics

• Thermodynamics

– The study of the interrelationships among heat, work, and the energy content of a system at equilibrium

– Tells whether a particular reaction is energetically possible in the direction in which it is written and the composition of

the reaction system at equilibrium

– Does not say anything about whether an energetically feasible reaction will actually occur as written

– Tells nothing about the rate of the reaction or the pathway by which it will occur

– Provides a bridge between the macroscopic properties of a substance and the individual properties of its

constituent molecules and atoms



18.1 Thermodynamics and Work


18.1 Thermodynamics and Work• A system is that part of the universe in which we are interested; the

surroundings are everything else—the rest of the universe.

• System + surroundings = universe.

• A closed system cannot exchange matter with its surroundings; an open system can.

• State function—the property of a system that depends only on the present state of the system and not on its history.

• A change in state function depends only on the difference between the initial and final states, not on the pathway used to go from one to the other.

• Thermodynamics is concerned with state functions and does not deal with how the change between the initial and final state occurs.


The Connections among Work, Heat, and Energy

• The internal energy (E) of a system is the sum of the potential energy and the kinetic energy of all the components; internal energy is a state function.

• A closed system cannot exchange matter with its surroundings, but it can exchange energy with its surroundings in two ways: 1. By doing work 2. By releasing or absorbing heat, the flow of thermal energy

• Work and heat are two distinct ways of changing the internal energy of a system.


The Connections among Work, Heat, and Energy

• Work (w) is defined as a force (F) acting through a distance (d): w = Fd.

• Work occurs only when an object moves against an opposing force; work requires that the system and its surroundings be physically connected.

• The flow of heat, the transfer of energy due to differences in temperature between two objects, represents a thermal connection between the system and its surroundings.

• Work causes a physical displacement, and flow of heat causes a temperature change.

• Units of work and heat must be the same because both processes result in the transfer of energy; units are joules (J).


PV Work

• In chemistry, most work is expansion work (PV work) done as the result of a volume change during a reactionwhen air molecules are pushed aside.

• Amount of work done by an expanding gas is given by the equation w = – PV, where P is the pressure againstwhich the system must push and V is the change in volume of the system.

• When the pressure or volume of a gas ischanged, any mechanical work done isPV work.


PV Work

• Work done by the system on the surroundings has anegative value, and work done on the system by the surroundings has a positive value.

• Work is not a state function; it depends on the path taken.



18.2 The First Law of Thermodynamics



• The Relationship between the energy change of the system and that of the surroundings is given by the first law of thermodynamics, which states that the energy of the universe is constant.

• This law can be expressed mathematically as

Euniv = Esys + Esurr = 0

Esys = – Esurr

The change in energy of the system is identical in magnitude but opposite in sign to the change in energy of the surroundings.

• One of the most important factors that determine the outcome of a chemical reaction is the tendency of all systems to move toward the lowest possible energy state.



• Heat and work are the only two ways in which energy can be transferred between a system and the surroundings.

• Any change in the internal energy of the system is the sum of the heat transferred, q, and the work done, w:

Esys = q + w

• q and w are not state functions on their own; their sum, Esys, is independent of the path taken and is therefore a state function.

• Any machine that converts energy to work is designed to want to maximize the amount of work obtained and to minimize the amount of energy released to the environment as heat


Enthalpy

• To understand the relationship between heat flow, q, and the resulting change in internal energy E, one must look at two sets of limiting conditions: 1. Reactions that occur at constant volume

2. Reactions that occur at constant pressure

• Assume that PV work is the only kind of work possible for the system, so E = q – PV


Enthalpy

• Constant volume

– If reaction occurs in a closed vessel, the volume of the system is fixed and V is zero

– Heat flow (qv) must equal E

qv = E

– No PV work can be done, and the change in the internal energy of the system is equal to the amount of heat transferred from the system to the surroundings, or vice versa


Enthalpy

• Constant pressure

– If reaction occurs in an open container at a constant pressure of 1 atm, heat flow is given the symbol qp

– Replacing q with qp gives the equation qp = E + PV

– At constant pressure, the heat flow for any process is equal to the change in the internal energy of the system plus the PV work done

– A new state function called enthalpy (H) is defined as H = E + PV

– At constant pressure, the change in the enthalpy of a system is H = E + (PV) = E + PV

– At constant pressure, the change in the enthalpy of a system is equal to the heat flow: H = qp


The Relationship between H and E• If H for a reaction is known, one can use the change in the

enthalpy of the system to calculate its change in internal energy.

• When a reaction involves only solids, liquids, liquid solutions, or any combination of these, the volume does not change (V = 0), so H = E.

• If gases are involved, H and E can differ significantly; one can calculate E from the measured value of H by using the equation H = E + PV and the ideal gas law, PV = nRT.

• (PV) = (nRT), so H = E + (PV) = E + (nRT).

• At constant temperature, (nRT) = RTn, where n is the difference between the final and initial moles of gas, so E = H – RTn.


The Relationship between H and E

• For reactions that result in a net production of gas, n > 0 and E < H.

• Endothermic reactions that result in a net consumption of gas have n < 0 and E > H.



18.3 The Second Law of Thermodynamics


• How to predict whether a particular process or reaction would occur spontaneously – Most spontaneous reactions are exothermic, but there are

many that are not exothermic. – Reactions can be both spontaneous and highly endothermic. – Enthalpy changes are not the only factors that determine

whether a process is spontaneous. – An additional state function called entropy (S) can help explain

why some processes proceed spontaneously in only one direction.

– Entropy is a thermodynamic property of all substances that is proportional to their degree of disorder.

18.3 The Second Law of Thermodynamics


• Chemical and physical changes in a system are accompanied by either an increase or decrease in the disorder of the system, corresponding to an increase in entropy (S > 0) or a decrease in entropy (S < 0), respectively.

• A change in entropy is defined as the difference between the entropies of the final and initial states: S = Sf – Si.

• When a gas expands into a vacuum, its entropy increases because the increased volume allows for greater atomic or molecular disorder; the greater the number of atoms or molecules in the gas, the greater the disorder.

• The magnitude of the entropy of a system depends on the number of microscopic states, or microstates, associated with it; the greater the number of microstates, the greater the entropy.

Entropy


• A disordered system has a greater number of possible microstates than does an ordered system, so it has a higher entropy.

• Liquids that have highly ordered structures due to hydrogen bonding or other intermolecular interactions tend to have significantly higher values of Svap.

• The formation of a solution is a process that is accompanied by entropy changes; formation of a liquid solution from a crystalline solid and a liquid solvent results in an increase in the disorder of the system and in its entropy.

Entropy


• In a reversible process, every intermediate state between the extremes is an equilibrium state, regardless of the direction of the change.

• An irreversible process is one in which the intermediate states are not equilibrium states, and change occurs spontaneously in only one direction.

• A reversible process can change direction at any time, whereas an irreversible process cannot.

• Work done during the expansion of a gas depends on the opposing external pressure (w = PextV), so work done in a reversible process is always equal to or greater than work done in a corresponding irreversible process: wrev wirrev.

Reversible and Irreversible Changes


• Whether a process is reversible or irreversible, E = q + w.

• E is a state function, so the magnitude of E does not depend on reversibility and is independent of the path taken: E = qrev + wrev = qirrev + wirrev.

• E for a process is the same whether that process is carried out in a reversible or an irreversible manner.

Reversible and Irreversible Changes


• The quantity of heat transferred, qrev, is directly proportional to the absolute temperature of an object, T (qrev T), so the hotter the object, the greater amount of heat transferred.

• Adding heat to a system increases the kinetic energy of the component atoms and molecules and their disorder (S qrev).

• For any reversible process S = qrev/T or qrev = TS; units of S are joules/kelvin (J/K).

• Work done in a reversible process at constantpressure is wrev = –PV, so E = qrev + wrev = TS – PV; change in the internal energy of the system is related to the change in entropy,the absolute temperature, and the PV work done.

The Relationship between Internal Energy and Entropy


• Entropy of the universe is unchanged in reversible processes and constitutes part of the second law of thermodynamics: the entropy of the universe remains constant in a reversible process, whereas the entropy of the universe increases in an irreversible (spontaneous) process.

The Relationship between Internal Energy and Entropy



18.4 Entropy Changes and the Third Law of

Thermodynamics


• The atoms, molecules, or ions that make up a chemical system can undergo several types of molecular motion: translation, rotation, and vibration.

• The greater the molecular motion of a system, the greater the number of possible microstates and the higher the entropy.

• A perfectly ordered system, a perfect crystal at a temperature of absolute zero (0 K) that exhibits no motion, with only a single microstate available would have an entropy of zero.

18.4 Entropy Changes and the Third Law of Thermodynamics



• Absolute zero is an ideal temperature that is unobtainable, and a perfect single crystal is an ideal that cannot be achieved, however, the combination of these two ideals constitutes the basis for the third law of thermodynamics: The entropy of any perfectly ordered, crystalline substance at absolute zero is zero.

• The third law of thermodynamics has two important consequences:

1. It defines as positive the sign of the entropy of any substance at temperatures above absolute zero

2. It provides a fixed reference point that allows the measurement of the absolute entropy of any substance at any temperature



• Two different ways to calculate S for a reaction or physical change

1. Uses tabulated values of absolute entropies of substances, based on the definition of absolute entropy provided by the third law

2. Uses a thermodynamic cycle, based on the fact that entropy is a state function


Calculating S from Standard Molar Entropy Values

• One way of calculating S for a reaction is to use tabulated values of the standard molar entropy (Sº), which is the entropy of 1 mol of a substance at a standard temperature of 298 K

• Units of Sº are J/(molK)

• It is possible to obtain absolute entropy values by measuring the entropy change that occurs between the reference point of 0 K, corresponding to S = 0, and 298 K

• For substances with the same molar mass and number of atoms, Sº values fall in the order Sº(gas) > Sº(liquid) > Sº(solid)



• Substances with similar molecular structures have similar Sº values

1. Those with the lowest entropies tend to be rigid crystals composed of small atoms linked by strong, highly directional bonds

2. Those with higher entropies are soft crystalline substances that contain larger atoms and increased molecular motion and disorder



• Absolute entropy of a substance tends to increase with increasing molecular complexity because the number of available microstates increases with molecular complexity

• Substances with strong hydrogen bonds have lower values of Sº, reflecting a more ordered structure

• To calculate Sº for a chemical reaction from standard molar entropies, the “products minus reactants” rule is used; here the absolute entropy of each reactant and product is multiplied by its stoichiometric coefficient in the balanced chemical equation


Calculating S from Thermodynamic Cycles

• A change in entropy can also be calculated using a thermodynamic cycle

– The molar heat capacity Cp is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant pressure

– Cv is the amount of heat needed to raise the temperature of 1 mol of a substance by 1ºC at constant volume

– Increase in entropy with increasing temperature is proportional to the heat capacity of the substance

– Entropy change S is related to heat flow, qrev, by S = qrev/T



– qrev = nCpT at constant pressure or nCvT at constant volume, where n is the number of moles of substance present

– The change in entropy for a substance whose temperature changes from T1 to T2 is S =nCplnT2/T1 (constant pressure) or S = nCvlnT2/T1 (constant volume)

– A combination of heat capacity easurements and experimentally measured values of enthalpies of fusion or vaporization can be used to calculate the entropy change corresponding to a change in the temperature of the sample





18.5 Free Energy


18.5 Free Energy

• One major goal of chemical thermodynamics is to establish criteria for predicting whether a particular reaction or process will occur spontaneously

• The sign of Suniv is a universally applicable and infallible indicator of the spontaneity of a reaction; if Suniv > 0, the process will occur spontaneously as written; if Suniv < 0, a process cannot occur spontaneously; and if Suniv = 0, the system is at equilibrium

• Using Suniv requires the calculation of S for both the system and the surroundings. This is not useful because we are much more interested in the system than in the surroundings; it is also difficult to make quantitative measurements of the surroundings

• A criterion of spontaneity that is based solely on state functions of the system is more convenient and is provided by a new state function called the Gibbs free energy


Gibbs Free Energy and the Direction of Spontaneous Reactions

• The Gibbs free energy (G), or free energy, is defined in terms of three other state functions—enthalpy, temperature, and entropy—and is a state function itself:

G = H – TS

• The criterion for predicting spontaneity is based on G, the change in G at constant temperature and pressure

G = H – TS,where all thermodynamic quantities are those of the system

• At constant pressure, H = q whether a process is reversible or irreversible, and TS = qrev, so G = q – qrev

• So G is the difference between the heat released during a process (via a reversible or an irreversible path) and the heat released for the same process occurring in a reversible manner



• To understand how the sign of G for the system determines the direction in which change is spontaneous, the equation S = qrev/T and q = H is rewritten to give Ssurr = – Hsys/T

• The entropy change of the surroundings is related to the enthalpy change of the system, and since for a spontaneous reaction, Suniv > 0, the equation becomes

Suniv = Ssys + Ssurr > 0 or Suniv = Ssys – Hsys/T > 0

• Multiplying both sides of the inequality by –T reverses its sign and rearranges the equation to Hsys– TS < 0, which is equal to G; therefore, for a spontaneous process, G < 0



• Relationship between the entropy change of the surroundings and the heat gained or lost by the system provides the key connection between the thermodynamic properties of the system and the change in entropy of the universe

• This relationship allows one to predict spontaneity by focusing exclusively on the thermodynamic properties and temperature of the system. Highly exothermic processes (H << 0) that increase the disorder of the system (Ssys >> 0) would occur spontaneously

• For a system at constant temperature and pressure,

1. if G < 0, the process occurs spontaneously 2. if G = 0, the system is at equilibrium 3. if G > 0, the process is not spontaneous as written but occurs

spontaneously in the reverse direction




The Relationship between G and Work

• Change in free energy, G, is equal to the maximum amount of work that a system can perform on the surroundings while undergoing a spontaneous change (at constant temperature and pressure): G = wmax


Standard Free-Energy Change

• Absolute free energies cannot be measured. However, changes in free energy can.

• The standard free-energy change (Gº) is the change in free energy when one substance or set of substances in their standard states is converted to one or more other substances also in their standard states

• The standard free-energy change can be calculated from the definition of free energy if the standard enthalpy and entropy changes are known: Gº = Hº – TSº

• If Sº and Hº for a reaction have the same sign, then the sign of Gº depends on the relative magnitudes of the Hº and TSº terms



• The standard free energy of formation (Gºf) of a

compound is the change in free energy that occurs when 1 mol of a substance in its standard state is formed from the elements in their standard states

• Standard free energy of formation of an element in its standard state is zero at 298.15 K

• Standard free energy of formation of a compound can be calculated from the standard enthalpy of formation, Hº

f, and from the standard entropy of formation, Sº

f, using the definition of free energy: Gº

f = Hºf – TSº

f



• Using standard free energies of formation, the standard free energy of a reaction can be calculated by employing the “products minus reactants” rule:

Gºrxn = mGº

f (products) – nGºf (reactants),

where m and n are the stoichiometric coefficients of each product and reactant in the balanced chemical equation

• The effect of temperature on the spontaneity of a reaction depends on the sign and magnitude of both Hº

and Sº; the temperature at which a given reaction is at equilibrium can be calculated by setting Gº = 0



18.6 Spontaneity and Equilibrium


18.6 Spontaneity and Equilibrium• Three criteria have been identified for whether a given

reaction will occur spontaneously

1. Suniv > 0

2. Gsys < 03. The relative magnitude of the reaction quotient Q versus the

equilibrium constant K

a. Q < K, reaction proceeds spontaneously to the right as written, resulting in the net conversion of reactants to products

b. Q > K, reaction proceeds spontaneously to the left as written, resulting in the net conversion of products to reactants

c. Q = K, system at equilibrium, no net reaction occurs


Free Energy and the Equilibrium Constant

• Because H º and S

º determine the magnitude of Gº

and because the equilibrium constant K is a measure of the ratio of the concentrations of products to the concentrations of reactants, K can be expressed in terms of Gº and vice versa

• For a reversible process that does not involve external work, the change in free energy can be expressed in terms of volume, pressure, entropy, and temperature, eliminating H from the equation for G: G = VP – ST and G = VP at constant temperature (T = 0)



• Assuming ideal gas behavior in the equation G = VP, V can be replaced by nRT/P (where n is the number of moles of gas and R is the ideal gas constant). G can be expressed in terms of the initial and final pressures (P1 and P2, respectively).

G = (nRT/P)P = nRT(P/P) = nRTln(P2 /P1)

• If the initial state is the standard state with P1 = 1 atm, then the change in free energy upon going from the standard state to any other state with a pressure P can be written as G = Gº + nRTlnP

• Using the hypothetical reaction aA + bB ⇋ cC + dD, in which all reactants and products are ideal gases and the lowercase letters correspond to the stoichiometric coefficients for the various species, the expression for G can be written as G = Gproducts – Greactants



• Substituting G = Gº + nRTlnP into the equation:

G = [(cGºC + cRTlnPC) + (dGº

D + dRTlnPD)] – [(aGºA + aRTlnPA) + (bGº

B + bRTlnPB)]

• Combining terms gives the following relationship between G and the reaction quotient Q

G = Gº + RTln(PcCPd

D/PaAPb

B) = Gº + RTlnQ where Gº indicates that all reactants and products are in

their standard states

• For gases Q = Kp at equilibrium, and for a system G = 0 at equilibrium, so the relationship between Gº and Kp for gases can be described as Gº = –RTlnKp



• If the products and reactants are in their standard states and Gº < 0, then Kp > 1 and products are favored over reactants; if Gº > 0, then Kp < 1 and reactants are favored over products; if Gº = 0, then Kp = 1 and neither reactants nor products are favored and the system is at equilibrium

• Kp is defined in terms of the partial pressures of reactants and products, and the equilibrium constant K is defined in terms of the concentrations of reactants and products; therefore, Kp = K(RT)n, where n is the number of moles of gaseous product minus the number of moles of gaseous reactant

• For reactions where n = 0, Kp = K, so Gº = –RT ln K



• The following equation provides insight into how the components of Gº influence the magnitude of the equilibrium constant: Gº = Hº – TSº = –RT ln K

– K becomes larger as Sº becomes more positive, indicating that the magnitude of the equilibrium constant is directly influenced by the tendency of the system to move toward maximum disorder

– K increases as Hº decreases, so the magnitude of the equilibrium constant is also directly influenced by the tendency of the system to seek the lowest energy state possible


Temperature Dependence of the Equilibrium Constant

• The fact that Gº and K are related explains why equilibrium constants are temperature-dependent

ln K = – Hº/RT + Sº/R

• Assuming Hº and Sº are temperature-dependent, for an exothermic reaction (Hº < 0), the magnitude of K decreases with increasing temperature and for an endothermic reaction (Hº > 0), the magnitude of K increases with increasing temperature

• The magnitude of Hº dictates how rapidly K changes as a function of temperature and the magnitude and sign of Sº affects the magnitude of K, but not its temperature dependence


Temperature Dependence of the Equilibrium Constant

• If the value of K at a given temperature and the value of Hº for a reaction are known, the value of K can be estimated at any other temperature, even in the absence of information on Sº

• If K1 and K2 are the equilibrium constants for a reaction at temperatures T1 and T2, respectively, then

ln K2 – ln K1 = ln K2/K1 = Hº/R(1/T1 – 1/T2)



18.7 Comparing Thermodynamics and

Kinetics


18.7 Comparing Thermodynamics and Kinetics

• Thermodynamics

– Deals with state functions and can be used to describe the overall properties, behavior, and equilibrium composition of a system

– Provides a significant constraint on what can occur during a reaction process

• Kinetics– Concerned with the particular pathway by which physical or

chemical changes occur, so it can address the rate at which a particular process will occur

– Describes the detailed steps of what actually occurs on an atomic or molecular level



• The following table gives the numerical values of the equilibrium constant K that correspond to various values of Gº

– If Gº + 10 kJ/mol or Gº –10 kJ/mol, an equilibrium is ensured to lie all the way to the left or to the right, respectively

– If Gº is quite small (10 kJ/mol), significant amounts of both products and reactants are present at equilibrium



• Most reactions have equilibrium constants greater than 1, with the equilibrium strongly favoring either products or reactants

• In many cases, reactions that are strongly favored by thermodynamics do not occur at a measurable rate, and reactions that are not thermodynamically favored do occur under certain nonstandard conditions

• A reaction that is not thermodynamically spontaneous under standard conditions can be made to occur spontaneously by varying reaction conditions, by using a different reaction to obtain the same product, by supplying external energy, or by coupling the unfavorable reaction to another reaction for which

Gº<< 0



18.8 Thermodynamics and Life


18.8 Thermodynamics and Life

• A living cell can be viewed as a low-entropy system that is not in equilibrium with its surroundings and is capable of replicating itself

• A constant input of energy is needed to maintain the cell’s highly organized structure and its intricate system of chemical reactions

• A cell needs energy to synthesize complex molecules from simple precursors, to create and maintain differences in the concentrations of various substances inside and outside of the cell, and to do mechanical work


Energy Flow between the Cell and Its Surroundings

• A cell is an open system that can exchange matter with its surroundings as well as absorb energy from its environment in the form of heat or light

• Cells utilize the energy obtained to maintain the nonequilibrium state that is essential for life

• Nonequilibrium thermodynamics have been developed to quantitatively describeopen systems such as living cells

• The only way a cell can maintain a low-entropy, nonequilibrium state characterized by a high degree of structural organization is to increase theentropy of the surroundings; a cell releases some of the energy it obtains from its environment as heat that is transferred to its surroundings, resulting inan increase in Ssurr


Extracting Energy from the Environment

• Organisms can be divided into two categories1. Phototrophs, whose energy source is light2. Chemotrophs, whose energy source is chemical compounds,

obtained by consuming or breaking down other organisms

• All organisms utilize oxidation-reduction, or redox, reactions to drive the synthesis of complex biomolecules

– Organisms that can use only O2 as the oxidant are aerobic organisms that can’t survive in the absence of O2

– Many organisms that use other oxidants or oxidized organic compounds can live only in the absence of O2 and are called anaerobic organisms


Extracting Energy from the Environment

• Fundamental reaction by which all green plants and algae (phototrophs) obtain energy from sunlight is photosynthesis, the photochemical reduction of CO2 to a reduced carbon compound

• One of the main processes chemotrophs use to obtain energy is respiration, which is the reverse of photosynthesis

• Some chemotrophs obtain energy by fermentation, in which both the oxidant and reductant are organic compounds


The Role of NADH and ATP in Metabolism

• Regardless of the identity of the substances from which an organism obtains energy, the energy must be released in very small increments if it is to be useful to the cell

• Cells store part of the energy that is released as ATP (adenosine triphosphate)

• Most organisms use a number of intermediate species to shuttle electrons between the terminal reductant and the terminal oxidant; intermediate species oxidizes the energy-rich reduced compound, and the now-reduced intermediate migrates to another site, where it is oxidized


• The most important of these electron-carrying intermediates is NAD+, whose reduced form is NADH



• Energy from the oxidation of nutrients is made available to cells through the synthesis of ATP; its energy is used by the cell to synthesize substances through coupled reactions and to perform work

• For biochemical reactions, a new standard state has been defined in which the H+ concentration is 1 x 10–7 M (pH 7) and all other reactants and products are present in standard-state conditions (1 M or 1 atm)

• The free-energy change and equilibrium constant for a reaction under these new standard conditions are denoted by the addition of a prime sign (´) to the conventional symbol



Energy Storage in Cells

• All organisms use ATP as the immediate free-energy source in biochemical reactions, but ATP is not an efficient form in which to store energy on a long-term basis

• The body stores energy as sugars, proteins, and fats before using it to produce ATP


19 Electrochemistry


CHAPTER OBJECTIVES

• To distinguish between galvanic and electrolytic cells

• To predict spontaneous reactions using redox potentials

• To balance redox reactions using half-reactions

• To understand the relationship between cell potential and the equilibrium constant

• To be able to measure solution concentrations using cell potentials

• To describe how commercial galvanic cells operate

• To describe the process of corrosion

• To understand electrolysis and to be able to describe it quantitatively


Electrochemistry

• In oxidation-reduction (redox) reactions, electrons are transferred from one species (the reductant) to another (the oxidant).

• Transfer of electrons provides a means for converting chemical energy to electrical energy, or vice versa.

• The study of the relationship between electricity and chemical reactions is called electrochemistry.



19.1 Describing Electrochemical Cells



• Electrochemical process—electrons flow from one chemical substance to another, driven by an oxidation-reduction (redox) reaction

• Redox reaction – Occurs when electrons are transferred from a substance that

is oxidized to one that is being reduced

– Reductant is the substance that loses electrons and is oxidized in the process

– Oxidant is the species that gains electrons and is reduced in the process



– Described as two half-reactions, one representing the oxidation process and one the reduction process

Reductive half-reaction: Br2 (aq) + 2e– 2Br –(aq)

Oxidative half-reaction: Zn (s) Zn2+(aq) + 2e–

– Adding the two half-reactions gives the overall chemical reaction Zn (s) + Br2 (aq) ZnBr2 (aq)

– A redox reaction is balanced when the number of electrons lost by the reductant is equal to the number of electrons gained

by the oxidant; overall process is electrically neutral – An electric current is produced from the flow of electrons from

reductant to oxidant



• Electrochemical cell

– An apparatus that is used to generate electricity from a spontaneous redox or that uses

electricity to drive a nonspontaneous redox reaction

– There are two types of electrochemical cells 1. Galvanic cell (voltaic cell)—uses the energy released

during a spontaneous redox reaction (G < 0) to generate electricity

2. Electrolytic cell—consumes electrical energy from an external source, using it to cause a nonspontaneous redox reaction to occur (G > 0)





– Both types of cells contain two electrodes, which are solid metals connected to an external circuit that provides an

electrical connection between systems

– Oxidation half-reaction occurs at one electrode, the anode, and the reduction half-reaction occurs at the other, thecathode

– When circuit is closed, electrons flow from the anode to the cathode; electrodes are connected by an electrolyte,

which is an ionic substance or solution that allows ions to transfer between the electrodes, thereby maintaining the system’s electrical neutrality


Galvanic (Voltaic) Cells

• To illustrate the basic principles of a galvanic cell

– look at the reaction of metallic zinc with cupric ion (Cu2+) to give copper metal and Zn2+ ion

Zn(s) + Cu2+(aq) Zn2+

(aq) + Cu(s)

– a copper strip is inserted into a beaker that contains a 1 M solution of Cu2+ ions, and a zinc strip is inserted into a different beaker that contains a 1 M solution of Zn2+ ions

– two metal strips serve as electrodes and are connected by a wire that allows electricity to flow; the compartments are connected by a salt bridge, a U-shaped tube inserted into both solutions and contains a concentrated liquid or gelled electrolyte to maintain electrical neutrality



– when the circuit is closed, a spontaneous reaction occurs: zinc metal is oxidized to Zn2+ ions at the zinc electrode (the anode), and Cu2+ ions are reduced to Cu metal at the copper electrode (the cathode)

– as reaction progresses, the zinc strip dissolves and the concentration of Zn2+ ions in the Zn2+ solution increases; the copper strip gains mass and the concentration of Cu2+ ions in the Cu2+ solution decreases

– electrons that are released at the anode flow through the wire, producing an electric current; galvanic cells transform chemical energy into electrical energy that can be used to do work

– the electrolyte in the salt bridge serves two purposes: to complete the circuit by carrying electrical charge and to maintain electrical neutrality in both solutions by allowing ions to migrate between the two solutions





– a voltmeter is used to measure the difference in electrical potential between the two compartments

– the potential of the cell, measured in volts, is the difference in electrical potential between the two half-reactions; electrical potential is related to the energy needed to move a charged particle in an electric field

– electrons from the oxidative half-reaction are released at the anode, so the anode in a galvanic cell is negatively charged; the cathode, which attracts electrons, is positively charged


Constructing a Cell Diagram

• Because galvanic cells are cumbersome to describe in words, a line notation called a cell diagram has been developed

• In a cell diagram

– the identity of the electrodes and the chemical contents of the compartments are indicated by their chemical formulas, with the anode written on the far left and the cathode on the far right;

– phase boundaries are shown by single vertical lines;– the salt bridge, which has two phase boundaries, is shown by a

double vertical line;Here’s a cell diagram for Zn/Cu cell:

Zn(s)| Zn2+(aq, 1M) || Cu2+(aq, 1 M) | Cu(s) Anode Salt Bridge Cathode


Constructing a Cell Diagram

• In a single-compartment galvanic cell, the voltage produced by a redox reaction can be measured more accurately using two electrodes immersed in a single beaker containing an electrolyte that completes the circuit; arrangement reduces errors caused by resistance to the flow of charge at a boundary, called the junction potential

– Cell diagram does not include a double vertical line for the salt bridge (no salt bridge) and does not include solution concentrations

Pt(s) | H2(g) | HCl(aq) | AgCl(s) | Ag(s)



19.2 Standard Potentials



• In a galvanic cell, current is produced when electrons flow externally through the circuit from the anode to the cathode because of a difference in potential energy between two electrodes in the electrochemical cell

• The flow of electrons in an electrochemical cell depends on the identity of the reacting substances, the difference in the potential energy of their valence electrons, the concentrations of the reacting species, and the temperature of the system



• The potential of the cell under standard conditions (1 M for solutions and 1 atm for gases, pure solids, or liquids for other substances) and at a fixed temperature (25ºC) is called the standard cell potential, Eº

cell

– Used in order to develop a scale of relative potentials that will allow the prediction of the direction of an electrochemical reaction and the magnitude of the driving force for the reaction

– Used to measure the potentials for oxidations and reductions of different substances under comparable conditions


Measuring Standard Electrode Potentials

• Impossible to measure the potential of a single electrode; only the difference between the potentials of two electrodes can be measured

• Can compare the standard cell potentials for two different galvanic cells that have one kind of electrode in common—allows the measurement of the potential difference between two dissimilar electrodes

• All tabulated values of standard electrode potentials by convention are listed as standard reduction potentials in order to compare standard potentials for different substances


Measuring Standard Electrode Potentials

• The standard cell potential is the reduction potential of the reductive half-reaction minus the reduction potential of the oxidative half-reaction (Eº

cell = Eºcathode – Eº

anode).

• The potential of the standard hydrogen electrode (SHE) is defined as 0 V under standard conditions.

• The potential of a half-reaction measured against the SHE under standard conditions is called the standard electrode potential for that half-reaction.

• The standard cell potential is a measure of the driving force for a given redox reaction.

• All Eº values are independent of the stoichiometric coefficients for the half-reactions.


Balancing Redox Reactions Using the Half-Reaction Method

• Redox reactions can be balanced using the half-reaction method, where the overall redox reaction is divided into an oxidation half-reaction and a reduction half-reaction, each one balanced for mass and charge

• The half-reactions selected from tabulated lists must exactly reflect reaction conditions



• In an alternative method, the atoms in each half-reaction are balanced, and then the charges are balanced; one does not need to use the tabulated half-reactions; instead, focus on the atoms whose oxidation states change by using the following steps:

1. Write the reduction half-reaction and the oxidation half-reaction

2. Balance the atoms by balancing elements other than O and H; then balance O atoms by adding H2O, and balance H atoms by adding H+

3. Balance the charges in each half-reaction by adding electrons



4. Multiply the reductive and oxidative half-reactions by appropriate integers to obtain the same number of electrons in both half-reactions

5. Add the two half-reactions and cancel substances that appear on both sides of the equation

6. Check to make sure that all atoms and charges are balanced


Calculating Standard Cell Potentials

• The standard cell potential for a redox reaction, Eºcell, is a

measure of the tendency of the reactants in their standard states to form the products in their standard states—it is a measure of the driving force for the reaction (voltage)

• Calculations for the standard potential for the Zn/Cu cell represented by the cell diagram:

Zn(s) | Zn2+(aq, 1 M || Cu2+(aq, 1M) | Cu(s)

Cathode: Cu2+(aq) + 2e– Cu(s) Eºcathode = 0.34 V

Anode: Zn(s) Zn2+(aq, 1M) + 2e– Eºanode = –0.76 V

Overall: Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s)

Eºcell = Eº

cathode – Eºanode = 1.10 V


Calculating Standard Cell Potentials

• If the value of Eºcell (the standard cell potential) is positive,

the reaction will occur spontaneously as written

• If the value of Eºcell is negative, then the reaction is not

spontaneous and it will not occur as written under standard conditions; it will proceed spontaneously in the opposite direction


Reference Electrodes and Measuring Concentrations

• When using a galvanic cell to measure the concentration of a substance, we are interested in the potential of only one of the electrodes of the cell, the indicator electrode, whose potential is related to the concentration of the substance being measured

• To ensure that any change in the measured potential of the cell is due to only the substance being analyzed, the potential of the other electrode, the reference electrode, must be constant

• Whether oxidation or reduction occurs depends on the potential of the sample versus the potential of the reference electrode



• Types of reference electrodes

1. Standard hydrogen electrode (SHE)—consists of a strip of platinum wire in contact with an aqueous solution containing 1 M H+, which is in equilibrium with H2 gas at a

pressure of 1 atm at the Pt-solution interface

2. Silver-silver chloride electrode—consists of a silver wire coated with a thin layer of AgCl that is dipped into a chloride ion solution with a fixed concentration

3. Saturated calomel electrode (SCE)—consists of a platinum wire inserted into a moist paste of liquid mercury, Hg2Cl2, and KCl



• One of the most common uses of electrochemistry is to measure the H+ ion concentration of a solution

– A glass electrode is used for this purpose, in which an internal Ag/AgCl electrode is immersed in a 0.10 M HCl solution that is separated from the solution by a very thin glass membrane that absorbs protons

– The extent of the adsorption on the inner side is fixed but the adsorption of protons on the outer surface depends on the pH of the solution



• Ion-selective electrodes

– Used to measure the concentration of a particular species in solution; designed so that their potential depends on only the concentration of the desired species

– Contains an internal reference electrode that is connected by a solution of an electrolyte to a crystalline inorganic material or membrane, which acts as the sensor



19.3 Comparing Strengths of Oxidants

and Reductants


• The following table lists the standard potentials for a wide variety of chemical substances that allow us to compare the oxidative and reductive strengths of a variety of substances

• The half-reaction for the standard hydrogen electrode lies halfway down on the table

– All species that lie above it in the table are stronger oxidants than H+, and all those that lie below it are weaker

– All species that lie below H2 are stronger reductants than H2, and those that lie above H2 are weaker

19.3 Comparing Strengths of Oxidants and Reductants


• Because the half-reactions in the table are arranged in order of their Eº values, the table can be used to predict the relative strengths of various oxidants and reductants

– Any species on the left side of a half-reaction will spontaneously oxidize any species on the right side of another half-reaction that lies below it in the table

– Any species on the right side of one half-reaction will spontaneously reduce any species on the left side of another half-reaction that lies above it in the table

19.3 Comparing Strengths of Oxidants and Reductants



19.4 Electrochemical Cells and

Thermodynamics


The Relationship between Cell Potential and Free Energy

• Electrochemical cells convert chemical to electrical energy, and vice versa

• Total amount of energy produced by an electrochemical cell and the amount of energy available to do electrical work depends on both the cell potential and the total number of electrons that are transferred from the reductant to the oxidant during the course of the reaction

• Resulting electric current measured in coulombs (C), an S unit that measures the number of electrons passing a given point in 1 s; coulomb defined as 6.25 x 1018 e–/s and relates electrical potential (in volts) to energy (in joules)

1J/1V = 1 coulomb = 6.25 x 1018 e–/s



• Electric current is measured in amperes (A); 1 ampere is defined as the flow of 1 coulomb per second past a given point (1C = 1A/s)

• In chemical reactions one must relate the coulomb to the charge on a mole of electrons; multiplying the charge on the electron by Avogadro’s number gives the charge on 1 mol of electrons, the faraday (F)

F = (1.60218 x 10–19C) (6.02214 x 1023/1 mol e–) =

9.64855 x 104C/mol e– = 96,485.5 J(V·mol e–)

• Total charge transferred from the reductant to the oxidant is nF,

where n is the number of moles of electrons



• The maximum amount of work that can be produced by an electrochemical cell, wmax, is equal to the product of the cell potential, Ecell, and the total charge transferred during the reaction, nF: wmax = –nFEcell

• Work is expressed as a negative number because work is being done by the system on the surroundings

G is also a measure of the maximum amount of work that can be performed during a chemical reaction (G = wmax; there must be a relationship between the potential of an electrochemical cell and the change in free energy, G

G = –nFEcell

• A spontaneous redox reaction is characterized by a negative value of G and a positive value of Ecell


Potentials for the Sums of Half-Reactions

• When the standard potential for a half-reaction is not available, the relationships between standard potentials and free energy can be used to obtain the potential of any other half-reaction that can be written as the sum of two or more half-reactions whose standard potentials are available

• Values of Eº for half-reactions cannot be added to give Eº for the sum of the half-reactions because Eº is not a state function

• Because Gº is a state function, the sum of the G values for the individual reactions gives Gº for the overall reaction, which is proportional to both the potential and the number of electrons (n) transferred


Potentials for the Sums of Half-Reactions

• To obtain the value of Eº for the overall half-reaction, the values of Gº (= –nFEº) must be added for each half-reaction to obtain Gº for the overall half-reaction

• Substitute values into equation Gº = nFEºcell and solve

for Eº


The Relationship between Cell Potential and the Equilibrium Constant

• Can use the relationship between Gº and the equilibrium constant K to obtain a relationship between Eº

cell and K

• For a general reaction of the type aA + bB cC + dD, the standard free-energy change and the equilibrium constant are related by the equation Gº = –RTlnK

• Given the relationship between the standard free-energy change and the standard cell potential, the following equation can be written: –nFEº

cell = –RTlnK



• Rearranging the equation gives

Eºcell = (RT/nF)lnK

• For T = 298 K, the equation is simplified to

Eºcell = (RT/nF)lnK = [8.314 J/(mol·K)] (298 K) 2.303 log K

n[96,486 J/(V·mol)] = (0.0591 V/n)log K

• The standard cell potential, Eºcell, is directly proportional

to the logarithm of the equilibrium constant



• The following figure summarizes the relationships developed based on properties of the system (based on the equilibrium constant, standard free-energy change, and standard cell potential) and the criteria for spontaneity (Gº < 0)


The Effect of Concentration on Cell Potential: The Nernst Equation

• The actual free-energy change for a reaction under non-standard conditions, G, is given by

G = Gº + RTln Q

We also know that G = –nFEcell and Gº = –nFEºcell, so

substituting these expressions in the preceding equation gives –nFEcell = –nFEº

cell + RT lnQ

• Dividing both sides of this equation by –nF gives the Nernst equation: Ecell = Eº

cell – (RT/nF)lnQ

• The Nernst equation determines the spontaneous direction of any redox reaction under any reaction conditions from values of the relevant standard reduction potentials



• When a redox reaction is at equilibrium (G = 0), the Nernst equation reduces to

Eºcell = (RT/nF)ln K because Q = K and there is no net

transfer of electrons (Ecell = 0)

• Substituting the values of the constants into the Nernst equation with T = 298 K and converting to base-10 logarithms gives the relationship of the actual cell potential (Ecell), the standard cell potential (Eº

cell), and the reactant and product concentrations at room temperature (contained in Q):

Ecell = Eºcell – (0.0591 V/n)logQ




Concentration Cells

• A voltage can be generated by constructing an electrochemical cell in which each compartment contains the same redox active solution but at different concentrations; voltage is produced as the concentrations equilibrate

• An electrochemical cell in which the anode and cathode compartments are identical except for the concentration of a reactant is called a concentration cell

• Because G = 0 at equilibrium, the measured potential of a concentration cell is zero at equilibrium


Using Cell Potentials to Measure Solubility Products

• A galvanic cell can be used to measure the solubility product of a sparingly soluble substance

• Measure the solubility product of AgCl, Ksp = [ Ag+][Cl–]– One compartment contains a silver wire inserted into a 1.0 M

solution of Ag+

– The other compartment contains a silver wire inserted into a 1.0 M Cl– solution saturated with AgCl

– The potential due to the difference in [Ag+] between the two cells can be used to determine Ksp


Using Cell Potentials to Measure Concentrations

• A galvanic cell can be used to calculate the concentration of a species given a measured potential and the concentrations of all the other species by using the Nernst equation


Chemistry: Principles, Patterns,and Applications, 1e

19.5 Commercial Galvanic

Cells


19.5 Commercial Galvanic Cells

• Galvanic cells can be self-contained and portable and can be used as batteries and fuel cells

1. A battery (storage cell) is a galvanic cell (or a series of galvanic cells) that contains all the reactants needed to produce electricity.

2. A fuel cell is a galvanic cell that requires a constant external supply of one or more reactants in order to generate electricity.


Batteries

• Two basic kinds of batteries 1. Disposable, or primary, batteries in which the electrode

reactions are effectively irreversible and which cannot be recharged

2. Rechargeable, or secondary, batteries, which form an insoluble product that adheres to the

electrodes; can be recharged by applying an electrical potential in the reverse direction, which temporarily converts a rechargeable battery from a galvanic cell to an electrolytic cell

• Major difference between batteries and galvanic cells is that commercial batteries use solids or pastes rather than solutions as reactants to maximize the electrical output per unit mass


Batteries

• When a battery consists of more than one galvanic cell, the cells are connected in series—that is, with the positive (+) terminal of one cell connected to the negative (–) terminal of the next, and so on

• The overall voltage of the battery is the sum of the voltages of the individual cells


Batteries

• Leclanché dry cell– A “wet cell” in which the electrolyte is an acidic

water-based paste containing MnO2, NH4Cl, ZnCl2, graphite, and starch

– Used in flashlights, Walkmen, and GameBoys and is disposable

– Cell not very efficient in producing electrical energy and has a limited shelf life

– The alkaline battery is a Leclanché cell adapted to operate under alkaline, or basic, conditions; has a longer shelf life and more constant output voltage than the Leclanché dry cell


Batteries

• “Button” batteries– The anode is a zinc-mercury amalgam, and the cathode

can be either HgO or Ag2O as the oxidant

– Are reliable and have a high output-to-mass ratio, which allows them to be used in calculators, cameras, hearing aids, and watches, where their small size is crucial

– Disposable


Batteries

• Lithium-iodine battery– Water-free battery– Consists of two cells separated by a metallic nickel mesh

that collects charge from the anodes– The anode is lithium metal, and the cathode is a solid

complex of 2

– Electrolyte is a layer of solid Li that allows Li+ ions to diffuse from the cathode to the anode

– Highly reliable and long-lived– Used in cardiac pacemakers, medical implants, smoke

alarms, and in computers – Disposable


Batteries


Batteries

• Nickel-cadmium (nicad) battery– Used in small electrical appliances and in devices like

drills and portable vacuum cleaners– A water-based cell with a cadmium anode and a highly

oxidized nickel cathode– This design maximizes the surface area of the electrodes

and minimizes the distance between them, which gives the battery both a high discharge current and a high capacity

– Lightweight, rechargeable, and high capacity but tend to lose capacity quickly and do not store well; also presents disposal problems because of the toxicity of cadmium


Batteries


Batteries

• Lead-acid (lead storage) battery– Provides the starting power in automobiles and boats;

can be discharged and recharged many times– The anodes in each cell of this rechargeable battery are

plates or grids of lead containing spongy lead metal, while the cathodes are similar grids containing powdered lead dioxide, PbO2

– The electrolyte is an aqueous solution of sulfuric acid– The value of Eº for such a cell is 2 V; connecting three

cells in series produces a 6-V battery, and a typical 12-V car battery contains six of these cells connected in series


Batteries


Fuel Cells

• A galvanic cell that requires an external supply of reactants because the products of the reaction are continuously removed

• Does not store electrical energy but allows electrical energy to be extracted directly from a chemical reaction

• Have reliability problems and are costly

• Used in space vehicles



19.6 Corrosion


19.6 Corrosion

• Corrosion is a galvanic process by which metals deteriorate through oxidation, usually but not always to their oxides

• One of the most common techniques used to prevent corrosion is to apply a protective coating of another metal that is more difficult to oxidize

• Alternatively, a more easily oxidized metal can be applied to a metal surface, thus providing cathodic protection of the surface; galvanized steel is protected by a thin layer of zinc

• Sacrificial electrodes can also be attached to an object to protect it



19.7 Electrolysis


19.7 Electrolysis

• Galvanic cells—a spontaneous chemical reaction is used to generate electrical energy

• In an electrolytic cell, the opposite process, called electrolysis, occurs: an external voltage is applied to drive a nonspontaneous reaction


Electrolytic Cells

• An electrochemical cell in which one electrode is copper metal immersed in a 1 M Cu2+ solution and the other electrode is cadmium metal immersed in a 1 M Cd2+ solution is set up, and then the circuit is closed

– Cadmium electrode begins to dissolve (Cd is oxidized to Cd2+) and thus is the anode, while metallic copper will be deposited on the copper electrode (Cu2+ is reduced to Cu), which is the cathode

– Overall reaction is thermodynamically spontaneous as written (Gº < 0); in this direction, the system is acting as a galvanic cell

– The reverse reaction, the reduction of Cd2+ by Cu, is thermodynamically nonspontaneous and will only occur with an input of an applied voltage


Electrolytic Cells

– Can force the reaction to proceed in the reverse direction by applying an electrical potential from an external power supply; applied voltage forces electrons through the circuit in the reverse direction, converting a galvanic cell to an electrolytic cell

– The copper electrode is now the anode (Cu is oxidized) and the cadmium electrode is now the cathode (Cd2+ is reduced)

– Signs of the electrodes have changed to reflect the flow of electrons in the circuit


Electrolytic Cells


Electrolytic Cells

• Differences between galvanic and electrolytic cells


Electrolytic Reactions

• At sufficiently high temperatures, ionic solids melt to form liquids that conduct electricity extremely well due to the high concentrations of ions

• Sodium metal is produced commercially by electrolysis of molten mixture of NaCl and CaCl2 in a Downs cell

• The Hall-Heroult process is used to produce aluminum commercially by electrolysis of a molten mixture of aluminum oxide and cryolite

• Electrolysis can also be used to drive the thermodynamically nonspontaneous decomposition of water into its constituent elements, H2 and O2, by adding a small amount of an ionic solute to

the water to make it electrically conductive


Electrolytic Reactions

• Overvoltages are needed in all electrolytic processes

• An overvoltage is an added voltage and represents the additional driving force required to overcome barriers such as a large activation energy and a junction potential


Electroplating

• In a process called electroplating, a layer of a second metal is deposited on the metal electrode that acts as the cathode during electrolysis

• Electroplating is used to enhance the appearance of metal objects and protect them from corrosion


Quantitative Considerations

• The amount of material consumed or produced in a reaction can be calculated from the stoichiometry of an electrolysis reaction, the amount of current passed, and the duration of the electrolytic reaction

Charge (C) = current (A) X times(s)

moles e– = charge (C) 96,486 C/mol (1 faraday)

• The stoichiometry can be used to determine the combination of current and time needed to produce a given amount of material


20 Nuclear Chemistry


CHAPTER OBJECTIVES• To understand the factors that affect nuclear stability

• To know the different kinds of radioactive decay

• To be able to balance a nuclear reaction

• To be able to interpret a radioactive decay series

• To know the differences between ionizing and nonionizing radiation and their effects on matter

• To be able to identify natural and artificial sources of radiation

• To be able to calculate a mass-energy balance and a nuclear binding energy

• To understand the differences between nuclear fission and fusion

• To understand how nuclear reactors operate

• To understand how nuclear transmutation reactions led to the formation of the elements in the stars and how they can be used to synthesize transuranium elements


Nuclear Reactions

• Differences between nuclear reactions and chemical processes

1. In a nuclear reaction, the identities of the elements change2. Nuclear reactions are accompanied by the release of

enormous amounts of energy3. The yields and rates of a nuclear reaction are unaffected

by changes in temperature, pressure, or the presence of catalysts



20.1 The Components of the Nucleus


20.1 The Components of the Nucleus

• Most of the known elements have at least one isotope whose atomic nucleus is stable indefinitely

• A great majority of elements also have isotopes that are unstable and disintegrate, or decay, at measurable rates by emitting radiation

• Some elements have no stable isotopes and eventually decay to other elements

• The process of nuclear decay is a nuclear reaction that results in changes inside the atomic nucleus


The Atomic Nucleus

• Each element can be represented by the notation Z

X

– A is the mass number, the sum of the numbers of protons and neutrons

– Z is the atomic number, the number of protons– The protons and neutrons that make up the nucleus of

an atom are called nucleons– An atom with a particular number of protons and

neutrons is called a nuclide– Nuclides that have the same number of protons but

different numbers of neutrons are called isotopes– The number of neutrons is equal to A – Z

A


The Atomic Nucleus

• Isotopes of oxygen can be represented in any of these ways:

A X: 16O 17O 18O

Z

8 8 8

AX: 16O 17O 18O

Element-A: Oxygen-16 Oxygen-17 Oxygen-18

• Isotopes of naturally occurring elements on Earth are present in nearly fixed proportions with each proportion constituting an isotope’s natural abundance


The Atomic Nucleus

• Any nucleus that is unstable and decays spontaneously is said to be radioactive, emitting subatomic particles and electromagnetic radiation

• The emissions are collectively called radioactivity and can be measured

• Isotopes that emit radiation are called radioisotopes

• The rate at which radioactive decay occurs is characteristic of the isotope and is reported as a half-life (t½), the amount of time required for half the initial number of nuclei present to decay in a first-order reaction


Nuclear Stability

• The nucleus of an atom occupies a tiny fraction of the volume of the atom and contains the number of protons and neutrons that is characteristic of a given isotope

• Electrostatic repulsions would cause the positively charged protons to repel each other, but the nucleus does not fly apart because of the strong nuclear force, an extremely powerful but very short-range attractive force between nucleons

• All stable nuclei except the hydrogen-1 nucleus contain at least one neutron to overcome the electrostatic repulsion between protons


Nuclear Stability

• As the number of protons in the nucleus increases, the number of neutrons needed for a stable nucleus increases even more rapidly; too many protons (or too few neutrons) in the nucleus result in an imbalance between forces, which leads to nuclear instability

• Relationship between the numbers of protons and neutrons in stable nuclei is shown in the following figure

– The stable isotopes form a “peninsula of stability” in a “sea of instability”– Only three stable isotopes, 1H, 3He, and 4He, have a neutron-to-proton ratio less

than or equal to 1; all other stable nuclei have a higher neutron-to-proton ratio, which increases steadily to about 1.5 for the heaviest nuclei

– All elements with Z > 83 are unstable and radioactive


Nuclear Stability

• More than half of the stable nuclei have even numbers of both neutrons and protons; only 6 of the 279 stable nuclei do not have odd numbers of both

• Certain numbers of neutrons or protons result in especially stable nuclei; these are the so-called magic numbers 2, 8, 20, 50, 82, and 126

• Nuclei with magic numbers of both protons and neutrons are said to be “doubly magic” and are even more stable


Superheavy Elements

• In addition to the “peninsula of stability,” the preceding figure shows a small “island of stability” that exists in the upper right corner

• The island corresponds to the superheavy elements, with atomic numbers near the magic number of 126, and may be stable enough to exist in nature



20.2 Nuclear Reactions


20.2 Nuclear Reactions• Two general kinds of nuclear reactions

1. Nuclear decay reaction (or radioactive decay) – An unstable nucleus emits radiation and is transformed into the

nucleus of one or more other elements – Resulting daughter nuclei have a lower mass and are lower in

energy (more stable) than the parent nucleus that decayed– Occur spontaneously under all conditions

2. Nuclear transmutation reaction– A nucleus reacts with a subatomic particle or another nucleus to

form a product nucleus that is more massive than the starting material

– Occur spontaneously only under special conditions


• Each of the three general classes of radioactive nuclei is characterized by a different decay process or set of processes

1. Neutron-rich nuclei– Have too many neutrons and have a neutron-to-proton ratio that is

too high to give a stable nucleus – These nuclei decay by a process that converts a neutron to a

proton, thereby decreasing the neutron-to-proton ratio2. Neutron-poor nuclei

– Have too few neutrons and have a neutron-to-proton ratio that is too low to give a stable nucleus

– These nuclei decay by processes that convert a proton to a neutron, thereby increasing the neutron-to-proton ratio

Classes of Radioactive Nuclei


3. Heavy nuclei– Heavy nuclei (with A 200) are intrinsically unstable, regardless of

the neutron-to-proton ratio– All nuclei with Z > 83 are unstable– Decay by emitting an particle, which decreases the number of

protons and neutrons in the original nucleus by 2– Since the neutron-to-proton ratio in an particle is 1, the net result

of alpha emission is an increase in the neutron-to-proton ratio

Classes of Radioactive Nuclei


• Can use the number and type of nucleons present to write a balanced equation for a nuclear decay reaction– Procedure allows us to predict the identity of either the parent or

daughter nucleus if the identity of only one is known– Regardless of the mode of decay, the total number of nucleons

is conserved in all nuclear reactions, as is the total positive charge

• To describe nuclear decay reactions, the AX notation for

nuclides has been extended to include radioactive emissions

Nuclear Decay Reactions


• The following table lists the name and symbol for each type of emitted radiation

1. The left superscript in the symbol for a particle gives the mass number, which is the total number of protons and neutrons – For a proton or a neutron, A = 1– Because neither an electron nor a positron contains protons or

neutrons, its mass number is 0

2. The left subscript gives the charge of the particle– Protons carry a positive charge, so Z = +1 for a proton– A neutron contains no protons and is electrically neutral, so Z = 0– For an electron, Z = –1, and for a positron, Z = +1– Because rays are high-energy photons, both A and Z are 0



3. In some cases, two different symbols are used for particles that are identical but produced in different ways– Symbol

0e, simplified to e– represents a free electron or an electron

associated with an atom

– Symbol 0, simplified to – denotes an electron that originates from within the nucleus, which is a particle

– 4He refers to the nucleus of a helium atom, and 4 is an identical particle ejected from a heavier nucleus


-1

-1

22


• There are six fundamentally different kinds of nuclear decay reactions, each of which releases a different kind of particle or energy (see table)



1. Alpha decay – Nuclei with mass numbers greater than 200 undergo alpha

decay, which results in the emission of a helium-4 nucleus as an particle, 4

– The daughter nuclide contains two fewer protons and two fewer neutrons than the parent, thus -particle emission produces a daughter nucleus with a mass number A that is lower by 4 and a nuclear charge Z that is lower by 2 than the parent nucleus

AX

A-4X′ + 4

parent daughter αparticle


2Z Z-2→

2


2. Beta decay– Nuclei that contain too many neutrons undergo beta decay,

in which a neutron is converted to a proton and a high-energy electron that is ejected from the nucleus as a particle

n p + 0β

unstable neutron proton retained beta particle emitted in nucleus by nucleus by nucleus

– Beta decay does not change the mass number of the nucleus but results in an increase of +1 in the atomic number due to the addition of a proton in the daughter nucleus; beta decay decreases the neutron-to-proton ratio, moving the nucleus toward the band of stable nuclei

AX A X′ + 0βparent daughter particle


→

→

-1

Z+1

1

Z -1

0

1 1


3. Positron emission– A positron has the same mass as an electron but opposite

charge– Positron emission is the opposite of beta decay and is

characteristic of neutron-poor nuclei which decay by the transformation of a proton to a neutron and a high-energy positron that is emitted

1p 1n + 0 – Positron emission does not change the mass number of the

nucleus, however the atomic number of the daughter nucleus is lower by 1 than that of the parent. The neutron-to-proton ratio increases, moving nucleus closer to the band of stable nuclei

AX A X′ + 0

parent daughter positron


1 +10

Z-1 +1Z


4.Electron capture– A neutron-poor nucleus can decay by either positron

emission or electron capture (EC), in which an electron in an inner shell reacts with a proton to produce a neutron

1p + 0e 1 n

– When a second electron moves from an outer shell to take the place of the lower-energy electron that was absorbed by the nucleus, an X-ray is emitted. The overall reaction for electron capture is

AX + 0e A X’ + X-ray

parent electron daughter

– The mass number does not change, but the atomic number of the daughter nucleus is lower by 1 than that of the parent; neutron-to-proton ratio increases, moving the nucleus toward the band of stable nuclei


1 0-1

-1 Z-1Z


5. Gamma emission– Many nuclear decay reactions produce daughter nuclei that are in

a nuclear excited state– A nucleus in an excited state releases energy in the form of a

photon when it returns to the ground state– These high-energy photons are rays– Gamma emission can occur instantaneously or after a significant

delay

– General formula AX* AX + 0

– Because rays are energy, their emission does not affect either the mass number or the atomic number of the daughter nuclide; gamma-ray emission is the only kind of radiation that does not involve the conversion of one element to another but is observed in conjunction with some other nuclear decay reaction


Z 0Z


6. Spontaneous fission– Only very massive nuclei with high neutron-to-proton ratios can

undergo spontaneous fission, in which the nucleus breaks into two pieces that have different atomic numbers and atomic masses

– Process most important for trans-actinide elements with Z 104

– Spontaneous fission is accompanied by the release of large amounts of energy and is accompanied by the emission of several neutrons

– The number of nucleons is conserved; the sum of the mass numbers of the products equals the mass number of the reactant; the sum of the atomic numbers of the products is the same as the atomic number of the parent nuclide



• Impossible for any nuclide with Z > 85 to decay to a stable daughter nuclide in a single step, except via nuclear fission

• Radioactive isotopes with Z > 85 usually decay to a daughter nucleus that is radioactive, which in turn decays to a second radioactive daughter nucleus, and so forth, until a stable nucleus finally results

• This series of sequential alpha- and beta-decay reactions is called a radioactive decay series

Radioactive Decay Series


• Some nuclei spontaneously transform into nuclei with a different number of protons, producing a different element

• These naturally occurring radioactive isotopes decay by emitting subatomic particles

• Should be possible to carry out the reverse reaction, converting a stable nucleus to another more massive nucleus by bombarding it with subatomic particles in a nuclear transmutation reaction

Induced Nuclear Reactions


• Uranium (Z = 92) is the heaviest naturally occurring element; all the elements with Z > 92, the transuranium elements, are artificial and have been prepared by bombardment of suitable target nuclei with smaller particles

• Bombarding the target with more massive nuclei creates elements that have atomic numbers greater than that of the target nucleus

• Accelerating positively charged particles to the speeds needed to overcome the electrostatic repulsions between them and the target nuclei requires a device called a particle accelerator, which uses electrical and magnetic fields to accelerate the particles

Synthesis of Transuranium Elements


• Types of particle accelerators1. The linear accelerator is the simplest particle accelerator in

which a beam of particles is injected at one end of a long evacuated tube; rapid alternation of the polarity of the electrodes along the tube causes the particles to be alternately accelerated toward a region of opposite charge and repelled by a region with the same charge, resulting in a tremendous acceleration as the particle travels down the tube.

2. A cyclotron achieves the same outcome in less space and forces the charged particles to travel in a circular path; particles are injected into the center of a ring and accelerated by rapidly alternating the polarity of two large D-shaped electrodes above and below the ring, which accelerates the particles outward along a spiral path toward the target.



3. The synchrotron is a hybrid of the previous two designs and contains an evacuated tube similar to that of the linear accelerator, but the tube is circular and can be more than a mile in diameter; charged particles are accelerated around the circle by a series of magnets whose polarities rapidly alternate.




20.3 The Interaction of Nuclear Radiation with

Matter


• Nuclear reactions do not cause chemical reactions directly.

• The particles and photons emitted during nuclear decay are very energetic, and they can indirectly produce chemical changes in the matter surrounding the nucleus that has decayed.

20.3 The Interaction of Nuclear Radiation with Matter


• Effects of radiation on matter are determined by the energy of the radiation, which depends on the nuclear decay reaction that produced it.

1. Nonionizing radiation– Low in energy; when it collides with an atom in a molecule or ion,

most of its energy can be absorbed without causing a structural or chemical change

– The kinetic energy of the radiation is transferred to the atom or molecule with which it collides, causing it to rotate, vibrate, or move more rapidly

– This energy can be transferred to adjacent molecules or ions in the form of heat, so many radioactive substances are warm to the touch

Ionizing versus Nonionizing Radiation


2. Ionizing radiation– Higher in energy and some of its energy can be transferred to

one or more atoms with which it collides as it passes through matter

– If enough energy is transferred, electrons can be excited to very high energy levels, resulting in the formation of positively charged ions

– Molecules ionized in this way are highly reactive and can decompose or undergo other chemical changes that create a cascade of reactive molecules that can damage biological tissues and other materials

Ionizing versus Nonionizing Radiation


• The effects of ionizing radiation depend on four factors

1. The type of radiation, which dictates how far it can penetrate into matter

2. The energy of the individual particles or photons

3. The number of particles or photons that strike a given area per unit time

4. The chemical nature of the substance exposed to the radiation

The Effects of Ionizing Radiation on Matter


• The relative abilities of the various forms of ionizing radiation to penetrate tissues are:

1. radiation – Reacts strongly with matter because of its high charge and mass– Does not penetrate deeply into an object and can be stopped by

clothing or skin– Alpha particles most damaging if their source is inside the body

because their energy is absorbed by internal tissues



2. radiation rays, with no charge and no mass, do not interact strongly with matter

and penetrate deeply into most objects, including the human body– Lead or concrete needed to completely stop rays– The most dangerous type when they come from a source outside the

body

3. radiation– Intermediate in mass and charge between particles and rays, so

interaction with matter is intermediate– Beta particles penetrate paper or skin but can be stopped by wood or a

thin sheet of metal



• There are many ways to measure radiation exposure, or the dose

– The roentgen (R) is used to measure the amount of energy absorbed by dry air and is used to describe exposure quantitatively

– Damage to biological tissues is proportional to the amount of energy absorbed by tissues, not air

– The most common unit to measure the effects of radiation on biological tissue is the rad (radiation absorbed dose); S unit is the gray (Gy)



– Rad is defined as the amount of radiation that causes 0.01 J of energy to be absorbed by 1 kg of matter, and the gray is defined as the amount of radiation that causes 1 J of energy to be absorbed per kilogram

1 rad = 0.010 J/kg 1 Gy = 1J/kg– The amount of tissue damage caused by 1 rad of particles is

much greater than the damage caused by 1 rad of particles or rays because particles have higher masses and charge



– A unit called the rem (roentgen equivalent in man) describes the actual amount of tissue damage caused by a given amount of radiation

– The number of rems of radiation is equal to the number of rads multiplied by the RBE (relative biological effectiveness) factor, which is 1 for particles, rays, and X-rays, and 20 for particles

– Most measurements are reported in millirems



• We are continuously exposed to measurable background radiation from a variety of natural sources, which is equal to about 150–600 mrem/yr

1. Cosmic rays, high-energy particles, and rays emitted by the sun and other stars that bombard Earth continuously

2. Cosmogenic radiation, produced by the interaction of cosmic rays with gases in the upper atmosphere

3. Terrestrial radiation, due to the remnants of radioactive elements that were present on the primordial Earth and their decay products

Natural Sources of Radiation


4. Tissues also absorb radiation (40 mrem/yr) from naturally occurring radioactive elements present in our bodies

5. Radon is the most important source of background radiation– The heaviest of the noble gases and tends to

accumulate in enclosed spaces– Radon exposure can cause lung damage or cancer

Natural Sources of Radiation


• In addition to naturally occurring background radiation, humans are exposed to small amounts of radiation from a variety of artificial sources

1. X-rays used for diagnostic purposes in medicine and dentistry; X-rays are photons with much lower energy than rays

2. Television screens and computer monitors with cathode-ray tubes that produce X-rays

3. Luminescent dials

4. Residual fallout from atmospheric nuclear-weapons testing

5. Nuclear power industry

Artificial Sources of Radiation


• The radiation exposure from artificial sources, when combined with the exposure from natural sources, poses a significant risk to human health

• The effects of single radiation doses of different magnitudes on humans are listed in the following table

Assessing the Impact of Radiation Exposure


• A large dose of radiation spread over time is less harmful than the same total amount of radiation administered over a short time

• Tissues most affected by large, whole-body exposures are bone marrow, intestinal tissue, hair follicles, and reproductive organs

Assessing the Impact of Radiation Exposure



20.4 Thermodynamic Stability of the Atomic

Nucleus


20.4 Thermodynamic Stability of the Atomic Nucleus

• Nuclear reactions are accompanied by changes in energy

• Energy changes in nuclear reactions are enormous compared with those of even the most energetic chemical reactions

• Energy changes in a typical nuclear reaction are so large that they result in a measurable change of mass


Mass-Energy Balance

• Nuclear reactions are accompanied by large changes in energy, which result in detectable changes in mass.

• The relationship between mass, m, and energy, E, is expressed in the equation E = mc2, where c is the speed of light (2.998 x 108 m/s), and energy and mass are expressed in units of joules and kilograms, respectively.

• Every mass has an associated energy, and any reaction that involves a change in energy must be accompanied by a change in mass.

• Large changes in energy in nuclear reactions are reported in units of keV or MeV; a change in energy that accompanies a nuclear reaction can be calculated from the change in mass (1 amu = 931 MeV).

• Chemical reactions are accompanied by changes in mass, but these changes are too small to be detected


Nuclear Binding Energies

• The mass of an atom is always less than the sum of the masses of its component particles; the only exception is hydrogen-1.

• The difference between the sum of the masses of the components and the measured atomic mass is called the mass defect of the nucleus.

• The amount of energy released when a nucleus forms from its component nucleons is the nuclear binding energy.

• The magnitude of the mass defect is proportional to the nuclear binding energy, so both values indicate the stability of the nucleus.


Nuclear Binding Energies

• Not all nuclei are equally stable; the relative stability of different nuclei are described by comparing the binding energy per nucleon, which is obtained by dividing the nuclear binding energy by the mass number A of the nucleus.

• The binding energy per nucleon increases rapidly with increasing atomic number until Z = 26, where it levels off and then decreases slowly.


Nuclear Fission and Fusion

• Nuclear fission– The splitting of a heavy nucleus into two lighter ones– Nucleus usually divides asymmetrically rather than into equal

parts, and the fission of a given nuclide does not give the same products every time

– In a typical nuclear fission reaction, more than one neutron is released by each dividing nucleus; when these neutrons collide with and induce fission in other neighboring nuclei, a self-sustaining series of nuclear fission reactions known as a nuclear chain reaction can result

– Each series of events is called a generation– The minimum mass capable of supporting sustained fission is

called the critical mass





– If the mass of the fissile isotope is greater than the critical mass, then under the right conditions, the resulting supercritical mass can release energy explosively

• Nuclear fusion– Two light nuclei combine to produce a heavier, more stable

nucleus and is the opposite of a nuclear fission reaction– The positive charge on both nuclei results in a large

electrostatic energy barrier to fusion; barrier can be overcome if one or both particles have sufficient kinetic energy to overcome the electrostatic repulsions, allowing the two nuclei to approach close enough for a fusion reaction to occur





20.5 Applied Nuclear Chemistry


Nuclear Reactors

• When a critical mass of a fissile isotope has been achieved, the resulting flux of neutrons can lead to a self-sustaining reaction; a variety of techniques can be used to control the flow of neutrons, which allows nuclear fission reactions to be maintained at safe levels

• Many levels of control are required, along with a fail-safe design; otherwise, the chain reaction can accelerate so rapidly that it releases enough heat to melt or vaporize the fuel and the container, causing the release of enough radiation to contaminate the surrounding area

• If the neutron flow in a reactor is carefully regulated so that only enough heat is released to boil water, then the resulting steam can be used to produce electricity


Nuclear Reactors

• Light-water reactors

– Used to produce electricity– Fuel rods containing a fissile isotope in a structurally

stabilized form (uranium oxide pellets encased in a corrosion-resistant zirconium alloy) are suspended in a cooling bath that transfers the heat generated by the fission reaction to a secondary cooling system

– Heat is used to generate steam for the production of electricity

– Control rods are utilized to absorb neutrons and control the rate of the nuclear chain reaction

– Pulling the control rods out increases the neutron flow, allowing the reactor to generate more heat; inserting the rods completely stops the reaction


Nuclear Reactors


Nuclear Reactors

• Heavy-water reactors

– Deuterium (2H) absorbs neutrons less effectively than does hydrogen (1H), but it is about twice as effective at scattering neutrons

– A nuclear reactor that uses D2O instead of H2O as the moderator is so efficient that it can use unenriched uranium as fuel, which reduces the operating costs and eliminates the need for plants that produce enriched uranium


Nuclear Reactors

• Breeder reactors

– A nuclear fission reactor that produces more fissionable fuel than it consumes; the fuel produced is not the same as the fuel consumed

– Overall reaction is the conversion of nonfissile 238U to fissile 239Pu, which can be isolated chemically and used to fuel a new reactor


Nuclear Reactors

• Nuclear fusion reactors

– Nuclear fusion reactions are thermodynamically spontaneous, but the positive charge on both nuclei results in a large electrostatic energy barrier to the reaction; high temperatures are required to overcome the electrostatic repulsions and initiate a fusion reaction

– Achieving these temperatures, controlling the materials to be fused, and extracting the energy released by the fusion reaction are difficult problems

– These nuclear reactions are called thermonuclear reactions because a great deal of thermal energy must be invested to initiate the reaction; amount of heat released by the reaction is several orders of magnitude greater than the energy needed to initiate it


Uses of Radioisotopes

• Radiation is destructive to rapidly dividing cells such as tumor cells and bacteria, so it has been used medically to treat cancer; many radioisotopes are available for medical use, and each has specific advantages for certain applications

• Radiation therapy – Radiation is delivered by a source planted inside the body, or in

some cases, physicians take advantage of the body’s own chemistry to deliver a radioisotope to the desired location

– In cases where a tumor is surgically inaccessible, an external radiation source is used to aim a tightly focused beam of rays at it



• Medical imaging– A radioisotope is temporarily

localized in a particular tissue or organ where its emissions provide a map of the tissue or organ

– Positron emission tomography (PET) is an imaging technique that produces remarkably detailed three-dimensional images; biological molecules that have been tagged with a positron-emitting isotope can be used to probe the functions of organs



• Ionizing radiation is used in the irradiation of food to kill bacteria

• In addition to the medical uses of radioisotopes, radioisotopes have hundreds of other uses: smoke alarms, dentistry, detectors, and gauges



20.6 The Origin of the Elements


Relative Abundances of the Elements on Earth and in the Universe

• The relative abundances of the elements in the universe and on Earth relative to silicon are shown in the following figure



• Data are estimates based on the characteristic emission spectra of the elements in stars, the absorption spectra of matter in clouds of interstellar dust, and the approximate composition of Earth as measured by geologists

• Data illustrate two points1. Except for hydrogen, the most abundant elements have

even atomic numbers2. The relative abundances of the elements in the universe

and on Earth are very different



• All the elements originally present on Earth were synthesized from hydrogen and helium nuclei in the interiors of the stars that have long since exploded and disappeared

• Six of the most abundant elements in the universe (carbon, oxygen, neon, magnesium, silicon, and iron) have nuclei that are integral multiples of the helium-4 nucleus, which suggests that helium-4 is the primary building block for heavier nuclei


Synthesis of the Elements in Stars

• Elements are synthesized in discrete stages during the lifetime of a star, and some steps occur only in the most massive stars known

– All stars are formed by the aggregation of interstellar dust, which is mostly hydrogen

– As the cloud of dust slowly contracts due to gravitational attraction, its density reaches 100g/cm3 and the temperature increases to 1.5 x 107 K, forming a dense plasma of ionized hydrogen nuclei

– Self-sustaining nuclear reactions begin and the star ignites, creating a yellow star

– In the first stages of life, the star is powered by a series of nuclear fusion reactions that convert hydrogen to helium



– Overall reaction is the conversion of four hydrogen nuclei to a helium-4 nucleus, accompanied by the release of two positrons, two rays, and a great deal of energy

– When large amounts of helium-4 have been formed, they become concentrated in the core of the star, which slowly becomes denser and hotter

– At a temperature of 2 x 108 K, the helium-4 nuclei begin to fuse, producing beryllium-8, which is unstable and decomposes in 10–

16 s, long enough for it to react with a third helium-4 nucleus to form the stable carbon-12



– Sequential reactions of carbon-12 with helium-4 produce the elements with even numbers of protons and neutrons up to magnesium-24

– So much energy is released by these reactions that it causes the surrounding mass of hydrogen to expand, producing a red giant that is 100 times larger than the original yellow star

– As the star expands, the heavier nuclei accumulate in its core, which contracts to a density of 50,000 g/cm3 and becomes hotter



– At a temperature of 7 x 108 K, carbon and oxygen nuclei undergo nuclear fusion reactions to produce sodium and silicon nuclei

– At these temperatures, carbon-12 reacts with helium-4 to initiate a series of reactions that produce more oxygen-16, neon-20, magnesium-24, and silicon-28, as well as heavier nuclides such as sulfur-32, argon-36, and calcium-40

– Energy released by these reactions causes a further expansion of the star to form a red supergiant



– Core temperature increases steadily, at a temperature of 3 x 109 K, the nuclei that have been formed exchange protons and neutrons freely

– This equilibration process forms heavier elements up to iron-56 and nickel-58, which have the most stable nuclei known


Formation of Heavier Elements in Supernovas

• All naturally occurring elements heavier than nickel are formed in the rare but spectacular cataclysmic explosions called supernovas



– Fuel in the core of a massive star is consumed, so its gravity causes it to collapse in about 1 s

– As the core is compressed, the iron and nickel nuclei within it disintegrate to protons and neutrons, and many of the protons capture electrons to form neutrons

– The resulting neutron star is so dense that atoms no longer exist– The energy released by the collapse of the core causes the

supernova to explode in a violent event



– Force of the explosion blows the star’s matter into space, creating a gigantic and rapidly expanding dust cloud called a nebula

– The concentration of neutrons is so great that multiple neutron-capture events occur, leading to the production of the heaviest elements and many of the less-stable nuclides

– Force of the explosion distributes these elements throughout the galaxy surrounding the supernova and are eventually captured in the dust that condenses to form new stars


21 Periodic Trends and the s-Block Elements


CHAPTER OBJECTIVES

• To be able to describe the physical and chemical properties of hydrogen and to predict its reactivity

• To be able to describe how the alkali and alkaline earth metals are isolated

• To become familiar with the reactions, compounds, and complexes of the alkali and alkaline earth metals

• To know some of the uses of the alkali and alkaline earth metals

• To become familiar with the role of the s-block elements in biology



21.1 Overview of Periodic Trends



• The single most important unifying principle in understanding the chemistry of the elements is the systematic increase in atomic number, accompanied by the orderly filling of atomic orbitals by electrons, which leads to periodicity in such properties as atomic and ionic size, ionization energy, electronegativity, and electron affinity

• Same factors lead to periodicity in valence-electron configurations, which for each group results in similarities in oxidation states and the formation of compounds with common stoichiometries



• The most important periodic trends in atomic properties are summarized in the following table:



– These trends are based on periodic variations in a single fundamental property, the effective nuclear charge (Zeff), which increases from left to right and from bottom to top in the periodic table

– The diagonal line separates the metals (to the left of the line) from the nonmetals (to the right)

1. Metals have low electronegativities; they tend to lose electrons in chemical reactions to form compounds in which they have positive oxidation states2. Nonmetals have high electronegativities; they tend to

gain electrons in chemical reactions to form compounds in which they have negative oxidation states



– The semimetals lie along the diagonal line dividing metals and nonmetals; they exhibit properties and reactivities intermediate between those of metals and nonmetals

– Elements of Groups 13, 14, and 15 span the diagonal line separating metals and nonmetals, and their chemistry is more complex than predicted based solely on their valence-electron configuration


Unique Chemistry of the Lightest Elements

• The chemistry of the second-period element of each group (n = 2; Li, Be, B, C, N, O, and F) differs in many important aspects from that of the heavier members, or congeners, of the group

• The elements of the third period (n = 3; Na, Mg, Al, Si, P, S, and Cl) are generally more representative of the group to which they belong



• The anomalous chemistry of second-period elements results from three important characteristics

1. Small radii– Due to their small radii, second-period elements have

lower electron affinities than would be predicted from general periodic trends

– When an electron is added to such a small atom, increased electron-electron repulsions substantially destabilize the anion

– The small sizes of these elements prevent them from forming compounds in which they have more than four nearest neighbors



– Simple binary ionic compounds of second-period elements have more covalent character than the corresponding compounds formed from their heavier congeners

– The very small cations derived from second-period elements have a high charge-to-radius ratio and can polarize the filled valence shell of an anion

– Bonding in these compounds has a significant covalent component, giving the compounds properties that can differ significantly from those expected for simple ionic compounds



2. Energetically unavailable d orbitals– Because d orbitals are never occupied for principal

quantum numbers less than 3, the valence electrons of second-period elements occupy 2s and 2p orbitals only

– Electron configurations with more than four electron pairs around a central, second-period element are not observed

3. Tendency to form bonds with other atoms– One of the most dramatic differences between the

lightest main group elements and their heavier congeners is the tendency of the second-period elements to form species that contain multiple bonds



• Another important trend to note in main-group chemistry is the chemical similarity between the lightest element of one group and the element immediately below and to the right of it in the next group, a phenomenon known as the diagonal effect


The Inert-Pair Effect

• The inert-pair effect refers to the empirical observation that the heavier elements of Groups 13—17 have oxidation states that are lower by 2 than the maximum predicted for their group

• Two major reasons for the inert-pair effect 1. Increasing ionization energies

– Filled (n –1)d or (n –2)f subshells are poor at shielding electrons in ns orbitals

– The two electrons in the ns subshell experience a high effective nuclear charge Zeff and are strongly attracted to the nucleus, reducing their participation in bonding


The Inert-Pair Effect

2. Decreasing bond strengths– Going down a group, the atoms become larger and the

overlap between the valence orbitals of the bonded atoms decreases

– Bond strengths tend to decrease down a column

• The net effect of these two factors is that as you go down a group in the p block, the additional energy released by forming two additional bonds eventually is not great enough to compensate for the additional energy required to remove the two ns2 electrons



21.2 The Chemistry of Hydrogen


Isotopes of Hydrogen• Hydrogen

– The most abundant element in the universe– The ultimate source of all the other elements by the process of

nuclear fusion

• There are three isotopes of hydrogen, all of which contain one proton and one electron per atom


Isotopes of Hydrogen

1. Protium (1H or H)—most common isotope 2. Deuterium (2H or D)—has an additional neutron 3. Tritium (3H or T)—the rarest isotope of hydrogen

– Produced in the upper atmosphere by a nuclear reaction when cosmic rays strike nitrogen and other atoms; it is then washed into the oceans by rainfall

– Radioactive, decaying to 3He with a half-life of 12.3 years


Isotopes of Hydrogen

• Different masses of the three isotopes of hydrogen cause them to have different physical properties; H2, D2, and T2 differ in their melting points, boiling points, densities, and heats of fusion and vaporization

• Deuterium and tritium are important research tools

– By incorporating these isotopes into specific positions in selected molecules, they act as labels, or tracers

– Tracers are substances that enable biochemists to follow the path of a molecule through an organism or cell and to provide information about the mechanism of enzymatic reactions


Bonding in Hydrogen and Hydrogen-Containing Compounds

• The 1s1 electron configuration of hydrogen indicates a single valence electron; the 1s orbital has a maximum capacity of two electrons, so hydrogen can form compounds with other elements in three ways:



1. By losing its electron to form a proton (H+) with an empty 1s orbital

– The proton is a Lewis acid that can accept a pair of electrons from another atom to form an electron-pair bond

2. By accepting an electron to form a hydride ion (H–), which has a filled 1s2 orbital

– Hydrogen reacts with electropositive metals, such as the alkali metals and alkaline earths, to form ionic hydrides, which contain metal cations and H– ions



3. By sharing its electron with an electron on another atom to form an electron-pair bond

– With a half-filled 1s1 orbital, the hydrogen atom can interact with singly occupied orbitals on other atoms to form either a covalent or polar covalent electron-pair bond, depending on the electronegativity of the other atom



• Hydrogen can also act as a bridge between two or more atoms. Two example of this are:

1. The hydrogen bond, an electrostatic interaction between a hydrogen bonded to an electronegative atom and an atom that has one or more lone pairs of electrons



2. The three-center bond, in which a hydride ion bridges two electropositive atoms

− In these bonds, only two bonding electrons are used to hold three atoms together and are called electron-deficient bonds


Synthesis, Reactions, and Compounds of Hydrogen

• The first known preparation of elemental hydrogen was in 1671, when Boyle dissolved iron in dilute acid and obtained a colorless, odorless, gaseous product

• Hydrogen was identified as an element in 1766, when Cavendish showed that water was the sole product of the reaction of the gas with oxygen

• Explosive properties of mixtures of hydrogen with air were discovered in the eighteenth century

• Due to its low molecular mass, hydrogen gas is difficult to condense to a liquid and solid hydrogen has one of the lowest melting points known



• Hydrogen gas

– Most common way to produce small amounts of highly pure hydrogen gas is to react an active metal with dilute acid

– Hydrogen gas can also be generated by the reaction of metals with a strong base

– Also produced by the reaction of ionic hydrides with water; expensive—used for specialized purposes

– On an industrial scale, H2 is produced from methane by means of catalytic steam reforming, a method used to convert hydrocarbons to a mixture of CO and H2 known as synthesis gas, or syngas



• Most of the elements in the periodic table form binary compounds with hydrogen, called hydrides, which can be divided into three classifications, each with its own characteristic properties

1. Covalent hydrides contain hydrogen bonded to another atom via a covalent or polar covalent bond and are molecular substances that are volatile and have low melting points

2. Ionic hydrides contain the hydride ion as the anion and cations derived from electropositive metals; they and are nonvolatile solids that contain three-dimensional lattices of cations and anions, which decompose upon heating to H2

gas and the parent metal



3. Metallic hydrides are formed by hydrogen and less electropositive metals such as the transition metals

– Have properties similar to those of the parent metal

– Best viewed as metals that contain many hydrogen atoms present as interstitial impurities



21.3 The Alkali Metals (Group 1)


• Alkali metals are so reactive that they are never found in nature in elemental form

• Because the alkali metals are among the most potent reductants known, obtaining them in pure form requires a considerable input of energy

– Pure Li, Na, and K are prepared by electrolytic reduction of the molten chlorides

– Metallic sodium and potassium are produced by the electrolysis of molten mixtures of NaCl and CaCl2 or KCl and CaCl2

– Rubidium and cesium are obtained by reaction of their hydroxide salts with a reductant such as Mg

Preparation of Alkali Metals


– Massive deposits of pure NaCl and KCl are found in nature and are the major sources of sodium and potassium

– Other alkali metals found in low concentrations in a wide variety of minerals

– Alkali metals are obtained from silicate ores in a multistep process that uses the pH-dependent solubility of selected salts of each metal ion



• The steps in this process are:

1. leaching—use sulfuric acid to dissolve the desired alkali metal and Al3+ from the ore

2. basic precipitation—to remove Al3+ from the mixture as Al(OH)3

3. selective precipitation of the insoluble alkali metal salt

4. dissolution of the salt in hydrochloric acid5. isolation of the metal by evaporation and

electrolysis



• Various properties of the Group-1 elements are summarized in the following table

General Properties of Alkali Metals


– The atomic and ionic radii increase smoothly from Li to Cs, and the first ionization energies decrease as the atoms become larger

– Due to their low first ionization energies, the alkali metals have a tendency to form an ion with a +1 charge—they have high electron affinities because the addition of an electron produces an anion (M–) with an ns2 electron configuration

– Densities of the elements increase from Li to Cs



– Melting and boiling points decrease from Li to Cs– Standard reduction potentials, Eº, of the alkali metals do not

follow the trend based on ionization energies; lithium is the strongest reductant and sodium is the weakest

– Li+ is much smaller than the other alkali metal cations, and its hydration energy is the highest; lithium metal is the strongest reductant in aqueous solution



• All alkali metals are electropositive elements with an ns1

valence-electron configuration, forming the monocation (M+) by the loss of the single valence electron

• Chemistry of the alkali metals is largely that of ionic compounds that contain the M+ ions

• The lighter Group-1 elements form a series of organometallic compounds that contain polar covalent M–C bonds

• All of the alkali metals react vigorously with the halogens (Group 17) to form the corresponding ionic halides

Reactions and Compounds of Alkali Metals


• Alkali metals react with the heavier chalcogens (sulfur, selenium, and tellurium in Group 16) to produce metal chalcogenides

• The reaction of the alkali metals with oxygen is complex, and the stoichiometry of the product depends on both the metal:oxygen ratio and the size of the metal

• Alkali metal peroxides and superoxides are potent oxidants that react with a wide variety of reducing agents

• Lithium, the lightest alkali metal, is the only one that reacts with atmospheric nitrogen, forming lithium nitride



• All the alkali metals react with the larger Group-15 elements phosphorus and arsenic to form metal phosphides and arsenides

• Alkali metals react with all the Group-14 elements, but the compositions and properties of the products vary significantly

• The heavier alkali metals ( K, Rb, and Cs) react with carbon in the form of graphite, where the metals insert themselves between the sheets of carbon atoms to give new substances called graphite intercalation compounds



• All the alkali metals react directly with gaseous hydrogen at elevated temperatures to produce ionic hydrides (M+H–) and all are capable of reducing water to produce hydrogen gas

• Alkali metal cations are found in a wide variety of ionic compounds; any alkali metal salt can be prepared by reacting the alkali metal hydroxide with an acid and then evaporating the water

• Hydroxides of alkali metals can react with organic compounds that contain an acidic hydrogen to produce a salt



• Because of their low positive charge (+1) and large ionic radii, alkali metal cations have only a weak tendency to react with simple Lewis bases to form metal complexes

• Complex formation is most significant for the smallest cation, Li+, and decreases with increasing radius

• Complex formation is due to the electrostatic interaction of the metal cation with the polar water molecules; anhydrous salts containing Li+ and Na+ ions are used as drying agents due to their high affinity for water

Complexes of Alkali Metals


• Electrostatic interactions allow alkali metal ions to form complexes with certain cyclic polyethers and related compounds, such as crown ethers and cryptands

– Crown ethers are cyclic polyethers that contain four or more oxygen atoms separated by two or three carbon atoms; they also have a central cavity that can accommodate a metal ion coordinated to the ring of oxygen atoms

– Cryptands are spherical analogues of crown ethers and are more powerful and selective complexing agents; they consist of three (-CH2CH2O-)n chains connected by two nitrogen atoms and can completely surround a metal ion of the appropriate size, coordinating to the metal by a lone pair of electrons on each O atom and the two N atoms

Complexes of Alkali Metals


• Alkali metals dissolve reversibly in liquid ammonia which produces hydrogen gas and the metal salt of the conjugate base of the solvent (the amide ion NH2

–)

M(s) + NH3 (l) 1/2H2 (g) + M+(am)NH2–(am)

– (am) designation refers to an ammonia solution – Reaction needs a catalyst

– In many cases the alkali metal amide salt (MNH2) is not very soluble in liquid ammonia and precipitates, but when dissolved, solutions of the alkali metal are produced that can be very concentrated

• Solutions of alkali metals in liquid ammonia are intensely colored and are good conductors of electricity due to the presence of solvated electrons, e–(NH3), which are not attached to single atoms

Liquid Ammonia Solutions


• In addition to solvated electrons, solutions of alkali metals in liquid ammonia contain the metal cation (M+), the neutral metal atom (M), metal dimers (M2), and the metal anion (M–)

– Anion is formed by the addition of an electron to the singly occupied ns valence orbital of the metal atom

– These solutions are not stable and decompose to the thermodynamically favored products M+NH2

–

and hydrogen gas– Solvated electron is a potent reductant

Liquid Ammonia Solutions


• Organometallic compounds contain a metal covalently bonded to a carbon atom of an organic species

• Properties and reactivities of organometallic compounds differ greatly from those of either the metallic or organic components

– Lithium forms an extensive series of covalent organolithium compounds that are volatile, low-melting-point solids or liquids that can be sublimed or distilled at low temperatures and are soluble in nonpolar solvents; the molten solids do not conduct electricity and have a tendency to form oligomers

– Organosodium and organopotassium compounds are more ionic than organolithium compounds, contain discrete M+ and R– ions, and are insoluble or only sparingly soluble in nonpolar solvents

Organometallic Compounds of the Group-1 Elements


• Sodium remains liquid over a wide temperature range and is used as a coolant in specialized high-temperature applications

• Cesium, because of its low ionization energy, is used in photosensors in automatic doors, toilets, burglar alarms, and other electronic devices

• Compounds of sodium and potassium are produced on a huge scale in industry: NaOH, used in a wide variety of industrial processes; Na2CO3, used in the manufacture of glass; K2O, used in porcelain glazes; and Na4SiO4, used in detergents

• Li2CO3 is an effective treatment for manic depression, or bipolar disorder

Uses of the Alkali Metals



21.4 The Alkaline Earth Metals (Group 2)


21.4 The Alkaline Earth Metals (Group 2)

• The alkaline earth metals are so reactive that they are never found in elemental form in nature; they form +2 ions that have very negative reduction potentials so large amounts of energy are needed to isolate them from their ores

• Four of the six Group-2 elements—magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba)—were isolated in the early nineteenth century by Davy

• Beryllium (Be), the lightest alkaline earth metal, was obtained in 1828 by Wöhler and Bussy

• Radium was discovered in 1898 by the Curies


Preparation of Alkaline Earth Metals

• Alkaline earths are produced for industrial use by electrolytic reduction of their molten chlorides

• Group-2 metal chlorides are obtained from a variety of sources

• Chemical reductants can also be used to obtain the Group-2 elements

• Alkaline earths are somewhat easier than the alkali metals to isolate from their ores because their carbonate, sulfate, and some hydroxide salts are insoluble


General Properties of Alkaline Earth Metals

• Several important properties of the alkaline earths are summarized in the following table



– Many of these properties are similar to those of the alkali metals, but certain key differences are attributable to the differences in the valence-electron configuration of the two groups (ns2 for the alkaline earth metals versus ns1 for the alkali metals)

– Atomic and ionic radii of the alkaline earth metals increase smoothly from Be to Ba, and the ionization energies decrease

– The first ionization energy of an alkaline earth, with an ns2 valence-electron configuration, is always higher than that of the alkali metal immediately preceding it

– The density of Ca is lower than that of Be and Mg, the two lightest members of the group, and Mg has the lowest melting and boiling points



– The heaviest alkaline earth, Ba, is the strongest reductant, and the lightest, Be, is the weakest

– Reduction potentials of Ca and Sr are not very different from that of Ba, indicating that the opposing trends in ionization energies and hydration energies are of equal importance

– One major difference between the Group-1 and Group-2 elements is their electron affinities; alkaline earths have little or no tendency to accept an additional electron because their ns valence orbitals are already full, while the alkali metals have a significant affinity for an additional electron due to their half-filled ns orbitals


Reactions and Compounds of Alkaline Earth Metals

• With their low first and second ionization energies, the Group-2 elements exclusively form ionic compounds that contain the M+2 ions

• The lightest element, Be, with its higher ionization energy and small size, forms compounds that are largely covalent; some compounds of Mg2+ have significant covalent character; so organometallic compounds are important for Be and Mg in Group 2

• All the alkaline earth metals react vigorously with the halogens (Group 17) to form the corresponding halides (MX2)

– these compounds are ionic in nature, containing the M2 cation

and two X– anions (with the exception of the beryllium halides)



• Beryllium halides, with properties more typical of covalent compounds, have a polymeric halide-bridged structure in the solid state

– These compounds are volatile, producing vapors that contain the linear X-Be-X molecules

– They have four valence electrons around the central atom– They are potent Lewis acids and react readily with Lewis

bases to form tetrahedral adducts in which the central beryllium is surrounded by an octet of electrons



• Reactions of the alkaline earth metals with oxygen are less complex than those of the alkali metals

– All the Group-2 elements, except barium, react directly with oxygen to form the simple oxide MO

– barium forms barium peroxide (BaO2)– BeO is prepared by direct reaction with oxygen; other

alkaline earth oxides are prepared by thermal decomposition of carbonate salts



• The reactions of the alkaline earths with the heavier chalcogens (Y) are similar to those of the alkali metals

– When the reactants are present in a 1:1 ratio, the binary chalcogenides (MY) are formed

– at higher Y:M ratios, salts containing polychalcogenide ions (Yn

2–) are formed

• Oxides of Ca, Sr, and Ba react with CO2 to form carbonate; the carbonates of the alkaline earths react with aqueous acid to give CO2 and H2O

• Except for BeO, which has significant covalent character and is amphoteric, all the alkaline earth oxides are basic and react with water to form the hydroxides, M(OH)2, and dissolve in aqueous acid



• Hydroxides of the lighter alkaline earths are insoluble in water, but their solubility increases as the atomic number of the metal increases; BeO and MgO are more inert than the other Group-2 oxides

• Reactivities of the alkaline earth metals with nitrogen is the opposite of that observed for the alkali metals

– Only the lightest element, Be, does not react readily with N2 to form the nitride (M3N2), although finely divided Be will react at high temperatures

– The higher lattice energy due to the highly charged M2+ and N3–

ions is sufficient to overcome the chemical inertness of the N2 molecule

• All alkaline earths react with the heavier Group-15 elements to form binary compounds such as phosphides and arsenides with the general formula M3Z2



• When heated, all the alkaline earths, except for beryllium, react directly with carbon to form ionic carbides with the general formula MC2

– Most important is calcium carbide, which reacts with water to produce acetylene

– Beryllium reacts with carbon to form Be2C, which reacts with water or aqueous acid to produce methane

• Beryllium does not react with hydrogen, although BeH2 can be prepared by an indirect route

– All the heavier alkaline earths (Mg through Ba) react directly with hydrogen to produce the binary hydrides (MH2), which are ionic, but BeH2 and MgH2 have polymeric structures with covalent character

– All alkaline earth hydrides are good reducing agents that react rapidly with water or aqueous acid to produce hydrogen gas



• Like the alkali metals, the heavier alkaline earths are electropositive and dissolve in liquid ammonia

– In this case, two solvated electrons are formed per metal atom, and no equilibria involving metal dimers or metal anions are known

• Like the alkali metals, the alkaline earths form a wide variety of simple ionic salts with oxoanions such as carbonate, sulfate, and nitrate

– Nitrate salts tend to be soluble, but the carbonates and the sulfates are quite insoluble because of the higher lattice energy due to the doubly charged cation and anion

– Solubility of the carbonates and the sulfates decreases rapidly down the group because hydration energies decrease with increasing cation size


Complexes of Alkaline Earth Metals

• Because of their higher positive charge (+2) and smaller ionic radii, the alkaline earths have a greater tendency to form complexes with Lewis bases than do the alkali metals. This tendency is most important for the lightest cation, Be2+, and decreases rapidly with increasing radius of the metal ion

• Chemistry of Be2+ dominated by its behavior as a Lewis acid, forming complexes with Lewis bases that produce an octet of electrons around the beryllium, which is amphoteric

• The heavier alkaline earths also form complexes, but with a coordination number of 6 or higher; this behavior is most important for the smaller cations Mg2+ and Ca2+

• Like the alkali metals, the alkaline earths form complexes with neutral cyclic ligands like the crown ethers and cryptands


Organometallic Compounds Containing Group 2 Elements

• Like the alkali metals, the lightest alkaline earths (Be and Mg) form the most covalent-like bonds with carbon, and they form the most stable organometallic compounds

• Organometallic compounds of magnesium with the formula RMgX, where R is an alkyl or aryl group and X is a halogen, are called Grignard reagents, which are used to synthesize various organic compounds


Uses of the Alkaline Earth Metals

• Elemental magnesium is the only alkaline earth metal that is produced on a large scale

– Its low density makes it an important component of lightweight metal alloys used in aircraft frames and aircraft and automobile engine parts

– Serves as a reductant for the production of a number of metals

• Beryllium is widely used but is extremely toxic– Increases the strength of copper and nickel alloys– Its low atomic number gives it the lowest tendency to absorb

X-rays of all the metallic elements, which makes it suited for applications involving radioactivity


Uses of the Alkaline Earth Metals

• Tons of calcium compounds are used every year– CaCl2 is used as road salt to lower the freezing point of water

on roads in cold temperatures– CaCO3 is a major component of cement and an ingredient in

antacids– “Quicklime” (CaO) is used in the steel industry to remove

oxide impurities, for making glass, and to neutralize acidic soil

• BaSO4 used in milkshakes for identifying digestive problems by X-rays

• Various alkaline earth compounds are used to produce brilliant colors seen in fireworks



21.5 The s-Block Elements in Biology


21.5 The s-Block Elements in Biology

• The s-block elements play important roles in biological systems

• Covalent hydrides are the building block of organic compounds, and other compounds and ions containing s-block elements are found in tissues and cellular fluids


• There are three major classes of hydrides—covalent, ionic, and metallic—but only covalent hydrides occur in living cells and have any biochemical significance

– Hydrogen is less electronegative than oxygen, nitrogen, or sulfur (all symbolized by Z)

– The H-Z bond in the hydrides of these elements is polarized so the hydrogen atoms in H-Z bonds are acidic

– Hydrides in which H is bonded to O, N, or S atoms are polar, hydrophilic molecules that form hydrogen bonds and undergo acid-base reactions by transferring a proton

Covalent Hydrides


• Hydrogen bonds are crucial in biochemistry because they help hold proteins in their biologically active folded structures

– Hydrogen bonds connect the two intertwining strands of DNA, the substance that contains the genetic code of all organisms

– Hydrogen bonds are easier to break than the covalent bonds that form the individual DNA strands, so the two intertwined strands can be separated to give intact single strands, which is essential for the duplication of genetic information

• The extensive hydrogen-bonding network in water is one of the keys to the existence of life on our planet

Covalent Hydrides


• The members of Group 1 and Group 2 that are present in the largest amounts in organisms are sodium, potassium, magnesium, and calcium, all of which form monatomic cations with a charge of +1 (Group 1, M+) or +2 (Group 2, M2+); these are known as macrominerals

Macrominerals


• Ion transport– Na+ and Ca2+ are found in extracellular fluids, and K+ and Mg2+

are found in intracellular fluids– Energy is needed to transport each of these ions across the

cell membrane toward the side with the higher concentration– Biological machines responsible for the selective transport of

these metal ions are complex assemblies of proteins called ion pumps, which recognize and discriminate between metal ions with a high affinity for ions of a certain charge and radius

– Defects in the ion pumps or their control mechanisms result in major health problems

Macrominerals


– Some of the most important biological functions of the Group-1

and Group-2 metals are due to small changes in the cellular concentrations of the metal ion

– Within cells, K+ and Mg2+ activate particular enzymes by binding to specific negatively charged sites in the enzyme structure

• Ionophores– Molecules that facilitate the transport of metal ions across

membranes, because the health of cells depends on maintaining the proper levels of cations in intracellular fluids

– Potent antibiotics

Macrominerals


22 The p-Block Elements


CHAPTER OBJECTIVES

• To understand how valence-electron configurations and periodic trends in atomic properties determine the chemical properties of the p-block elements

• To use thermodynamics and kinetics to understand the reactivity of the p-block elements

• To understand why the chemistry of the lightest member of each group differs from that of the heavier elements of the group

• To be able to predict the types of reactions the p-block elements undergo


The p-Block Elements

• p-block elements

– The line that divides metals from nonmetals in the periodic table crosses the p block diagonally

– The differences between metallic and nonmetallic properties are evident within each group, even though all members of the group have the same valence-electron configuration

– The p-block only portion of the periodic table where the inert-pair effect is seen

– The chemistry of the lightest member of each group in the p block differs sharply from its heavier congeners but is similar to the element immediately below and to the right of it in the next group; diagonal similarities in chemistry are seen across the p block



22.1 The Elements of Group 13



• Group 13, the first group to span the dividing line between metals and nonmetals

• Its chemistry is more diverse than that of Groups 1 and 2, which include only metallic elements

• Except for the lightest element, boron, the Group-13 elements are all electropositive; they tend to lose electrons in chemical reactions rather than gain them

• None of these elements was known until the early nineteenth century because they are never found in nature in their free state


Preparation and General Properties Of Group-13 Elements

• Group-13 elements are not as powerful of reductants as are the alkali metals and alkaline earths

• Their compounds with oxygen are thermodynamically stable, and large amounts of energy are needed to isolate them from their oxide ores

• The two most accessible elements are boron and aluminum

• The other members of Group 13 are rather rare, and these metals are usually obtained as by-products in the processing of other metals



• The following table summarizes some important properties of the Group-13 elements





– Large differences between boron and aluminum in size, ionization energy, electronegativity, and reduction potential due to the fact that boron behaves chemically like a nonmetal and aluminum like a metal

– All the Group-13 elements have ns2np1 valence-electron configurations, and all tend to lose their three valence electrons to form compounds in the +3 oxidation state

– Heavier elements in the group also form compounds in the +1 oxidation state by loss of the single np valence electron

– Neutral compounds of the Group-13 elements contain only six valence electrons and are all strong Lewis acids



– In contrast to Groups 1 and 2, the Group-13 elements show no consistent trends in ionization energies, electron affinities, and reduction potentials

– Electronegativity increases from aluminum to thallium– Many of the inconsistencies observed in the properties of the

Group-13 elements can be explained by the increase in Zeff that arises from poor shielding of the nuclear charge by the filled (n–1)d10 and (n–2)f14 subshells; although actual nuclear charge increases by 32 from indium to thallium, screening by the filled 5d and 4f subshells is so poor that Zeff increases significantly from indium to thallium; therefore, the first ionization energy of thallium is higher than that of indium


Reactions and Compounds of Boron

• Elemental boron is a semimetal that is unreactive; the other Group-13 elements all exhibit metallic properties and reactivity and have fewer valence electrons than valence orbitals, which results in delocalized, metallic bonding

• Boron – High ionization energy, low electron affinity, low

electronegativity, and small size – Does not form a metallic lattice with delocalized valence

electrons; forms unique and intricate structures that contain multicenter bonds, in which a pair of electrons holds together three or more atoms

– Basic building block of elemental boron is not the individual boron atom, as would be the case in a metal, but rather the B12 icosahedron, which do not pack together well and have voids, resulting in low density



– Elemental boron can be induced to react with many nonmetallic elements to give binary compounds that have a variety of applications

1. Boron carbide (B4C)—used in armor 2. Boron nitride (BN)—produced by heating boron with excess

nitrogen and is similar in many ways to elemental carbon 3. Boron oxide (B2O3)—formed when boron is heated with excess

oxygen, and it dissolves many metal and nonmetal oxides to give a wide range of important borosilicate glasses

4. Boron trihalides (BX3)—formed by heating boron with excess halogen



− At high temperatures, boron also reacts with all metals to give metal borides that contain regular three-dimensional networks, or clusters, of boron atoms; metal borides are hard and corrosion-resistant, and they are used in turbine blades and rocket nozzles

− Binary hydrides were discovered in the early twentieth century and have multicenter bonds


Reactions and Compounds of the Heavier Group-13 Elements

• Neutral compounds of the Group-13 elements are electron deficient and behave like Lewis acids

• All four of the heavier elements (Al, Ga, In, and Tl) react readily with the halogens to form compounds with the stoichiometry MX3– Of the halides, only the fluorides exhibit typical behavior of an

ionic compound with high melting points and low solubility in nonpolar solvents

– The trichlorides, tribromides, and triiodides of aluminum, gallium, and indium, as well as TlCl3, and TlBr3, are more covalent in character and form halogen-bridged dimers, in which the bonding is described as electron-pair bonds

– Group-13 trihalides are potent Lewis acids and react with Lewis bases to form a Lewis acid-base adduct



– In water, the halides of the Group-13 metals hydrolyze to produce the metal hydroxide [M(OH)3]; halides of the heavier metals (In and Tl) are less reactive with water because of their lower charge-to-radius ratio and dissolve to form the hydrated metal ions [M(H2O)6]3+

• All the heavier Group-13 elements react with excess oxygen at elevated temperatures to give the trivalent oxide (M2O3)

– All the oxides dissolve in dilute acid, but aluminum and gallium oxides are amphoteric and also dissolve in concentrated aqueous base to form solutions that contain M(OH)4

– ions



• Aluminum, gallium, and indium react with the other Group-16 elements (chalcogens) to form chalcogenides with the stoichiometry M2Y3; thallium forms only the thallium() chalcogenides with the stoichiometry Tl2Y

• Only aluminum reacts directly with N2 at high temperatures to give AlN; GaN and InN are prepared by other methods

• All the metals, except Tl, react with the heavier Group-15 elements (pnicogens) to form the -V compounds, which are semiconductors

• The heavier Group-13 elements do not react directly with hydrogen; only aluminum and gallium hydrides are known and are prepared indirectly


Complexes of Group-13 Elements

• Boron has a limited tendency to form complexes

• Aluminum, gallium, indium, and thallium form a large number of complexes; the simplest are the hydrated metal ions, M(H2O)6

3+, that are strong Brønsted–Lowry acids

• Group-13 metal ions also form stable complexes with compounds that contain two or more negatively charged groups; stability of such complexes increases as the number of coordinating groups provided by the ligand increases






• The elements of Group 14 show a greater range of chemical behavior than any other family in the periodic table

• Three of the five elements—carbon, tin, and lead—have been known since ancient times


• The natural abundance of the Group-14 elements varies tremendously – Elemental carbon ranks 17th on the list of constituents of

Earth’s crust

– After oxygen, the most abundant element on Earth is silicon, the next member of Group 14; pure silicon is obtained

by the reaction of impure silicon with Cl2 to give SiCl4, followed by reduction with H2; ultrapure silicon and germanium form the basis of the modern electronics industry

– Concentrations of germanium and tin in the Earth’s crust are 1–2 ppm and lead is 13 ppm, which makes lead the

most abundant of the heavy Group-14 elements

Preparation and General Properties of Group-14 Elements


– No concentrated ores of germanium are known, so germanium is recovered from flue dusts obtained by processing the

ores of metals and is used in optical devices

– Tin and lead are soft metals and are too weak for structural applications; tin is used in food packaging, magnets,

and low- melting-point alloys, lead is used in lead-storage batteries



• All the Group-14 elements form compounds in which they lose either the two np and the two ns valence electrons or just the two np valence electrons, giving compounds in the +4 or +2 oxidation state, respectively

• The relative stability of the +2 oxidation state increases smoothly from carbon to lead because covalent bonds decrease in strength with increasing atomic size, and the ionization energies for the heavier elements of the group are higher than expected due to a higher Zeff

• Many carbon compounds contain multiple bonds formed by overlap of singly occupied 2p orbitals on adjacent atoms



• Compounds of silicon, germanium, tin, and lead with the same stoichiometry as those of carbon, tend to have different structures and properties

• The tendency to catenate (to form chains of like atoms) decreases rapidly going down Group 14 because bond energies for both the E–E and E–H bonds decrease with increasing atomic number (where E is any Group-14 element); the thermal stability of catenated compounds decreases from carbon to lead

• Group-14 elements all have ns2np2 valence-electron configurations



• As shown in the following table, there is a large difference between the lightest element, C, and the others in size, ionization energy, and electronegativity





– As in Group 13, the second and third elements (Si and Ge) are similar

– There is a reversal in the trends of some properties, such as ionization energy, between the fourth and fifth elements (Sn and Pb), which can be explained by the presence of filled (n–1)d and (n–2)f subshells, whose electrons are poor at screening the outermost electrons from the higher nuclear charge



• Carbon – The building block of all organic compounds; inorganic

compounds of carbon include metal carbonates

– Chemistry of carbon differs from that of its heavier congeners

– structures of the allotropes of carbon—diamond, graphite, fullerenes, and nanotubes—are distinct, but they all

contain simple electron-pair bonds

– All the carbon tetrahalides (CX4) are known; they are not obtained by the direct reaction of carbon with the

elemental halogens but by indirect methods; their stability decreases as the halogen increases in size because of poor orbital overlap and increased crowding

Reactions and Compounds of Carbon


– Reacts with oxygen to form either CO or CO2, depending on the stoichiometry

– CO can be prepared by dehydrating formic acid with concentrated sulfuric acid; CO reacts with halogens to form the oxohalides (COX2)

– CO2 can be prepared by the reaction of any metal carbonate or bicarbonate salt with strong acid; CO2 reacts with water to form acidic solutions that contain carbonic acid (H2CO3)

– Reaction of carbon with sulfur at high temperatures produces carbon disulfide (CS2)

– Binary compounds of carbon with less electronegative elements are called carbides



• The chemical and physical properties of carbides depend on the identity of the second element, resulting in three general classes

1. Ionic carbides – Produced by the reaction of carbon at high temperatures with

electropositive metals such as those of Groups 1 and 2 and aluminum

– Contain discrete metal cations and carbon anions (C4–, methide or C2

2–, acetylide); identity of the anions depends on the size of the second element

– Reaction of ionic carbides with dilute aqueous acid results in protonation of the anions to give the parent hydrocarbons, CH4 or C2H2



2. Interstitial carbides – Produced by the reaction of carbon with most transition metals at

high temperatures

– Contain covalent metal-carbon interactions, which result in different properties:

a. Good conductors of electricity

b. Have high melting points

c. Among the hardest substances known

– Exhibit a variety of nominal compositions, and they are nonstoichiometric compounds whose carbon content can vary over a wide range



3. Covalent carbides – Formed with elements with an electronegativity similar to that of

carbon

– Extremely hard, high melting, and chemically inert



• Silicon, germanium, tin, and lead in their +4 oxidation states form binary compounds with the same stoichiometry as carbon, but the structures and properties of these compounds are different from those of the carbon analogues

• Silicon is amphoteric; it dissolves in strong aqueous base to produce hydrogen gas and solutions of silicates; the only aqueous acid it reacts with is hydrofluoric acid

• Germanium is amphoteric and is more metallic in its behavior than silicon; tin has an even more metallic character and is amphoteric; shows that metallic behavior increases going down the group

• Lead is the only element in the group that behaves purely like a metal



• All the Group-14 dichlorides are known, but their stability increases as the atomic number of the central atom increases

• The first four elements of Group 14 form tetrahalides (MX4) with all the halogens, but only fluorine is able to oxidize lead to the +4 oxidation state – Tetrahalides of the semimetals silicon and germanium react rapidly

with water to give amphoteric hydroxides – Tetrahalides of tin and lead react with water to give hydrated metal

ions

• The heavier Group-14 elements react with O2 or S8 at elevated temperatures to form the corresponding dioxide or disulfide, respectively; silicon has a tremendous affinity for oxygen because of partial Si–O bonding



• Dioxides of the Group-14 elements become increasingly basic going down the group and their metallic character increases

• Compounds with anions that contain only silicon and oxygen are called silicates – Basic building block of all silicates is the SiO4

4– unit – The number of oxygen atoms shared between silicon atoms

and the way in which the units are linked vary in different silicates

– In aluminosilicates, some of the Si atoms are replaced by Al atoms and have three-dimensional framework structures with large cavities connected by small tunnels



• Silicon and germanium react with nitrogen at high temperature to form nitrides (M3N4) that are strong, hard, and chemically inert

• Silicides of active metals are ionic compounds that contain the Si4–

ion and react with aqueous acid to form silicon hydrides

• Unlike carbon, catenated silicon hydrides become thermodynamically less stable as the chain lengthens and the hydrides become thermodynamically less stable going down the group

• As atomic size increases, multiple bonds between or to the Group-14 elements become weaker



• Only important organic derivatives of lead are compounds such as tetraethyllead because Pb–C bonds are weak

• Compounds that contain Si–C and Si–O bonds are stable and important – High-molecular-mass polymers called silicones contain an

(Si–O–)n backbone with organic groups attached to Si

– Properties of silicones are determined by the chain length, the type of organic group, and the extent of cross-linking

between the chains




22.3 The Elements of Group 15 (the Pnicogens)


• The lightest member of Group 15, nitrogen, is found in nature as the free element

• The heaviest elements have been known for centuries because they are easily isolated from their ores

22.3 The Elements of Group 15 (the Pnicogens)


• The atmosphere contains tons of elemental nitrogen with a purity of 80%, so it is a huge source of nitrogen gas – Distillation of liquefied air yields nitrogen gas that is about

100% pure – Small amounts of very pure nitrogen gas can be obtained from

the thermal decomposition of sodium azide – Earth’s crust is poor in nitrogen

• Phosphorus constitutes about 0.1% of Earth’s crust – More abundant in ores than nitrogen – Always found in combination with oxygen, and large inputs of

energy are required to isolate it



• The other three pnicogens are much less abundant

– Arsenic is found in Earth’s crust at a concentration of 2 ppm, antimony is an order of magnitude less abundant,

and bismuth is rare

– All three elements have a high affinity for the chalcogens and are found as the sulfide ores (M2S3), in combination with sulfides of other heavy elements

– Major source of antimony and bismuth is flue dust obtained by smelting the sulfide ores of the more abundant metals



• In Group 15, there are large differences between the lightest element, N, and its congeners in size, ionization energy, electron affinity, and electronegativity as seen in the following table





• The chemical behavior of the elements are:

– nitrogen and phosphorus behave chemically like nonmetals, arsenic and antimony like semimetals, and bismuth like a metal

– they have ns2np3 valence-electron configurations

– they all form compounds by losing the three np valence electrons to form the +3 oxidation state, or by losing the three np and two ns valence electrons to give the +5 oxidation state, whose stability decreases smoothly from phosphorus to bismuth



– the high electron affinity of the lighter pnicogens enables them to form compounds in the –3 oxidation state, in which three electrons are added to the neutral atom to give a filled np subshell

– nitrogen has a high electron affinity and small size and has the ability to form compounds in nine different oxidation states, including –3, +3, and +5

– neutral covalent compounds of the trivalent pnicogens contain a lone pair of electrons on the central atom and tend to behave like Lewis bases



• Nitrogen – Has four valence orbitals (one 2s and three 2p), so it can

participate in four electron-pair bonds by using sp3 hybrid orbitals

– Nitrogen is smaller than carbon and has less tendency to accommodate more than four nearest neighbors

– Unlike carbon, nitrogen does not form long chains due to repulsive interactions between lone pairs of electrons on adjacent atoms

– Stable compounds with N–N bonds are limited to chains of no more than three N atoms

– Only pnicogen that normally forms multiple bonds with other second-period atoms, using overlap of adjacent np

orbitals

Reactions and Compounds of Nitrogen


– The stable form of elemental nitrogen is N2 with a strong triple bond

– Compounds containing N–N single and NN double bonds are thermodynamically unstable and potentially explosive;

the formation of the NN triple bond is thermodynamically favored

– In contrast to carbon, nitrogen undergoes only two important chemical reactions at room temperature

1. Reacts with metallic lithium to form lithium nitride 2. It is reduced to ammonia by certain microorganisms

– At higher temperatures, N2 reacts with more electropositive elements to give binary nitrides, which

range from covalent to ionic in character



– Binary compounds of nitrogen with oxygen, hydrogen, or other nonmentals are covalent molecular substances

– Few binary molecular compounds of nitrogen are formed by direct reaction of the elements: at elevated

temperatures, N2 reacts with H2 to form ammonia, with O2 to form a mixture of NO and NO2 , and with carbon to form cyanogen (NC–CN), but elemental nitrogen does not react with the halogens or the other chalcogens

– All the binary nitrogen halides (NX3) are known; except for NF3, all are toxic, thermodynamically unstable, and explosive,

and all are prepared by the reaction of the halogen with NH3 rather than N2



– The three oxides of nitrogen (NO, N2O, and NO2) are thermodynamically unstable

– At elevated temperatures, nitrogen reacts with highly electropositive metals to form ionic nitrides, which consist of

ionic lattices formed by Mn+ and N3– ions – With less electropositive metals, nitrogen forms a range of

interstitial nitrides, in which nitrogen occupies holes in a close- packed metallic structure; these substances are hard, high- melting-point materials that have metallic luster and

conductivity – Reacts with semimetals at very high temperatures to produce

covalent nitrides, which are solids with extended covalent network structures and are high melting and chemically inert



– Ammonia (NH3) is one of the few thermodynamically stable binary compounds of nitrogen with a nonmetal

– Forms two other important binary compounds with hydrogen 1. Hydrazoic acid (HN3), a colorless, highly toxic, and explosive

substance

2. Hydrazine (N2H4), also explosive



• The heavier pnicogens form catenated compounds that contain only single bonds, whose stability decreases rapidly going down the group

• Phosphorus forms multiple allotropes: white phosphorus, an electrical insulator, and red phosphorus and black phosphorus, which are semiconductors

• The three heaviest pnicogens—arsenic, antimony, and bismuth—all have a metallic luster, are brittle, and are poor electrical conductors

Reactions and Compounds of the Heavier Pnicogens


• Reactivity of the heavier pnicogens decreases going down the column – Phosphorus is the most reactive, forming binary compounds

with every element in the periodic table except antimony, bismuth, and the noble gases

– Phosphorus reacts rapidly with O2, whereas arsenic burns in pure O2, and antimony and bismuth react with O2 only

when heated – None of the pnicogens reacts with nonoxidizing acids but all

dissolve in oxidizing acids – Only bismuth behaves like a metal



• Heavier pnicogens use energetically accessible 3d, 4d, or 5d orbitals to form dsp3, or d2sp3 hybrid orbitals for bonding; these elements have coordination numbers of 5 or higher

• Phosphorus and arsenic form halides that are covalent molecular species and behave like nonmetal halides, reacting with water to form the corresponding oxoacids

• All the pentahalides are potent Lewis acids

• Bismuth halides have extended lattice structures and dissolve in water to produce hydrated ions

• Except for BiF3, which is an ionic compound, the trihalides are volatile covalent molecules with a lone pair of electrons in the central atom and react rapidly with water



• With energetically accessible d orbitals, phosphorus and arsenic are able to form bonds with second period atoms such as N and O – Very strong P–O single bonds and even stronger PO double

bonds – First four elements in Group 15 react with oxygen to produce

the corresponding oxide in the +3 oxidation state – The two least metallic elements, phosphorus and arsenic, form

very stable oxides with the formula E4O10 in the +5 oxidation state

• Heavier pnicogens form sulfides that range from molecular species with three-dimensional cage structures to layered or ribbon structures



• Reaction of the heavier pnicogens with metals produces substances whose properties vary with the metal content – Metal-rich phosphides (M4P) are hard, high-melting-point,

electrically conductive solids with a metallic luster

– Phosphorus-rich phosphides (MP15) are lower melting and less thermally stable because they contain catenated Pn units

• Many of the organic or organometallic heavier pnicogens that contain from one to five alkyl or aryl groups are known, and their thermal stability decreases from phosphorus to bismuth




22.4 The Elements of Group 16 (the Chalcogens)


22.4 The Elements of Group 16 (the Chalcogens)

• The chalcogens are the first group in the p block that contain no stable metallic elements

– All isotopes of polonium (Po), the only metal in Group 16, are radioactive

– Only one element in the group, tellurium (Te), can be described as a semimetal

– The lightest element of Group 16, oxygen, is found in nature as the free element

– Of the Group-16 elements, only sulfur was known in ancient times; others were not discovered until the late eighteenth and nineteenth centuries



• Oxygen is the most abundant element in Earth’s crust and in the hydrosphere – Can be obtained by the electrolysis of water, the

decomposition of alkali metal or alkaline earth peroxides or superoxides, or the thermal decomposition of simple

inorganic salts

• Sulfur is not very abundant, but it is found as elemental sulfur in rock formations overlying salt domes; sulfur is also recovered from H2S and organosulfur compounds in crude oil and coal, and from metal sulfide ores

• Selenium and tellurium are found as minor contaminants in metal sulfide ores and are recovered as by-products



• Properties – Have ns2np4 electron configurations – Chalcogens are two electrons short of a filled valence shell;

they tend to acquire two additional electrons to form compounds in the –2 oxidation state; and this tendency

is greatest for oxygen, the chalcogen with the highest electronegativity

– Heavier, less electronegative chalcogens can lose either four np electrons or four np and two ns electrons to form compounds in the +4 and +6 oxidation state,

respectively – The lightest member in the group (oxygen) differs greatly from

the others in size, ionization energy, electronegativity, and electron affinity

– Second and third members (sulfur and selenium) have similar properties because of shielding effects; only polonium is metallic as seen in the following table




Reactions and Compounds of Oxygen

• The lightest Group-16 member has the greatest tendency to form multiple bonds, so elemental oxygen is found in nature as a diatomic gas that contains a net double bond, OO

• Electrostatic repulsion between lone pairs of electrons on adjacent atoms prevents oxygen from forming stable catenated compounds – All compounds that contain O–O bonds are explosive – Ozone, peroxides, and superoxides are all dangerous in pure

form

• Despite the strength of the OO bond, O2 is extremely reactive, reacting directly with nearly all other elements except the noble gases; properties of O2 and related species are listed in the following table





• Chemistry of oxygen is restricted to negative oxidation states because of its high electronegativity – Oxygen does not form compounds in the +4 or +6 oxidation

state – Second only to fluorine in its ability to stabilize high oxidation

states of metals in both ionic and covalent compounds – Because oxygen is so electronegative, the O–H bond is highly

polar, creating a large bond dipole moment that makes hydrogen bonding more important for compounds of oxygen than for compounds of the other chalcogens

– Metal oxides are basic, nonmetal oxides are acidic, and oxides of elements that lie on or near the diagonal band of emimetals are amphoteric; nonmetal oxides are covalent compounds where the bonds between oxygen and the nonmetal are polarized and in water form oxoacids


Reactions and Compounds of the Heavier Chalcogens

• The tendency to catenate decreases going down the column – Sulfur and selenium form an extensive series of catenated species – There is only one stable allotrope of tellurium – Polonium shows no tendency to form catenated compounds

• There is a striking decrease in structural complexity from sulfur to polonium and a decrease in the strength of single bonds and an increase in metallic character going down the group

• Reactivity of elements in Group 16 decreases from lightest to heaviest

• Fluorine reacts directly with the chalcogens to produce hexafluorides (YF6); four additional stable fluorides of sulfur are known, but only two fluorides of selenium and three of tellurium are known



• Direct reaction of the heavier chalcogens with oxygen at elevated temperatures gives the dioxides (YO2), which exhibit a dramatic range of structures and properties – Going down the column, the dioxides become increasingly

metallic in character and the coordination number of the chalcogen increases

– Dioxides of sulfur, selenium, and tellurium react with water to produce the weak, diprotic oxoacids (H2YO3)

– Sulfuric and selenic acids are strong acids, but telluric acid is different because tellurium is larger than sulfur and

selenium and it forms weak bonds to oxygen – The most stable structure for telluric acid is Te(OH)6, with six

Te–OH single bonds rather than TeO double bonds – Sulfuric, selenic, and telluric acids are oxidants, and the

stability of the highest oxidation state decreases with increasing atomic number



• Sulfur and selenium react with carbon to form an extensive series of compounds that are structurally similar to their oxygen analogues

• Chalcogens react directly with nearly all metals to form compounds with a wide range of stoichiometries and a variety of structures – Metal chalcogenides can contain either the simple

chalcogenide ion (Y2–) or polychalcogenide ions (Yn2–)

• Ionic chalcogenides react with aqueous acid to produce binary hydrides – Strength of the Y–H bond decreases with increasing atomic

radius, so the stability of the binary hydrides decreases rapidly going down the column



22.5 The Elements of Group 17 (the Halogens)


22.5 The Elements of Group 17 (the Halogens)

• Halogens are highly reactive, but none are found in nature as the free element

• None of the halogens was recognized as an element until the nineteenth century


• All the halogens except iodine are found in nature as salts of the halide ions (X–), so the methods used for preparing F2, Cl2, and Br2 all involve oxidizing the halide

• Fluorine is a very powerful oxidant – Reaction of CaF2 with concentrated sulfuric acid produces

gaseous hydrogen fluoride

– Fluorine is produced by the electrolysis of a 1:1 mixture of HF and K+HF2

–

– Both F2 and HF are highly corrosive



• Chlorine is less abundant than fluorine, but elemental chlorine is produced on an enormous scale – There are large subterranean deposits of rock salt around

the world; seawater consists of about 2% NaCl by mass, and inland salt lakes are richer sources

– Chlorine is prepared by the chlor-alkali process

• Bromine is much less abundant than fluorine or chlorine but is easily recovered from seawater; salt lakes and underground brines are richer sources



• Iodine is the least abundant of the nonradioactive halogens and is a rare element

– Has low electronegativity and occurs in nature in an oxidized form

– Most commercially important deposits of iodine are iodate salts, so the production of iodine from these deposits requires reduction rather than oxidation, which occurs in two steps 1. Reduction of iodate to iodide with sodium hydrogen sulfite

2. Reaction of iodide with additional iodate



• The heaviest halogen, astatine (At) is continuously produced by natural radioactive decay

– All its isotopes are highly radioactive

– Most stable isotope has a half-life of 8 hours

– Least abundant naturally occurring element on Earth



• Properties – Halogens all have ns2np5 electron configurations, so their

chemistry is dominated by a tendency to accept an additional electron to form the closed-shell ion (X–)

– Only the electron affinity and the bond dissociation energy of fluorine differ significantly from the expected periodic trends as shown in the following table





– Fluorine has a small atomic volume, so repulsive electron-

electron interactions are important in the fluoride ion, making the electron affinity of fluorine lower than that of chlorine

– Repulsions between electron pairs on adjacent atoms are responsible for the low F–F bond dissociation energy



– Fluorine is the most electronegative element in the periodic

table, so it forms compounds in only the –1 oxidation state

– All the halogens except astatine have electronegativities higher than 2.5, making their chemistry that of nonmetals

– Halogens all have high ionization energies, but the energy required to remove electrons decreases going down the column

– Heavier halogens form compounds in positive oxidation states (+1, +3, +5, and +7), derived by the formal loss of ns and np electrons



• Fluorine is the most reactive element in the periodic table, forming compounds with every other element except helium, neon, and argon

– Reactions of fluorine with most other elements range from vigorous to explosive; only O2, N2, and Kr react slowly

– There are three reasons for the high reactivity of fluorine 1. Fluorine is so electronegative, it can remove or share the

valence electrons of any other element

2. Because of its small size, fluorine tends to form very strong bonds to other elements, making its compounds thermodynamically stable

Reactions and Compounds of the Halogens


– With highly electropositive elements, fluorine forms ionic compounds that contain the closed-shell F– ion—with less electropositive elements (or with metals in very high oxidation states), fluorine forms covalent compounds that contain terminal F atoms

– Because of its high electronegativity and 2s22p5 valence-electron configuration, fluorine participates in only one electron-pair bond; only a strong Lewis acid can share a lone pair of electrons with a fluorine atom


3. The F–F bond is weak due to repulsion between lone pairs of electrons on adjacent atoms, reducing both the thermodynamic and kinetic barriers to reaction


• The halogens (X2) react with metals (M) according to the general equation

M(s,l) + nX2(s,I,g) MXn(s,l)

• For elements that exhibit multiple oxidation states, fluorine tends to produce the highest possible oxidation state and iodine the lowest



• Metal halides in the +1 or +2 oxidation state are ionic halides, which have high melting points and are soluble in water; as the oxidation state of the metal increases, so does the covalent character of the halide due to polarization of the M–X bond

– Fluoride, with its high electronegativity, is the least polarizable, and iodide, with the lowest electronegativity, is the most polarizable of the halogens

– Halides of small trivalent metal ions tend to be covalent, and halides of larger trivalent metals are ionic



• All the halogens react vigorously with hydrogen to give

the hydrogen halides (HX) – Because the H–F bond in HF is highly polarized, liquid HF is

extensively hydrogen bonded, has a high boiling point and high dielectric constant, and is a polar solvent

• Except for fluorine, all the halogens react with water in a disproportionation reaction:

X2(g,l,s) + H2O(l) H+(aq) + X–(aq) + HOX(aq) (X = Cl, Br, )



• The most stable oxoacids are the perhalic acids, which contain the halogens in their highest oxidation state (+7)

– Acid strengths of the oxoacids of the halogens increase with increasing oxidation state, but their stability and acid strength decrease going down the group

– All the oxoacids are strong oxidants, but some react rather slowly at low temperatures

– Mixtures of the halogen oxoacids or oxoanions with organic compounds are explosive if heated or agitated

– Oxoacids and oxoanions of the halogens should never be allowed to come into contact with organic compounds because of the danger of explosions



• The halogens react with one another to produce interhalogen compounds

– In all cases, the heavier halogen, with the lower electronegativity, is the central atom

– The maximum oxidation state and the number of terminal halogens increase smoothly as the ionization energy of the central halogen decreases and the electronegativity of the terminal halogen increases

– Interhalogen compounds are very powerful Lewis acids with a strong tendency to react with halide ions to give complexes with higher coordination numbers



• The halogens react with one another to produce

interhalogen compounds

– All the Group-17 elements except fluorine form compounds in odd oxidation states (–1, +1, +3, +5, +7)

– Interhalogen compounds are potent oxidants and strong fluorinating agents; contact with water or organic materials can result in an explosion




22.6 The Elements of Group 18 (the Noble Gases)


22.6 The Elements of Group 18 (the Noble Gases)

• Noble gases were all isolated for the first time within a period of only 5 years at the end of the nineteenth century

• Their existence was not suspected until the eighteenth century, when work on the composition of air suggested that it contained small amounts of gases in addition to oxygen, nitrogen, carbon dioxide, and water vapor

• Elements of Group 18 are helium, neon, argon, krypton, xenon, and radon


• Fractional distillation of liquid air is the only source of all the noble gases except helium

• Helium is the second most abundant element in the universe; natural gas contains high concentrations of helium, and it is the only practical terrestrial source

• Elements of Group 18 all have closed-shell valence-electron configurations, ns2 np6, except for He, which is 1s2

• These elements have high ionization energies that decrease smoothly going down the column, as seen in the following table





• From their electron affinities, the noble gases are unlikely to form compounds in negative oxidation states – A potent oxidant is needed to oxidize noble gases and form

compounds in positive oxidation states

• Xenon and krypton should form covalent compounds with F, O, and Cl, in which they have even formal oxidation states (+2, +4, +6, and possibly +8)



• Noble gases form stable clathrates, solid compounds in which a gas—the guest—occupies holes in a lattice formed by a less volatile, chemically dissimilar substance—the host

• Ionization energies of helium, neon, and argon are high, so no stable compounds of these elements are known

• Ionization energies of krypton and xenon are lower but still high, and only highly electronegative elements (F, O, and Cl) can form stable compounds with xenon and krypton without being oxidized themselves

• Xenon reacts directly with only two elements, F2 and Cl2

Reactions and Compounds of the Noble Gases


• Halides of the noble gases are powerful oxidants and fluorinating agents, so they decompose rapidly upon contact with trace amounts of water and react violently with organic compounds or other reductants

• Xenon fluorides are Lewis acids and react with fluoride ion—the only Lewis base that is not oxidized immediately upon contact—to form anionic complexes

• Xenon has a high affinity for oxygen because of bonding between O and Xe, so xenon forms an extensive series of oxides and oxoanion salts

• Xenon forms stable compounds with fluorine and oxygen that contain xenon in even oxidation states up to +8

Reactions and Compounds of the Noble Gases


23 The d-Block Elements


CHAPTER OBJECTIVES

• To know periodic trends in the d-block elements

• To be able to use periodic trends to understand the chemistry of the transition metals

• To understand how metals are extracted from their ores

• To know the most common structures observed for metal complexes

• To be able to predict the relative stabilities of metal complexes

• To understand how crystal field theory can explain the electronic structures and colors of metal complexes

• To become familiar with some of the roles of transition-metal complexes in biological systems


The d-Block Elements

• The d-block elements are also called transition metals

• All d-block elements are metals, so these elements exhibit significant horizontal and vertical similarities in chemistry, and all have a common set of characteristic properties due to partially filled d subshells

• Alloys and compounds of d-block elements are important components of the materials the modern world depends on for its continuing technological development; most of the first-row transition metals are essential for life



23.1 General Trends among the Transition Metals


Electronic Structure and Reactivity of the Transition Metals

• Valence-electron configurations of the first-row transition metals are given in the following table

– Going across the row from left to right, electrons are added to the 3d subshell to neutralize the increase in the positive charge of the nucleus as the atomic number increases

– The 3d subshell is filled based on the aufbau principle and Hund’s rule with two important exceptions:

1. Chromium has a 4s13d5 electron configuration rather than a 4s23d4 configuration

2. Copper is 4s13d10 rather than 4s23d 9

– Anomalies due to the extra stability associated with half-filled subshells



• In the second-row transition metals, electron-electron repulsions within the 4d subshell cause additional irregularities in electron configurations that are not easily predicted

• Further complications occur among the third-row transition metals, in which the 4f, 5d, and 6s orbitals are close in energy

• From this point to element 71, added electrons enter the 4f subshell, giving rise to the 14 elements known as the lanthanides

• After the 4f subshell is filled, the 5d subshell is populated, producing the third row of the transition metals; the seventh period comes next, where the actinides have three subshells (7s, 6d, and 5f) that are so similar in energy that their electron configurations are more unpredictable



• Reactivity– The size of neutral atoms of the d-block elements gradually

decreases going from left to right across a row, due to an increase in the effective nuclear charge (Zeff) with increasing atomic number

– The atomic radius increases going down a column– Because of the lanthanide contraction, the increase in size

between the 3d and 4d metals is much greater than between the 4d and 5d metals

– Effective nuclear charge experienced by valence electrons in the d-elements does not change as the nuclear charge increases across a row

– Ionization energies of these elements increase very slowly going across a given row



– As seen in the following table, going from the top left to the bottom right corner of the d block,

1. electronegativities increase

2. densities and electrical and thermal conductivities increase

3. enthalpies of hydration of the metal cations decrease

– Transition metals become steadily less reactive and more “noble” in character going from left to right across a row


Trends in Transition Metal Oxidation States

• Similarity in ionization energies and the small increase in successive ionization energies lead to the formation of metal ions with the same charge for many of the transition metals, which results in extensive horizontal similarities in chemistry that are most noticeable for the first-row transition metals and for the lanthanides and actinides

– All first-row transition metals except Sc form stable compounds that contain the 2+ ion

– Due to the small difference between the second and third ionization energies for these elements, all except Zn also form stable compounds that contain the 3+ ion



• Oxidation states– The small increase in successive ionization energies causes the

transition metals to exhibit multiple oxidation states, separated by a single electron

– Because of the slow increase in ionization potentials going across a row, high oxidation states become progressively less stable for the elements on the right side of the d block

– Occurrence of multiple oxidation states separated by a single electron causes the compounds of the transition metals to be paramagnetic, with one to five unpaired electrons



• The electronegativities of the first-row transition metals increase smoothly from Sc to Cu

• The standard reduction potential Eº for the reaction M2+

(aq) + 2e– Mº(s) becomes less negative from Ti to Cu

• Exceptions to overall trends attributable to the stability associated with filled and half-filled subshells

• The transition metals form cations by the initial loss of the ns electrons of the metal, even though the ns orbital is lower in energy than the (n–1)d subshell in the neutral atom; therefore, all transition-metal cations possess dn valence-electron configurations for the 2+ ions of the first-row transition metals, as seen in the following table





• The most common oxidation states of the first-row transition metals are shown in the following table; the second- and third-row transition metals behave similarly but with three important differences:



1. The maximum oxidation states observed for the second- and third-row transition metals in Groups 3–8 increase from +3 for Y and La to +8 for Ru and Os, corresponding to the formal loss of all ns and (n–1)d valence electrons; going farther to the right, the maximum oxidation state decreases, reaching +2 for the elements of Group 12, which corresponds to a filled (n–1)d subshell

2. Within a group, higher oxidation states become more stable going down a group

3. Cations of the second- and third-row transition metals in lower oxidation states (+2 and +3) are more easily oxidized than the corresponding ions of the first-row transition metals



• Binary transition-metal complexes such as the oxides and sulfides are written with idealized stoichiometries, but these compounds are cation deficient and never contain a 1:1 cation:anion ratio

• Acid-base character of transition-metal oxides depend strongly on the oxidation state of the metal and its ionic radius

– Oxides of metals in lower oxidation states have ionic character and tend to be basic

– Oxides of metals in higher oxidation states are more covalent and tend to be acidic, dissolving in strong base to form oxoanions



23.2 A Brief Survey of Transition-Metal

Chemistry


23.2 A Brief Survey of Transition-Metal Chemistry

• Beginning with Group 3 and continuing to Group 12, the chemistry of the transition metals will be studied

• It will be seen that the two heaviest members of each group exhibit substantial similarities in chemical behavior and are quite different from the lightest member


• Group 3 (Sc, Y, La, Ac)– Observed trends in the properties of the Group-3 elements

similar to those of Groups 1 and 2 (see table)

Groups 3, 4, and 5


– Due to their ns2 (n–1)d1 valence-electron configurations, the chemistry of all four elements is dominated by the +3 oxidation state formed by the loss of all three valence electrons

– Elements are highly electropositive metals and powerful reductants, with La (and Ac) being the most reactive

– React with water to produce the metal hydroxide and hydrogen gas

Groups 3, 4, and 5


– All dissolve readily in acidic solutions to produce hydrogen gas and a solution of the hydrated metal ion, M3+

(aq)

– React with nonmetals to form compounds that are ionic in character

– All the Group-3 elements react with air to form an oxide coating, and all burn in oxygen to form the sesquioxides, M2O3, which react with water or CO2 to form the corresponding hydroxides or carbonates, respectively

– Commercial uses of the Group-3 metals are limited

Groups 3, 4, and 5


• Group 4 (Ti, Zr, Hf)– Have a high affinity for oxygen so all three metals

occur naturally as oxide ores that contain the metal in the +4 oxidation state resulting from the loss of all four ns2(n–1)d2 valence electrons; isolated by initial conversion to the tetrachlorides followed by reduction of the tetrachlorides with an active metal

– Group-4 elements have important applications– Become denser, higher melting, and more

electropositive going down the column

Groups 3, 4, and 5


– +4 oxidation state is the most important for all three metals; only titanium has a chemistry in the +2 and +3 oxidation states

Groups 3, 4, and 5


– Reaction of the Group-4 metals with excess halogen forms the corresponding tetrahalides, MX4

– Titanium, the lightest element in the group also forms dihalides and trihalides; covalent character of the titanium halides increases as the oxidation state of the metal increases because of increasing polarization of the anions by the cation as its charge-to-radius ratio increases

– All three metals react with excess oxygen or the heavier chalcogens (Y) to form the corresponding dioxides, MO2, and dichalcogenides, MY2

– React with hydrogen, nitrogen, carbon, and boron to form hydrides, nitrides, carbides, and borides

Groups 3, 4, and 5


• Group 5 (V, Nb, Ta)– Found in nature as oxide ores that contain the metals in

their highest oxidation state (+5)– Trends in properties of the Group-5 metals are similar to

those of Group 4

Groups 3, 4, and 5


– Only vanadium, the lightest element, has any tendency to form compounds in oxidation states lower than +5

– All three metals react with excess oxygen to produce the corresponding oxides in the +5 oxidation state, M2O5, in which polarization of the oxide ions by the high-oxidation-state metal is so extensive that the compounds are covalent in character

Groups 3, 4, and 5


– React with the heavier chalcogens to form a complex set of binary chalcogenides; the most important are the dichalcogenides, MY2

– Form binary nitrides, carbides, borides, and hydrides whose stoichiometries and properties are similar to those of corresponding Group-4 compounds

Groups 3, 4, and 5


• Group 6 (Cr, Mo, W)– Encounter a metal (Mo) that occurs naturally as a sulfide ore

rather than as an oxide– Molybdenum is the only second- or third-row transition

element that is essential for humans– Group 6 metals are less electropositive than those of the

three preceding groups, and the two heaviest metals are the same size because of the lanthanide contraction

– All three elements have a total of six valence electrons, resulting in a maximum oxidation state of +6; compounds in the +6 oxidation state are highly covalent

Groups 6 and 7


– The lightest element, Cr, exhibits variable oxidation states; for Mo and W, the highest oxidation state (+6) is the most important

– Group-6 halides become more covalent as the oxidation state of the metal increases, their volatility increases, and their melting points decrease

– As the oxidizing strength of the halogen decreases, the maximum oxidation state of the metal decreases

– All three metals form hexafluorides– React with oxygen to form the covalent trioxides, which are

acidic, dissolving in base to form the corresponding oxoanions MO4

2–

Groups 6 and 7


• Group 6 (Cr, Mo, W)– The sesquioxide of the lightest element in the group is

amphoteric– At low pH, molybdate and tungstate form a series of

polymeric anions called isopolymetallates– Reaction of molybdenum or tungsten with heavier

chalcogens gives binary chalcogenide phases, most of which are nonstoichiometric and electrically conducting

– Elements of Group 6 form binary nitrides, carbides, and borides whose stoichiometries and properties are similar to those of the preceding groups

Groups 6 and 7


• Group 7 (Mn, Tc, Re)– All three Group-7 elements have seven valence electrons

and can form compounds in the +7 oxidation state; the lightest element (Mn) exhibits multiple oxidation states, has a low electronegativity, and is unreactive

– Reaction with less oxidizing halogens produces metals in lower oxidation states

– Tc and Re have similar size and electronegativity; they form high-valent oxides, called heptoxides, and form disulfides and diselenides with layered structures

– Group-7 metals form binary nitrides, carbides, and borides that are stable at high temperatures and exhibit metallic properties

Groups 6 and 7


Groups 6 and 7


• Elements of these three groups exhibit many horizontal similarities in their chemistry, in addition to the similarities within each column

• Horizontal similarities are due to the fact that the ionization potentials of the elements have become so large that the oxidation state corresponding to the formal loss of all valence electrons is encountered only rarely (Group 8) or not at all (Groups 9 and 10)

• Chemistry of all three groups is dominated by intermediate oxidation states, especially +2 and +3 for the first-row metals (Fe, Co, and Ni)

• Heavier elements of these three groups are called precious metals because they are rare in nature and are chemically inert

Groups 8, 9, and 10


• Group 8 (Fe, Ru, Os) – Chemistry of Group 8 is dominated by iron, whose high

abundance in Earth’s crust is due to the extremely high stability of its nucleus

– Ruthenium and osmium are extremely rare elements

• Group 9 (Co, Rh, Ir) – Cobalt is one of the least abundant of the first-row transition

metals

– Heavier elements of Group 9 are rare and are found in combination with the heavier elements of Groups 8 and 10 in

Ni-Cu-S ores

Groups 8, 9, and 10


• Group 10 (Ni, Pd, Pt) – Nickel silicates are easily processed

– Palladium and platinum are rare but are more abundant than the heavier elements of Groups 8 and 9

• Trends in Groups 8, 9, and 10 – Properties of the elements of Groups 8–10 are summarized in

the following table

Groups 8, 9, and 10


Groups 8, 9, and 10


– Similarities in size and electronegativity between the two

heaviest members of each group result in similarities in chemistry

– No longer a clear correlation between the valence-electron configuration and the preferred oxidation state

Groups 8, 9, and 10


– Most important oxidation states are +2 and +3 for Group 8, +3 and +1 for Group 9, and +2 and +4 for Group 10

– Higher oxidation states become less stable going across the d-block elements and more stable going down a group

1. Fe and Co form trifluorides, but Ni forms only the difluoride

2. Ru and Os form a series of fluorides

3. Hexafluorides of Rh and Ir are powerful oxidants

4. Pt is the only element in Group 10 that forms a hexafluoride

– Similar trends are observed among the oxides

Groups 8, 9, and 10


– The tendency of the metals to form the higher oxides decreases rapidly going farther across the d block

– Reaction of metals in Groups 8, 9, and 10 with the heavier chalcogens is complex

1. Oxidation state of Fe, Ru, Os, Co, and Ni in their disulfides is +2 because of the disulfide ion, S2

2–

2. Disulfides of Rh, Ir, Pd, and Pt contain the metal in the +4 oxidation state together with isolated sulfide ions, S2–

3. Combination of highly charged cations and easily polarized anions results in substances that are not simply ionic but have significant covalent character

– Groups 8–10 metals form a range of binary nitrides, carbides, and borides

Groups 8, 9, and 10


• Group 11 (Cu, Ag, Au) – Coinage metals—copper, silver, and gold—occur naturally and

were probably the first metals used by ancient humans; deposits of gold and copper are widespread and numerous, while deposits of silver are less common

– Properties of the coinage metals are listed in the following table

Groups 11 and 12


Groups 11 and 12


1. Electronegativity of gold is close to that of the nonmetals sulfur and iodine, so the chemistry of gold is unusual for a metal

2. Have the highest electrical and thermal conductivities of all the metals and also the most ductile and malleable

3. Have a ns1(n–1)d10 valence-electron configuration 4. Chemistry dominated by the +1 oxidation state due to loss of

the single ns electron 5. Higher oxidation states are also known because of the low

values of the second and third ionization energies 6. All three elements have significant electron affinities due to the

half-filled ns orbital in the neutral atoms

– All the Group-11 elements are unreactive, and their reactivity decreases from Cu to Au

Groups 11 and 12


– Copper reacts with O2 at high temperatures to produce Cu2O and reacts with sulfur to form Cu2S

– Neither silver nor gold reacts directly with oxygen

– Silver reacts with sulfur compounds to form Ag2S

– Gold is the only metal that does not react with sulfur, nitrogen, carbon, or boron

– All the coinage metals react with oxidizing acids, and all three metals dissolve in basic cyanide solutions in the presence of oxygen to form stable [M(CN)2]– ions

– Known: all the monohalides except CuF and AuF, all the copper () halides except the iodide, the dihalide of silver, and all the gold trihalides except the triiodide

– No binary nitrides, borides, or carbides are known

Groups 11 and 12


• Group 12 (Zn, Cd, Hg) – Are similar in abundance to those of Group 11 and are always

found in combination with sulfur

– Zinc and cadmium are chemically similar, so zinc ores contain cadmium

– All three metals are commercially important

– None of the elements has a partially filled (n–1)d subshell, so they are not strictly “transition metals”

– Much of their chemistry is similar to that of the elements that immediately precede them in the d block

– Properties of Group-12 metals are shown in the following table

Groups 11 and 12


Groups 11 and 12


– More electropositive than the elements of Group 11 and have less “noble” character

– Have lower melting and boiling points than the preceding transition metals

– Zn and Cd are similar to each other but are very different from the heaviest element (Hg)

– Zn and Cd are active metals and mercury is not—mercury is the only metal that is liquid at room temperature and can dissolve metals by forming amalgams

– All three elements have ns2(n–1)d10 valence-electron configurations and the +2 oxidation state, corresponding to the loss of the two ns electrons

Groups 11 and 12


– Mercury forms a series of compounds in the +1 oxidation state that contains the diatomic mercurous ion, Hg2

2+

– All the possible dihalides, MX2, are known and range from ionic to highly covalent

– Zinc and cadmium react with oxygen to form amphoteric MO, and mercury forms HgO within a narrow temperature range

– Zinc and cadmium dissolve in mineral acids, and mercury dissolves only in oxidizing acids

– All three metals react with sulfur and the other chalcogens to form the binary chalcogenides, and mercury has a high affinity for sulfur ligands

Groups 11 and 12



23.3 Metallurgy


• Very few of the transition metals are found in nature as the free metals; all metallic elements must be isolated from metal oxide or metal sulfide ores

• Metallurgy is the set of processes by which metals are extracted from their ores and converted to more useful forms

• Metallurgy consists of three general steps: 1. Mining the ore 2. Separating and concentrating the metal or the metal-

containing compound 3. Reducing to the metal

23.3 Metallurgy


• After an ore is mined, the first step in processing is to crush it, because the rate of chemical reactions increases with an increase in surface area

• Three general strategies are used to separate and concentrate the compound(s) of interest: 1. Settling and flotation—based on differences in density

between the desired compound and impurities

2. Pyrometallurgy—uses chemical reductions at high temperatures

3. Hydrometallurgy—employs chemical or electrochemical reduction of an aqueous solution of the metal

23.3 Metallurgy


• In pyrometallurgy, an ore is heated with a reductant in order to obtain the metal

• A reductant must be used that forms stable compounds with the metal of interest

• Pyrometallurgy is used in the iron and steel industries

Pyrometallurgy


• The most selective methods for separating metals

from their ores are based on the formation of metal

complexes

• In hydrometallurgy, metals are separated via the

formation of metal complexes by using chemical or

electrochemical reduction of an aqueous solution

Hydrometallurgy



23.4 Coordination Compounds



• One of the most important properties of metallic elements is their ability to act as Lewis acids that form complexes with a variety of Lewis bases

• Metal complex—consists of a central metal atom or ion that is bonded to one or more ligands; metal complexes can be neutral, positively charged, or negatively charged

• Ligands—are ions or molecules that contain one or more pairs of electrons that can be shared with the metal

• Electrically charged metal complexes are called complex ions; a coordination compound contains one or more metal complexes



• Coordination compounds are important for three reasons: 1. Most of the elements in the periodic table are metals, and

almost all metals form complexes 2. Many industrial catalysts are metal complexes, and these

catalysts are important as a way to control reactivity 3. Transition-metal complexes are essential in biochemistry

a. Hemoglobin, an iron complex that transports oxygen in blood b. Cytochromes, iron complexes that transfer electrons in cells c. Complexes that are components of enzymes, the catalysts for

all biological reactions


History of Coordination Compounds

• Coordination compounds have been known and used since ancient times, but their chemical nature was unclear

• Modern theory of coordination chemistry is based on the work of Werner, who studied the properties of several series of metal halide complexes with ammonia

• Data led Werner to postulate that metal ions have two different kinds of valence: 1. A primary valence (oxidation state) that corresponds to the

positive charge on the metal ion 2. A secondary valence (coordination number) that is the total

number of ligands bound to the metal ion


Structures of Metal Complexes

• Coordination numbers of metal ions in metal complexes can range from 2 to 9

• The differences in energy between different arrangements of ligands are greatest for complexes with low coordination numbers and decrease as the coordination number increases

• Only one or two structures are possible for complexes with low coordination numbers, and several different energetically equivalent structures are possible for complexes with high coordination numbers (n > 6)



• Coordination number 2 – Rare for most metals, but is common for the d10 metal ions,

especially Cu+, Ag+, Au+, and Hg2+

– Based on VSEPR, these complexes have the linear L–M–L structure

• Coordination number 3 – Encountered with d10 metal ions such as Cu+ and Hg2+

– Based on VSEPR, 3-coordinate complexes have the trigonal planar structure



• Coordination number 4 – Two common structures observed for 4-coordinate metal

complexes: tetrahedral and square planar

1. Tetrahedral structure is observed for all 4-coordinate complexes of nontransition metals and d10 ions; also found for 4-coordinate complexes of the first-row transition metals, especially those with halide ligands

2. Square planar structures are observed for 4-coordinate complexes of second- and third-row transition metals with d8

electron configurations, such as Rh+ and Pd2+, and are also encountered in some complexes of Ni2+ and Cu2+



• Coordination number 5 – This coordination number is less common than 4 and 6, but is

found in two different structures: trigonal bipyramidal and square pyramidal

– Many 5-coordinate complexes have distorted structures that lie somewhere between the two extremes

• Coordination number 6 – The most common – The six ligands are at the vertices of an octahedron or a

distorted octahedron – The only other 6-coordinate structure is the trigonal prism,

which is uncommon in simple metal complexes



• Coordination number 7

– Uncommon and is generally encountered for only large metals (such as the second- and third-row transition metals, lanthanides, and actinides)

– Three different structures are known, two of which are derived from an octahedron or a trigonal prism by adding a ligand to one face of the polyhedron to give a “capped” octahedron or trigonal prism; most common is the pentagonal bipyramid



• Coordination number 8 – Common for larger metal ions – The simplest structure is the cube, which is rare because it

does not minimize interligand repulsive interactions – Common structures are the square antiprism and the

dodecahedron, both of which can be generated from the cube

• Coordination number 9 – Found for larger metal ions – Most common structure is the tricapped trigonal prism


Stability of Metal Complexes

• The thermodynamic stability of a metal complex depends on the properties of the ligand and the metal ion, and on the type of bonding

• The metal-ligand interaction is an example of a Lewis acid-base interaction

• Lewis bases can be divided into two categories: 1. Hard bases—contain small, relatively nonpolarizable donor

atoms (such as N, O, and F) 2. Soft bases—contain larger, relatively polarizable donor atoms

(such as P, S, and Cl)



• Metal ions with the highest affinities for hard bases are hard acids, and metal ions with the highest affinity for soft bases are soft acids – Hard acids are cations of electropositive metals, are relatively

nonpolarizable, and have higher charge-to-radius ratios – Soft acids are cations of less electropositive metals, have

lower charge-to-radius ratios, and are more polarizable

• Can predict the relative stabilities of complexes formed by the d-block metals with a remarkable degree of accuracy by using a simple rule: Hard acids prefer to bind to hard bases, and soft acids prefer to bind to soft bases



• The interaction between hard acids and hard bases is electrostatic in nature, so the stability of complexes involving hard acids and hard bases increases as the positive charge on the metal ion increases and as its radius decreases

• The stability of complexes of divalent first-row transition metals with a given ligand varies inversely with the radius of the metal ion

• Because a hard metal interacts with a base in the same way as a proton—by binding to a lone pair of electrons on the base—the stability of complexes of hard acids with hard bases increases as the ligand becomes more basic



• The interaction between “soft” metals (such as the second- and third-row transition metals and Cu+) and “soft” bases is covalent in nature – Most soft-metal ions have a filled or nearly filled d subshell,

which suggests that metal-to-ligand bonding is important – Complexes of soft metals with soft bases are much more

stable than would be predicted based on electrostatic arguments

• The hard acid-hard base/soft acid-soft base concept helps to explain why metals are found in nature in different kinds of ore—due to an increase in the “soft” character of the metals going across the first row of the transition metals from left to right



• Ligands 1. Monodentate—they are attached to the metal via only a

single atom 2. Bidentate—they are attached to the metal at two sites 3. Tridentate—they are attached to the metal at three sites 4. Polydentate—they are attached to the metal at several sites

• When a bidentate ligand binds to a metal, a five-membered ring called a chelate ring is formed

• A polydentate ligand is a chelating agent, and complexes that contain polydentate ligands are called chelate complexes



• Metal complexes of polydentate ligands are more stable than the corresponding complexes of chemically similar monodentate ligands; observation is called the chelate effect

• The stability of a chelate complex depends on the size of the chelate rings – For ligands with a flexible organic backbone, complexes that contain

five-membered chelate rings and that have no strain are more stable than complexes with six-membered chelate rings, which are more stable

than complexes with four- or seven-membered rings


Isomers of Metal Complexes

• The existence of coordination compounds with the same formula but different arrangements of the ligands is important in the development of coordination chemistry – Two or more compounds that have the same formula but

different arrangements of the atom are called isomers – Isomers have different physical and chemical properties, and it

is important to know which isomer you are dealing with if more than one isomer is possible

– Coordination compounds exhibit the same types of isomers as organic compounds, as well as several kinds of unique isomers



• Structural isomers – Isomers that contain the same number of atoms of each kind

but differ in which atoms are bonded to one another are called structural isomers

– A trivial kind of isomerism consists of two compounds that have the same empirical formula but differ in the

number of formula units present in the molecular formula

• Geometrical isomers – Differ only in the arrangement of ligands around the metal ion – Metal complexes that differ only in which ligands are adjacent

to one another (cis) or directly across from one another (trans) in the coordination sphere of the metal are called geometrical isomers



• Geometrical isomers are most important for square planar and octahedral complexes 1. Square planar complexes

– Because all vertices of a square are equivalent, it does not matter which vertex is occupied by the ligand B in a square planar MA3B complex; only a single geometrical isomer is possible

– For an MA2B2 complex, there are two possible isomers: either the A ligands can be adjacent to one another (cis), in which case the B ligands must also be cis, or the A ligands can be across from one another (trans), in which case the B ligands must also be trans; cis and trans structures are different arrangements in space

– Square-planar complexes that contain symmetrical bidentate ligands have only one possible structure



2. Octahedral complexes – Only one structure is possible for octahedral complexes in

which only one ligand is different from the other five (MA5B) since all six vertices of an octahedron are equivalent

– If two ligands in an octahedral complex are different from the other four (MA4B2), two isomers are possible; the two B ligands can be cis or trans

– Replacing another A ligand by B gives an MA3B3 complex for which there are two isomers: fac and mer

1. Fac—the three ligands of each kind occupy opposite triangular faces of the octahedron

2. Mer—the three ligands of each kind lie on the meridian



23.5 Crystal Field Theory


23.5 Crystal Field Theory

• Crystal field theory (CFT) is a bonding model that explains many important properties of transition-metal complexes, including their colors, magnetism, structures, stability, and reactivity that cannot be explained using valence bond theory

• Central assumption of CFT is that metal-ligand interactions are purely electrostatic in nature

• In CFT, complex formation is assumed to be due to electrostatic interactions between a central metal ion and a set of negatively charged ligands or ligand dipoles arranged around the metal ion


d-Orbital Splittings

• Crystal field theory focuses on the interaction of the five (n–1)d orbitals with ligands arranged in a regular array around a transition-metal ion

• According to CFT, an octahedral metal complex forms because of the electrostatic interaction of a positively charged metal ion with six negatively charged ligands, or with the negative ends of dipoles associated with the six ligands and the ligands interact with one electrostatically



• The energies of the d orbitals of a transition-metal ion are affected by an octahedral arrangement of six negative charges

– The five d orbitals are initially degenerate (have the same energy)

– When the six negative charges are distributed uniformly over the surface of a sphere, the d orbitals remain degenerate, but their energy will be higher due to repulsive electrostatic interactions between the spherical shell of negative charge and electrons in the d orbitals



– If the six negative charges are placed at the vertices of an octahedron, the average energy of the d orbitals does not change, but it does remove their degeneracy and the five d orbitals split into two groups whose energies depend on their orientations

– The dx2 – y

2 and dz

2 orbitals (the eg orbitals) point directly at the

six negative charges, which increase their energy compared with a spherical distribution of negative charge; the dxy, dxz, and dyz (t2g orbitals) are all oriented at a 45º angle to the coordinate axes and point between the six negative charges, which decreases their energy compared with a spherical distribution

of charge





• The difference in energy between the two sets of d orbitals is called the crystal field splitting energy – Given the symbol o, where the subscript “o” stands for

“octahedral”

• The magnitude of the splitting depends on the charge on the metal ion, the position of the metal in the periodic table, and the nature of the ligands

• The splitting of the d orbitals in a crystal field does not change the total energy of the five d orbitals


Electronic Structures of Metal Complexes

• Using the d-orbital energy-level diagram, the electronic structures and some of the properties of transition-metal complexes can be predicted – Start with the Ti3+ ion, which contains a single d electron, and

proceed across the first row of the transition metals by adding a single electron at a time

– Additional electrons are placed in the lowest-energy orbital available while keeping their spins parallel

– For d1-d3 systems, the electrons successively occupy the three degenerate t2g orbitals with their spins parallel, giving

one, two, and three unpaired electrons, respectively



• Using the d-orbital energy-level diagram, the electronic structures and some of the properties of transition-metal complexes can be predicted – Reaching the d4 configuration, there are two possible choices for the

fourth electron: either in one of the empty eg orbitals or in one of the singly occupied t2g orbitals

– Placing an electron in an occupied orbital results in electrostatic repulsions that increase the energy of the system; this is called the spin-pairing energy (P)

– If o is less than the spin-pairing energy, then the lowest- energy arrangement has the fourth electron in one of the

empty eg orbitals; this results in four unpaired electrons and is called a high-spin configuration—a complex with this configuration is a high-spin complex



– If o is greater than the spin-pairing energy, the lowest-energy arrangement has the fourth electron in one of the

occupied t2g orbitals, which results in two unpaired electrons and is called a low-spin configuration; a complex with this electron configuration is called a low-spin complex

– Metal ions with the d5, d6, or d7 electron configurations can be either high spin or low spin, depending on the

magnitude of o

– Only one arrangement of d electrons is possible for metal ions with d8–d10 electron configurations




Factors That Affect the Magnitude of o

• The magnitude of o dictates whether a complex with four, five, six, or seven d electrons is high spin or low spin, which affects its magnetic properties, structure, and reactivity – Large values of o yield a low-spin complex; small

values of o produce a high-spin complex

• Magnitude of o depends on three factors: 1. The charge on the metal ion

2. The principal quantum number of the metal

3. The nature of the ligand



• Charge on the metal ion – Increasing the charge on a metal ion has two effects:

1. The radius of the metal ion decreases

2. Negatively charged ligands are more strongly attracted to it

– Both these factors decrease the metal-ligand distance, which causes the negatively charged ligands to interact more strongly with the d orbitals

– The magnitude of o increases as the charge on the metal ion increases



• Principal quantum number of the metal – For a series of complexes of metals from the same group in

the periodic table with the same charge and the same ligands, the magnitude of o increases with increasing quantum number:

o (3d) << o (4d) < o (5d)

– Increase in o with increasing principal quantum number is due to the larger radius of valence orbitals going down a

column – Repulsive ligand-ligand interactions are important for smaller

metal ions, which results in shorter M–L distances and stronger d-orbital-ligand interactions



• The nature of the ligands – For a series of chemically similar ligands, the magnitude of o

decreases as the size of the donor atom increases because smaller, more localized charges interact more strongly with the d orbitals of the metal ion

– A small neutral ligand with a highly localized lone pair results in larger o values

– The experimentally observed order of the crystal field splitting energies produced by different ligands is called the spectrochemical series

1. Strong-field ligands interact strongly with the d orbitals of the metal ions and give a large o

2. Weak-field ligands interact more weakly and give a smaller o


Colors of Transition-Metal Complexes

• The striking colors exhibited by transition-metal complexes are caused by the excitation of an electron from a lower-lying d orbital to a higher-energy d orbital, which is called a d-d transition


Colors of Transition-Metal Complexes

• For a photon to affect the transition, its energy must be equal to the difference in energy between the two d orbitals, which depends on the magnitude of o

• Color that is observed is due to transmitted or reflected light that is complementary in color to the light that is absorbed

• The energy of a photon of light is inversely proportional to its wavelength, so the color of a complex depends on the magnitude of

o, which depends on the structure of the complex


Crystal Field Stabilization Energies

• If the lower-energy set of d orbitals (the t2g orbitals) is selectively populated by electrons, then the stability of the complex increases

• The additional stabilization of a metal complex by selective population of the lower-energy d orbitals is called its crystal field stabilization energy (CFSE)

• CFSE of a complex can be calculated by multiplying the number of electrons in t2g orbitals by the energy of those orbitals, multiplying the number of electrons in eg orbitals by the energy of those orbitals, and summing the two

• CFSE is highest for low-spin d6 complexes





• CFSEs are important for two reasons:

1. The existence of CFSE accounts for the difference between experimentally measured values for bond energies in

metal complexes and values calculated based solely on electrostatic interactions

2. CFSEs represent large amounts of energy, which has important chemical consequences


Tetragonal and Square-Planar Complexes

• If two trans ligands in an octahedral complex are either chemically different from the other four or a different distance from the metal than the other four, the result is a tetragonally distorted octahedral complex

• Moving the two axial ligands away from the metal ion along the z axis gives an elongated octahedral complex and eventually produces a square-planar complex

• Axial elongation causes the dz2, dxz, and dyz orbitals to

decrease in energy and the dx2–y

2 and dxy orbitals to

increase in energy; change in energy is not the same for all five d orbitals


Tetrahedral Complexes

• In a tetrahedral complex, none of the five d orbitals points directly at or between the ligands

• The dxy, dxz, and dyz orbitals interact more strongly with ligands than do the dx

2 – y

2 and dz

2 orbitals, so the order of orbital

energies in a tetrahedral complex is the opposite of the order in an octahedral complex

• The splitting of the energies of the orbitals in a tetrahedral complex, o, is smaller than that in an octahedral complex for two reasons: 1. The d orbitals interact less strongly with the ligands in a

tetrahedral arrangement

2. There are only four negative charges rather than six, which decreases the electrostatic interactions


Consequences of d-Orbital Splitting

• The splitting of the d orbitals because of their interactions with the ligands in a complex has important consequences for the chemistry of transition-metal complexes, these can be divided into structural effects and thermodynamic effects



• Structural effects—two major kinds: effects on the ionic radius of metal ions with regular octahedral or tetrahedral geometries, and structural distortions that are observed for specific electron configurations 1. Ionic radii

– A plot of the ionic radii of the divalent first-row transition metal ions versus atomic number shows that only dº , high-

spin d5, and d10 fall on the smooth curve calculated based on the effective nuclear charge; this assumes that the distribution of d electrons is spherically symmetrical, which is effective at screening the ligands from the nuclear charge, giving a larger ionic radius, and making the metal-ligand distances longer



– All the other divalent ions fall below the curve because they have

asymmetrical distributions of d electrons; this makes a metal ion smaller because of poor shielding of the ligands from the nuclear charge and the metal-ligand distance is short



2. The John-Teller effect – Refers to the distortions observed for d4 and d9 complexes; occurs

in systems that have an odd number of electrons in the eg orbitals

– Electrons can occupy either one of two degenerate eg orbitals and have a degenerate ground state

– States that such systems are not stable and that they will undergo a distortion that makes the complex less symmetrical and splits the degenerate states, which decreases the energy of the system



• Thermodynamic effects—CFSEs are important factors in determining the magnitude of hydration energies, lattice energies, and other thermodynamic properties of the transition metals 1. Hydration energies

– Hydration energy of a metal ion is defined as the change in enthalpy for the reaction

M2+(g) + H2O(l) M2+

(aq)

– Cannot be measured directly but can be calculated from experimentally measured quantities using thermochemical cycles

– CFSEs are responsible for the differences between the measured and calculated values of hydration energies



2. Lattice energies – Defined as the negative of the enthalpy change for the reaction

M2+ (g) + 2Cl– (g) MCl2 (s)

– Determined indirectly by using a thermochemical cycle

– Transition-metal dichlorides are more stable due to CFSE



23.6 Transition Metals in Biology


Uptake and Storage of Transition Metals

• There are three possible dietary levels for any essential element: deficient, optimal, and toxic

– If the concentration of an essential element in the diet is too low, an organism must be able to extract

the element from the environment and concentrate it – If the concentration of an essential element in the diet is too

high, an organism must be able to limit its intake to avoid toxic effects

– Organisms must be able to store essential elements for future use



• There are three distinct steps involved in transition-metal uptake:

1. Mobilization—the metal must be “mobilized” from the environment and brought into contact with the cell in a form that can be absorbed

2. Transport—the metal must be transported across the cell membrane into the cell

3. Transfer—the element must be transported to its point of utilization within the cell or to other cells within the organism



• Process of iron uptake – To overcome the insolubility of Fe(OH)3, bacteria use organic

ligands called siderophores (cyclic compounds that use bidentate ligands) that have high affinity for Fe() and are secreted into the surrounding medium to increase the total concentration of dissolved iron

– The iron-siderophore complex is absorbed by the cell, and the iron is released by reduction to Fe()

– Mammals use the low pH of the stomach to increase the concentration of dissolved iron

– Iron is absorbed in the intestine, where it forms an Fe() complex with a protein called transferrin that is transferred to other cells for immediate use or storage in the form of ferritin


Metalloproteins and Metalloenzymes

• Metalloprotein is a protein that contains one or more metal ions tightly bound to amino acid side chains

• Metalloenzyme is a metalloprotein that catalyzes a chemical reaction

• All metalloenzymes are metalloproteins, but the converse is not true


Electron-Transfer Proteins

• Proteins whose function is simply to transfer electrons from one place to another are called electron-transfer proteins

– They do not catalyze a chemical reaction, so they are not enzymes

– They are biochemical reductants or oxidants that are consumed in an enzymatic reaction

– General reaction for an electron-transfer protein is Mn+ + e– M(n–1)+

– Many transition metals can exist in more than one oxidation state, so electron-transfer proteins

usually contain one or more metal ions that can undergo a redox reaction





• Incorporating a metal ion into a protein has three important biological consequences:

1. The protein environment can adjust the redox potential, Eº´, of

the metal ion over a large potential range, whereas the redox potential of the simple hydrated metal ion, Mn+

(aq), is ssentially fixed

2. The protein can adjust the structure of the metal complex to ensure that electron transfer is rapid

3. The protein environment provides specificity, ensuring that the electron is transferred to only the desired site



• Three important classes of metalloproteins transfer electrons: blue copper proteins, cytochromes, and iron-sulfur proteins, which generally transfer electrons at high, intermediate, and low potentials, respectively

• Although these electron-transfer proteins contain different metals with different structures, they are all designed to ensure rapid electron transfer to and from the metal

• When the protein collides with its physiological oxidant or reductant, electron transfer can occur before the two proteins diffuse apart; the metal sites in the oxidized and reduced forms of the protein must have similar structures


Reactions of Small Molecules

• Small molecules such as O2, N2, and H2 do not react with organic compounds under ambient conditions, but they do react with many transition-metal complexes

• All organisms use metalloproteins to bind, transport, and catalyze the reactions of these molecules

• Hemoglobin, hemerythrin, and hemocyanin, which contain heme iron, nonheme iron, and copper, respectively, are used by different kinds of organisms to bind and transfer O2


Enzymes Involved in Oxygen Activation

• Many of the enzymes involved in the biological reactions of oxygen contain metal centers with structures that are similar to those used for O2 transport

• Many of these enzymes also contain metal centers that are used for electron transfer, which have structures similar to those of the electron-transfer proteins

• Two important enzymes that insert oxygen into an organic molecule are dioxygenases and methane monooxygenase


Metal Ions as Lewis Acids

• Reactions catalyzed by metal ions that do not change their oxidation states during the reaction are group transfer reactions, in which a group is transferred

• Metalloenzymes use transition-metal ions as Lewis acids to catalyze group transfer reactions


Enzymes That Use Metals to Generate Organic Radicals

• An organic radical is an organic species that contains one or more unpaired electrons

• Organic radicals are essential components of several important enzymes, almost all of which use a metal ion to generate the organic radical within the enzyme

• These enzymes are involved in the synthesis of hemoglobin and DNA, and they are the targets of pharmaceuticals for the treatment of diseases


Enzymes That Use Metals to Generate Organic Radicals

• Some metalloenzymes use homolytic cleavage of the cobalt-carbon bond in certain derivatives of vitamin B12 to generate an organic radical that can abstract a hydrogen atom and thus cause molecular rearrangements to occur

• The metal is not involved in the actual catalytic reaction; it only provides the enzyme with a convenient mechanism for generating an organic radical, which does the actual work


24 Organic Compounds


CHAPTER OBJECTIVES

• To learn how the three-dimensional structure of organic compounds with the same molecular formula can vary

• To understand how variations in structure can lead to differences in the reactivity of related organic compounds

• To become familiar with the common classes of organic reactions

• To understand the general properties of functional groups and their differences in reactivity

• To be able to identify the common structural units found in important biologically relevant molecules



24.1 Functional Groups and Classes of Organic

Compounds


24.1 Functional Groups and Classes of Organic Compounds

• Organic compounds are covalent compounds composed primarily of carbon and hydrogen

• Carbon is unique among the elements in its ability to catenate, forming long chains and cyclic structures in a wide variety of compounds

• Functional groups are structural units that determine the chemical reactivity of a molecule under a given set of conditions – Can consist of a single atom or a group of atoms

– Organic compounds are classified into several major categories based on the functional groups they contain



• The following table summarizes five families, gives examples of compounds that contain each functional group, and lists the suffix or prefix used in the systematic nomenclature of compounds that contain each functional group




1. First family is the hydrocarbons, which include alkanes, with the general molecular formula CnH2n+2 where n is an integer; alkenes represented by CnH2n; alkynes represented by CnH2n–2; and arenes (CnHn)

2. Second family is the halogen-substituted alkanes, alkenes, and arenes, which include the alkyl halides and aryl halides



3. Third family is the oxygen-containing organic compounds, which are divided into two main types:

a. Those that contain at least one C–O single bond, which include alcohols, phenols, and ethers

b. Those that contain a carbonyl group (> CO), which include aldehydes, ketones, and carboxylic acids



4. Fourth family is the carboxylic acid derivatives; these are compounds in which the H atom on the –CO2H functional group is replaced either by an alkyl group, producing an ester, or by an amine, forming an amide

5. Fifth family is the nitrogen-containing organic compounds; these include amines, nitriles (which have a CN triple bond) and nitro compounds (which contain the NO2 group)



• Systematic and common nomenclature of organic compounds

– In the systematic nomenclature of organic compounds, the positions of substituents are indicated using the lowest

numbers possible to identify their locations in the carbon chain of the parent compound

– Many organic compounds are referred to by common names rather than by systematic names

1. Common nomenclature uses the prefix form- for a compound that contains no carbons other than those in the functional group

2. Uses acet- for those that have one carbon atom in addition



– In the systematic nomenclature of aromatic compounds, the positions of groups attached to the aromatic ring are indicated by numbers, starting with 1 and proceeding around the ring in the direction that produces the lowest possible numbers

– In common nomenclature, the prefixes ortho-, meta-, and para- are used to describe the relative positions of groups attached to an aromatic ring



24.2 Isomeric Variations in Structure


24.2 Isomeric Variations in Structure

• Isomers are different compounds that have the same molecular formula

• Three main types of isomers: 1. Conformational

2. Constitutional (structural)

3. Stereoisomers


Conformational Isomers

• The C–C single bonds in alkanes are formed by the overlap of an sp3 hybrid orbital on one carbon atom with an sp3 hybrid orbital on another carbon atom, forming a bond

• Differences in three-dimensional structure resulting from rotation about a bond are called differences in conformation, and each different arrangement is called a conformational isomer



• Differences between the conformations are depicted in drawings called Newman projections

– A Newman projection represents the view along a C–C bond axis, with the carbon that is in front shown as a point

and the carbon that is bonded to it shown as a circle; the C–H bonds to each carbon positioned at 120º from each other; the hydrogen atoms nearest the viewer are shown bonded to the front carbon, and the hydrogen atoms farthest from the viewer are shown bonded to the circle



– In one extreme, the eclipsed conformation, the C–H bonds on

adjacent carbon atoms are parallel and lie in the same plane

– In the other extreme, the staggered conformation, the hydrogen atoms are positioned as far from one another

as possible

– Rotation about the C–C bond produces an infinite number of conformations between these two extremes with the

staggered conformation being the most stable because electrostatic repulsion between the hydrogen atoms on adjacent carbons is minimized





• Newman projections are useful for predicting the stability of conformational isomers – The eclipsed conformation is higher in energy than the

staggered conformation because of electrostatic repulsions between hydrogen atoms

– The staggered conformation is the most stable because electrostatic repulsion between the hydrogen atoms on

adjacent carbons is minimized

• Longer-chain alkanes can also be represented by Newman projections and rotation can occur about each C–C bond in the molecule; Newman projections are useful for revealing steric barriers to rotation at a particular C–C bond due to the presence of bulky substituents


Constitutional (Structural) Isomers

• Constitutional (structural) isomers differ in the connectivity of the atoms – The two alcohols, 1–propanol and 2–propanol, have the same

molecular formula (C3H8O), but the position of the –OH group differs, which causes differences in their physical and

chemical properties

• In the conversion of one constitutional isomer to another, at least one bond must be broken and reformed at a different position in the molecule


Stereoisomers

• Stereoisomers are molecules that have the same connectivity but whose component atoms have different orientations in space

• Two types of stereoisomers: 1. Geometric isomers differ in the relative placement of substituents in a

rigid molecule; members of an isomeric pair are either cis or trans, with interconversion between the two forms requiring breaking and reforming one or more bonds; their structural differences causes them to have different physical and chemical properties and to exist as two distinct chemical compounds


Stereoisomers

2. Optical isomers are molecules that are mirror images but cannot be superimposed on one another in any orientation

a. Optical isomers have identical physical properties, although their chemical properties may differ

b. Molecules that are nonsuperimposable mirror images of each other are said to be chiral; an achiral object is one that can be superimposed on its mirror image


Stereoisomers


Stereoisomers

• Most organic molecules that are chiral have at least one carbon atom that is bonded to four different groups – This carbon is designated by an asterisk in structural drawings

and is called a chiral center, chiral carbon atom, asymmetric carbon atom, stereogenic center, or stereocenter

• A molecule and its nonsuperimposable mirror image are called enantiomers


Stereoisomers

• Optical activity of enantiomers– Enantiomers have identical density, melting and boiling points,

color, and solubility in most solvents– Differ in their interaction with plane-polarized light, which

consists of electromagnetic waves oscillating in a single plane– If plane-polarized light is passed through a solution, the

electromagnetic radiation interacts with the solute and solvent molecules

– If the solution contains an achiral compound, the plane-polarized light enters and leaves the solution unchanged because achiral molecules cause it to rotate in random directions and the solute is optically inactive


Stereoisomers

– If the solution contains a single enantiomer of a chiral compound, the plane-polarized light is rotated in only one direction, and the solute is said to be optically active; clockwise rotation is called dextrorotatory and is indicated in the compound’s name by (+); a counterclockwise rotation is called levorotatory and is designated by (–)

– Magnitude of the rotation of plane-polarized light is directly proportional to the number of chiral molecules in the solution and depends on their detailed molecular structure, the temperature, and the wavelength of the light


Stereoisomers

– Every chiral compound has a specific rotation defined as the amount (in degrees) by which

the plane of polarized light is rotated when the light is passed through a solution containing 1 g of solute per 1 mL of solvent in a tube 10 cm long

– A chiral solution that contains equal concentrations of a pair of enantiomers is called a racemic

mixture, where the rotations cancel one another and the solution is optically inactive


Stereoisomers


Stereoisomers

• Interactions of enantiomers with other chiral molecules

– In living organisms, every molecule with a stereocenter is found as a single enantiomer, not a racemic mixture

– At the molecular level, our bodies are chiral and interact differently with the individual enantiomers of a particular compound

– Only one enantiomer of a chiral substance interacts with a particular receptor, initiating a response; the other enantiomer may not bind at all, or it may bind to another receptor, producing a different response


Stereoisomers



24.3 Reactivity of Organic Molecules


• The reactivity of a molecule is affected by the degree of substitution of the carbon bonded to a functional group; the carbon is designated as primary, secondary, or tertiary – Primary carbon is bonded to only one other carbon and a

functional group

– A secondary carbon is bonded to two other carbons and a functional group

– A tertiary carbon is bonded to three other carbons and a functional group

• Identifying the transient species formed in a chemical reaction, some of which are charged, enables chemists to predict the mechanism and products of the reaction

24.3 Reactivity of Organic Molecules


• When cleaving a C–H bond, the most common species formed is C+, called a carbocation, which has only six valence electrons and is electron deficient

– A carbocation is an electrophile, a species that needs electrons to complete its octet

– A tertiary carbocation is more stable than one that is primary because it increases electron density at the carbocation

• Adding one electron to a carbocation produces a neutral species called a free radical, which is electron deficient and is an electrophile; free radicals can be stabilized by carbon substituents that can donate electron density, so a tertiary free radical is more stable than a primary one

Reactive Intermediates


• Adding an electron to a free radical produces a carbanion, a negatively charged carbon with eight valence electrons

– A carbanion is a nucleophile, an electron-rich species that has a pair of electrons available to be shared with another atom

– Carbanions are destabilized by groups that donate electrons, so their reactivity is the opposite of carbocations and free radicals; therefore, a tertiary carbanion is less stable than a primary one

• Electrophiles seek to gain electrons and have a strong tendency to react with nucleophiles, which are negatively charged species or substances with lone pairs of electrons






24.4 Common Classes of Organic Reactions


24.4 Common Classes of Organic Reactions

• Five common types of organic reactions:

1. Substitution 2. Elimination 3. Addition 4. Free-radical reactions 5. Oxidation-reduction reactions


Substitution

• In a substitution reaction, one atom or group of atoms in a substance is replaced by another atom or group of atoms from another substance

• A typical substitution reaction is the reaction of hydroxide ion with methyl chloride

CH3Cl + OH– CH3OH + Cl–

– Methyl chloride has a polar C–Cl bond, so the carbon atom has a partial positive charge

– Electronegative Cl atom is replaced by another electronegative species that is a stronger nucleophile, OH–

– Reactions of this type are called nucleophilic substitution reactions; for this reaction to occur, the nucleophilic reactant must possess a pair of electrons and have a greater affinity for the electropositive carbon atom than the original substituent does


Elimination

• Reactions in which adjacent atoms are removed, or “eliminated,” from a molecule with the formation of a multiple bond and a small molecule are called elimination reactions

• General form:

A B

CH2–CH2 CH2CH2 + A–B


Addition

• A reaction in which the components of a species A–B are added to adjacent atoms across a carbon-carbon multiple bond is called an addition reaction

• An example is the reaction of HCl with ethylene to give chloroethane:

HCl + CH2CH2 CH3CH2Cl


Addition

• Addition reaction– Although a multiple bond is stronger than a single bond, the

bonds of the multiple bond are weaker than the bond– The high electron density located between multiple-bonded

carbon atoms causes alkenes and alkynes to behave like nucleophiles, where nucleophilic attack occurs from the more weakly bound electrons; therefore alkenes and alkynes are regarded as functional groups

– Nucleophilic attack occurs on the H+ atom of the polar HCl bond, producing a carbon with only three bonds, a carbocation

– In a second nucleophilic attack, Cl–, the electrophile, attacks the carbocation


Addition

• Alcohols are produced by addition reactions

– Initial attack by the bond of an alkene on a H+ of H3O+

produces a carbocation; which undergoes nucleophilic attack by a lone pair of electrons from H2O, forming the alcohol


Free-Radical Reactions

• Many important organic reactions involve free radicals, and the best known is the reaction of a saturated hydrocarbon with a halogen:

CH3CH3 + Br2 CH3CH2Br + HBr

• Free radical reactions occur in three stages: initiation, propagation, and termination

– At high temperature or in the presence of light, the weak Br–Br bond is broken in an initiation step that produces a number of Br atoms

– During propagation, a bromine atom attacks ethane, producing a free radical, which then reacts with another bromine molecule to produce ethyl bromide; the sum of the propagation steps corresponds to the overall balanced equation for the reaction

– Three possible termination steps: the combination of two bromine atoms, of two ethyl radicals, or of an ethyl and a bromine radical


Oxidation-Reduction Reactions

• Oxidation-reduction reactions are common in organic chemistry and can be identified by changes in the number of oxygens at a particular position in the hydrocarbon skeleton or in the number of bonds between carbon and oxygen at that position

– An increase in either is an oxidation, whereas a decrease is a reduction

– An increase in the number of hydrogens in a hydrocarbon is an indication of a reduction

– In compounds with a carbon-nitrogen bond, the number of bonds between the C and N atoms increases as the oxidation state of the carbon increases



24.5 General Properties and Reactivity of

Functional Groups


24.5 General Properties and Reactivity of Functional Groups

• The functional groups characteristic of each class of organic compounds determine the general properties and reactivity of that class

• There are strong connections among the structure, physical properties, and reactivity for the compounds that contain the major functional groups


Alkanes, Alkenes, and Alkynes

• Alkanes – Boiling points of alkanes increase smoothly with increasing

molecular mass and are similar to those of the corresponding alkenes and alkynes because of similarities in molecular mass between analogous structures

– Melting points of alkanes, alkenes, and alkynes with similar molecular masses show a wider variation because

melting points depend on how the molecules stack in the solid state and are therefore sensitive to small differences in structure



– Consist of C–C and C–H bonds that are strong, not polar, and

not easily attacked by nucleophiles or electrophiles, so reactivity is limited

– Undergo catalytic cracking, which converts straight-chain alkanes to highly branched alkanes

– Catalytic cracking is an example of a pyrolysis reaction, in which the weakest bond is cleaved at high temperature, producing a mixture of free radicals

– Free radicals are also produced during the combustion of alkanes, with CO2 and H2O as the final products



• Alkenes– The multiple bond of an alkene produces geometric isomers (cis

and trans)– Cis and trans isomers of alkenes behave as distinct compounds

with different chemical and physical properties



• Alkynes– Terminal alkynes are alkynes in which the triple bond is located at one

end of a carbon chain and contain a hydrogen atom attached directly to a triply bonded carbon (R–CC–H)

– The hydrogen atom can be removed as H+, forming an acetylide ion (R–CC–)

– Acetylide ions are potent nucleophiles used for making longer carbon chains by a nucleophilic substitution reaction



• Alkenes and alkynes – Rotation about the carbon-carbon multiple bonds of alkenes

and alkynes cannot occur without breaking a bond, which constitutes a large energy barrier to rotation

– Alkenes and alkynes are prepared by elimination reactions


Arenes

• Most arenes with a single six-membered ring are volatile liquids

• Some arenes with substituents on the ring are solids at room temperature

• Undergo substitution rather than elimination because of enhanced stability from delocalization of their electron density; the –H on the arene is replaced by a group –E, such as –NO2, –SO3H, a halogen, or an alkyl group

• Are poor nucleophiles

• Many substituted arenes have potent biological activity


Alcohols and Ethers

• Alcohols– Have “bent” structures and are able to hydrogen-bond– Have higher boiling points than alkanes or alkenes of

comparable molecular mass– Good solvents for organic compounds– Prepared by the addition of water to the carbons of a double

bond or by substitution of an alkyl halide by hydroxide, a potent nucleophile

– Also prepared by the reduction of compounds containing the carbonyl functional group (> CO)

– Are classified as primary, secondary, or tertiary, depending on whether the –OH group is bonded to a primary, secondary, or tertiary carbon


Alcohols and Ethers

– Undergo two major types of reactions: those involving cleavage of the O–H bond, which produces an acid, and those involving cleavage of the C–O bond occurring under acidic conditions where the –OH is first protonated followed by a nucleophilic substitution

– Phenols are more acidic than alcohols because of interactions between the oxygen atom and the ring


Alcohols and Ethers

• Ethers– Have “bent” structures– Good solvents for organic compounds– Prepared by a substitution reaction in which the highly

nucleophilic alkoxide ion (RO–) attacks the carbon of the polarized C–X bond of an alkyl halide (R´ X)

– Unreactive because they lack the –OH unit


Aldehydes and Ketones

• Aldehydes and ketones– Contain the carbonyl functional group– Have higher boiling points than alkanes or alkenes of

comparable molecular mass because of strong intermolecular interactions

– Prepared by the oxidation of alcohols– Characterized by nucleophilic attack at the carbon atom of the

carbonyl functional group and electrophilic attack at the oxygen atom

– React with organometallic compounds that contain stabilized carbanions such as the Grignard reagents (RMgX, where X = Cl, Br, ), which convert the carbonyl functional group to an alcohol and lengthen the carbon chain


Aldehydes and Ketones

– Can be prepared by reducing a carboxyl group (–CO2H) to a carbonyl group, which requires a good reducing agent

– Aromatic aldehydes have intense and characteristic flavors and aromas, and many ketones also have intense aromas

– Ketones are found in hormones responsible for sex differentiation in humans


Carboxylic Acids

• Carboxylic acids – Pungent odors

– High boiling points due to strong hydrogen-bonding interactions between molecules

– Four lightest carboxylic acids are miscible with water, but as the alkyl chain lengthens, their solubility in water decreases

– Compounds that contain the carboxyl functional group are weakly acidic because of delocalization of the electrons, which causes them to lose a proton and form the carboxylate anion


Carboxylic Acids

– Prepared from the oxidation of alcohols and aldehydes or through the reaction of a Grignard reagent with CO2, followed by acidification

– Reactions of carboxylic acids are dominated by their polar carboxyl group and their acidity

– Reactions with strong bases produce carboxylate salts– Less susceptible to nucleophilic attack due to delocalization of

bonding over three atoms (O–C–O)


Carboxylic Acid Derivatives

• Substitution of the –OH of a carboxylic acid produces derivative compounds with different tendencies to participate in resonance with the CO functional group

• Resonance structures have significant effects on the reactivity of carboxylic acid derivatives, but their influence varies, being least important for halides and most important for the nitrogen of amides

• Two important carboxylic acid derivatives are esters and amides



• Esters– Have the general formula RCO2R´, where R and R´ can be

any alkyl or aryl group– Prepared by the reaction of an alcohol (RÓH) with a

carboxylic acid (RCO2H) in the presence of a catalytic amount of strong acid (an electrophile); this protonates the doubly bonded oxygen atom of the carboxylic acid (a nucleophile) to give a species that is more electrophilic than the parent carboxylic acid

– The nucleophilic oxygen atom of the alcohol attacks the electrophilic carbon atom of the carboxylic acid and a new C–O bond is formed



– General overall reaction OH+ O

R–C + RÓH R–C + H2O

OH OR´

– If an ester is heated with water in the presence of a strong acid or base, the reverse reaction will occur, producing the parent alcohol, RÓH, and either the carboxylic acid, RCO2H (under acidic conditions), or the carboxylate anion, RCO2

– (under basic conditions) – Have sweet aromas



• Amides – The two substituents on the amide nitrogen can be hydrogen

atoms, alkyl groups, aryl groups, or any combination of two of those species O

R1–C–N–R2

R3

– Prepared by the nucleophilic reaction of amines with other, more electrophilic carboxylic acid derivatives, such as esters

– Unreactive because of bonding interactions between the lone pair of electrons on nitrogen and the carbonyl group, which inhibits free rotation about the C–N bond

– Stability of amide bond is important in biology because they form the backbones of peptides and proteins


• Amines – Derivatives of ammonia in which one or more hydrogen

atoms have been replaced by alkyl or aryl groups – Analogous to alcohols and ethers – Classified as primary, secondary, or tertiary, depending on

the number of alkyl bonded to nitrogen 1. Primary amines—the nitrogen is bonded to two hydrogen

atoms and one alkyl group 2. Secondary amines—the nitrogen is bonded to hydrogen and

two alkyl groups 3. Tertiary amines—the nitrogen is bonded to three alkyl

groups

Amines


– Ammonia and simple amines have lower boiling points than

does water – Primary amines have boiling points intermediate between

those of the corresponding alcohol and alkane – Secondary and tertiary amines have lower boiling points than

primary amines of comparable molecular mass – Tertiary amines form cations in which all four H atoms are

replaced by alkyl groups and are called quaternary ammonium salts, which can be chiral if all four substituents are different

Amines


– Alkylamines can be prepared by nucleophilic substitution

reactions of polar alkyl halides with ammonia or other amines

– Reactions of amines are dominated by two properties: the ability of amines to act as weak bases and their tendency to act as nucleophiles, both resulting from the lone pair of electrons on the nitrogen atom

1. Amines behave as bases by accepting a proton from an acid to form an ammonium salt

2. Amines can react with any electrophile

– Aryl amines are weaker bases than alkylamines because the lone pair of electrons on nitrogen interacts with the bonds of the aromatic ring

Amines



24.6 The Molecules of Life


24.6 The Molecules of Life

• All the functional groups described are found in the organic molecules that constitute and maintain every living organism on Earth

• The most abundant substances found in living systems belong to four major classes: 1. Proteins

2. Carbohydrates

3. Lipids

4. Nucleic acids


• Proteins are biologically active polymers formed from amino acids linked together by amide bonds; in addition to an amine group and a carboxylic acid group, each amino acid contains a characteristic R group

– The nature of the R group determines the particular chemical properties of each amino acid

• All the amino acids found in proteins are chiral compounds except glycine, which suggests that their interactions with other chiral compounds are selective

• Some proteins are enzymes that catalyze biological reactions

Proteins


• Carbohydrates are the most abundant of the organic compounds found in nature; they constitute a substantial portion of food that is consumed to provide energy needed to support life

• Carbohydrates are polyhydroxy aldehydes or polyhydroxy ketones – The simplest carbohydrates consist of unbranched chains of

three to eight carbon atoms; one carbon is a carbonyl carbon and the others are bonded to hydroxyl groups

– The structure of a carbohydrate can be drawn either as a hydrocarbon chain, known as a Fisher projection, or as a ring, or cyclic form, called a Haworth projection

– The two cyclic forms in a Haworth projection are called anomers

Carbohydrates


Carbohydrates


• Carbohydrates are classified according to the number of single saccharide units they contain

1. The simplest are monosaccharides – Contain several chiral carbons and exist in several

isomeric forms – An example is glucose

2. A disaccharide consists of two linked monosaccharide units and an example is sucrose

3. A trisaccharide is three linked monosaccharide units

4. Polysaccharides contain more than 10 monosaccharide units

Carbohydrates


• Because carbohydrates have a carbonyl functional group and several hydroxyl groups, they can undergo a variety of biochemically important reactions

– The carbonyl group can be oxidized to form a carboxylic acid or can be reduced to form an alcohol

– The hydroxyl groups can undergo substitution reactions, resulting in derivatives of the original compound

– Can eliminate hydroxyl groups, producing alkenes

Carbohydrates


• Two familiar polysaccharides are starch and cellulose, which both hydrolyze to produce thousands of glucose units and differ only in the connection between glucose units and the amount of branching in the molecule

– Starches are branched or unbranched– Cellulose, the structural material of plants, is unbranched and

cannot be digested by humans

Carbohydrates


• Lipids – Characterized by their insolubility in water – Form a family of compounds that includes fats, waxes,

vitamins, and steroids – Fatty acids are the simplest lipids and have a long hydrocarbon

chain that ends with a carboxylic acid functional group 1. Saturated fatty acids—the hydrocarbon chains contain only C–C

single bonds that stack in a regular array 2. Unsaturated fatty acids—have a single double bond in the

hydrocarbon chain (monounsaturated) or more than one double bond (polyunsaturated); double bonds give fatty acid chains a kinked structure, which prevents the molecules from packing tightly

Lipids


• Unsaturated fatty acids– Melting point lower than that of a saturated fatty acid of

comparable molecular mass– Double bonds can be hydrogenated in an addition reaction that

produces a saturated fatty acid or oxidized to produce an aldehyde or carboxylic acid

– Are the starting compounds for the biosynthesis of prostaglandins, hormonelike substances

• Waxes are esters produced by nucleophilic attack of an alcohol on the carbonyl carbon of a long-chain carboxylic acid

• Triacylglycerols are esters that are used by the body to store fats and oils and are formed from one molecule of glycerol and three fatty acid molecules

Lipids


• Steroids are lipids whose structure is made up of three cyclohexane rings and one cyclopentane ring fused together; presence of various substituents on the basic steroid ring structure produces a family of steroid compounds with different biological activity

– Cholesterol is a steroid found in cellular membranes and is the starting point for the biosynthesis of steroid hormones, including testosterone, the primary male sex hormone, and progesterone, which helps maintain pregnancy

Lipids


• Nucleic acids are the basic structural components of DNA and RNA, the biochemical substances found in the nuclei of cells that transmit the information needed to direct cellular growth and reproduction

• Structures are derived from nitrogen-containing cyclic compounds called pyrimidines and purines, which can hydrogen-bond through the lone electron pair on nitrogen (in pyrimidine and purine) or through the hydrogen of the amine (in purine)

• When a pyrimidine or purine is linked to a sugar by a bond called a glycosidic bond, a nucleoside is formed; addition of a phosphoric acid group to the sugar produces a nucleotide

Nucleic Acids


• Nucleotides link to form a polymeric chain that consists of alternating sugar and phosphate groups that are the backbone of DNA and RNA

• The function of DNA is to preserve genetic information, and RNA translates the genetic information in DNA and carries that information to cellular sites where proteins are synthesized – Antibiotics function by interfering with the synthesis of proteins

in one or more kinds of bacteria – Mutations in an organism’s DNA lead to the synthesis of

defective proteins

Nucleic Acids

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14 Chemical Kinetics. Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings CHAPTER OBJECTIVES To understand the factors that