Chemical KineticsChemical Kinetics

KineticsKineticsThe study of reaction rates.The study of reaction rates.

Spontaneous reactions are reactions that Spontaneous reactions are reactions that will happen - but we can’t tell how fast. will happen - but we can’t tell how fast. (Spontaneity implies nothing about speed)(Spontaneity implies nothing about speed)

For example: Diamond will spontaneously For example: Diamond will spontaneously turn to graphite – so slow it is not turn to graphite – so slow it is not detectable.detectable.

Reaction mechanism- the steps by which a Reaction mechanism- the steps by which a reaction takes place.reaction takes place.

Reaction RateReaction Rate

Defined as the change in the Defined as the change in the concentration of a reactant or concentration of a reactant or product per unit time.product per unit time.

Rate=Rate=Conc.of A at tConc.of A at t22-Conc. of A at t-Conc. of A at t11

tt22 – t – t11

Rate =Rate =[A][A] tt

For this reaction: N2 + 3 H2 2 NH3

As the reaction progresses the concentration H2 goes down

CONCENTRATION

TIME

[H2][H2]

As the reaction progresses the concentration N2 goes down 1/3 as fast

[H2][H2][H2]

[N2][N2]

CONCENTRATION

TIME

As the reaction progresses the concentration NH3 goes up.

[H2]

[N2]

[NH3]

Calculating RatesCalculating Rates

Average rates are taken over long Average rates are taken over long intervalsintervals

Instantaneous rates are determined Instantaneous rates are determined by finding the slope of a line tangent by finding the slope of a line tangent to the curve at any given point to the curve at any given point because the rate can change over because the rate can change over timetime

Factors that Affect Reaction RatesFactors that Affect Reaction Rates

Nature of the reactantsNature of the reactants

Concentration of the reactantsConcentration of the reactants

TemperatureTemperature

Presence of a catalystPresence of a catalyst

Defining RateDefining Rate

We can define rate in terms of the We can define rate in terms of the disappearance of the reactant or in disappearance of the reactant or in terms of the rate of appearance of terms of the rate of appearance of the product.the product.

In our example:In our example: N N22 + 3H + 3H22 2NH 2NH33 - -[N[N22] ] = = -3-3[H[H22] ] = = 22[NH[NH33] ] t t t t

tt

Rate LawsRate LawsReactions are reversible.Reactions are reversible.As products accumulate they can As products accumulate they can begin to turn back into reactants.begin to turn back into reactants.Initially, the rate will depend on only Initially, the rate will depend on only the amount of reactants present.the amount of reactants present.Therefore, reactions must be studied Therefore, reactions must be studied at a point soon after the reactants at a point soon after the reactants are mixed.are mixed.This is called the This is called the Initial rate methodInitial rate method..

Rate LawsRate Laws

The concentration of the products do The concentration of the products do not appear in the rate law because not appear in the rate law because this is an initial rate.this is an initial rate.

The order must be determined The order must be determined experimentally, and experimentally, and can’tcan’t be be obtained from the equationobtained from the equation

2 NO2 NO2 2 22 NO + ONO + O22

The rate will only depend on the The rate will only depend on the concentration of the reactants.concentration of the reactants.

Rate = Rate = kk[NO[NO22]]nn

This is called a This is called a rate law expressionrate law expression..kk is called the rate constant. is called the rate constant.n is the “order” of the reactant -usually a n is the “order” of the reactant -usually a positive integer and must be determined positive integer and must be determined experimentallyexperimentallyOverall reaction order is the sum of the Overall reaction order is the sum of the orders for each individual reactant.orders for each individual reactant.

Types of Rate LawsTypes of Rate LawsDifferential Rate law - describes how rate Differential Rate law - describes how rate depends on concentration (often simply depends on concentration (often simply called rate law)called rate law)

Integrated Rate Law - describes how Integrated Rate Law - describes how concentration depends on time.concentration depends on time.

For each type of differential rate law there For each type of differential rate law there is an integrated rate law and vice versa.is an integrated rate law and vice versa.

Rate laws can help us better understand Rate laws can help us better understand reaction mechanisms.reaction mechanisms.

Determining the form of a rate lawDetermining the form of a rate law(Method of Initial Rates)(Method of Initial Rates)

The initial rate is the instantaneous rate The initial rate is the instantaneous rate right after the reaction begins (t=0)right after the reaction begins (t=0)

Eliminates the effect of the reverse Eliminates the effect of the reverse reaction.reaction.

The initial concentrations of the reactants The initial concentrations of the reactants are varied.are varied.

The reaction rate is determined for each The reaction rate is determined for each trial. trial.

See the example problem on p. 658See the example problem on p. 658

A + 2B A + 2B C CTrialTrial Initial [A]Initial [A] Initial [B]Initial [B] Initial Rate of Initial Rate of

formation of [C]formation of [C]

11 0.010 M0.010 M 0.010 M0.010 M 1.5 x 101.5 x 10-6-6 M/s M/s

22 0.010 M0.010 M 0.020 M0.020 M 3.0 x 103.0 x 10-6-6 M/s M/s

33 0.020 M0.020 M 0.010 M0.010 M 6.0 x 106.0 x 10-6-6 M/s M/s

A + B + C A + B + C products products

The rate law is determined to be The rate law is determined to be

rate = k[A][B]rate = k[A][B]22

What happens to the reaction rateWhat happens to the reaction rate

when we make the following changeswhen we make the following changes

to the concentrations?to the concentrations?

The concentration of A is doubled The concentration of A is doubled while B and C remain unchanged.while B and C remain unchanged.The concentration of B is doubled The concentration of B is doubled while A and C remain unchanged.while A and C remain unchanged.The concentration of C is doubled The concentration of C is doubled while A and B remain unchanged.while A and B remain unchanged.The concentration of all three The concentration of all three reactants are doubled reactants are doubled simultaneously. simultaneously.

Homework problems to be Homework problems to be completed by tomorrowcompleted by tomorrow

Chapter 16: problems 13-20, 21, 23, Chapter 16: problems 13-20, 21, 23, 25, 2725, 27

Collision Theory of Reaction RatesCollision Theory of Reaction Rates

For a reaction to occur, particles For a reaction to occur, particles must collide.must collide.

Increasing the concentration or Increasing the concentration or reactants results in a greater number reactants results in a greater number of collisions and therefore, a faster of collisions and therefore, a faster rate.rate.

Not all collisions are effective Not all collisions are effective collisions.collisions.

Effective CollisionsEffective Collisions

For a collision to be effective:For a collision to be effective:

1) particles must possess a 1) particles must possess a necessary minimum energy to break necessary minimum energy to break bonds and form new ones (activation bonds and form new ones (activation energy)energy)

2) particles must have proper 2) particles must have proper orientation at the time of the orientation at the time of the collision. (see page 677)collision. (see page 677)

Reaction MechanismReaction MechanismThe step by step pathway by which a The step by step pathway by which a reaction occurs is called its mechanism.reaction occurs is called its mechanism.

The individual steps are called elementary The individual steps are called elementary steps.steps.

The rate law for an elementary step can The rate law for an elementary step can be written from its molecularity.be written from its molecularity.

Molecularity is defined as the number of Molecularity is defined as the number of species that must collide to produce the species that must collide to produce the reaction indicated by that step.reaction indicated by that step.

Examples of Elementary StepsExamples of Elementary StepsElementary Elementary

StepStepMolecularityMolecularity Rate LawRate Law

A A products products UnimoleculaUnimolecularr

Rate = k[A]Rate = k[A]

A + A A + A products products BimolecularBimolecular Rate =k[A]Rate =k[A]22

A + BA + B products products BimolecularBimolecular Rate =k[A][B]Rate =k[A][B]A + A + BA + A + B products products TermoleculaTermolecula

rrRate=k[A]Rate=k[A]22[B][B]

A + B + CA + B + Cproductsproducts TermoleculaTermolecularr

Rate=k[A][B][C]Rate=k[A][B][C]

Reaction Mechanism (continued)Reaction Mechanism (continued)

In most mechanisms, one step is In most mechanisms, one step is slower than the others.slower than the others.

A reaction can never occur faster A reaction can never occur faster than its slowest step.than its slowest step.

The slow step is the The slow step is the rate-determining rate-determining step.step.

Determining Possible Reaction Determining Possible Reaction MechanismsMechanisms

The balanced equation for the overall The balanced equation for the overall reaction is equal to the sum of all of reaction is equal to the sum of all of the individual steps.the individual steps.

The rate law expression matches the The rate law expression matches the coefficients of the rate determining coefficients of the rate determining step.step.

ExampleExampleNONO22 + CO + CO NO + CO NO + CO22

rate = k[NOrate = k[NO22]]22

One proposed mechanism:One proposed mechanism:

NONO22 + NO + NO22 N N22OO44 (slow) (slow)

NN22OO44 + CO + CO NO + CO NO + CO22 + NO + NO22 (fast) (fast)

NONO22 + CO + CO NO + CO NO + CO22

NN22OO44 is an intermediate (forms in one step and is is an intermediate (forms in one step and is consumed in a later step)consumed in a later step)This proposed mechanism is consistent with the This proposed mechanism is consistent with the experimentally determined rate law.experimentally determined rate law.

Another possible mechanismAnother possible mechanismNONO22 + NO + NO22 NO NO33 + NO (slow) + NO (slow)

NONO33 + CO + CO NO NO22 + CO + CO22 (fast) (fast)

NONO22 + CO + CO NO + CO NO + CO22

In order to be a possible mechanism the In order to be a possible mechanism the following two criteria must be met:following two criteria must be met:1) The individual steps must add up to the 1) The individual steps must add up to the overall reactionoverall reaction2) The mechanism is consistent with the 2) The mechanism is consistent with the experimentally determined rate law experimentally determined rate law expressionexpression

Equilibrium StepEquilibrium StepAn equilibrium step is a step in which a An equilibrium step is a step in which a product can rapidly re-form the reactants product can rapidly re-form the reactants to reach equilibrium. to reach equilibrium. The concentration of products is equal to The concentration of products is equal to the concentration of the reactants at the concentration of the reactants at equilibrium.equilibrium.An equilibrium step is indicated by a An equilibrium step is indicated by a double arrow. (< -- > )double arrow. (< -- > )Substitutions can be made in the rate law Substitutions can be made in the rate law expression between the reactants and the expression between the reactants and the products.products.

ExampleExample 2NO + Br2NO + Br22 2NOBr 2NOBr

rate = k[NO]rate = k[NO]22[Br[Br22]]Proposed mechanism:Proposed mechanism:

NO + BrNO + Br22 < --> NOBr < --> NOBr22 (fast) (fast) NOBrNOBr22 + NO + NO 2NOBr (slow) 2NOBr (slow) 2NO + Br2NO + Br22 2NOBr 2NOBr

Rate = k[NOBrRate = k[NOBr22][NO] can be substituted ][NO] can be substituted withwithRate =k[NO][BrRate =k[NO][Br22][NO] or Rate=k[NO]][NO] or Rate=k[NO]22[Br[Br22]]

Homework problems to be Homework problems to be completed by tomorrowcompleted by tomorrow

Chapter 16: problems 65, 67, 69, 71, Chapter 16: problems 65, 67, 69, 71, 73, and 7573, and 75

Integrated Rate LawsIntegrated Rate Laws

Integrated Rate Laws express the Integrated Rate Laws express the reactant concentration as a function reactant concentration as a function of time (instead of rate as a function of time (instead of rate as a function of the reactant concentration).of the reactant concentration).

We will only be considering reactions We will only be considering reactions involving a single reactant.involving a single reactant.

First-Order Rate LawsFirst-Order Rate LawsConsider the following reaction:Consider the following reaction:

2N2N22OO55 4NO 4NO22 + O + O22

The rate law (differential) is The rate law (differential) is determined to be determined to be

Rate = k[NRate = k[N22OO55]]This means that if the concentration This means that if the concentration of Nof N22OO55 is doubled, the rate of is doubled, the rate of production of the products is also production of the products is also doubled.doubled.

Integrated First-Order Rate LawIntegrated First-Order Rate LawThe previous differential rate law can The previous differential rate law can be integrated and as a result, written be integrated and as a result, written in the following form:in the following form:

ln[Nln[N22OO55] = -kt + ln[N] = -kt + ln[N22OO55]]00

Where:Where:ln indicates the natural logln indicates the natural logt is the timet is the time

[N[N22OO55] is the concentration at time “t”] is the concentration at time “t”

[N[N22OO55]]oo is the initial concentration is the initial concentration

Integrated First-Order Rate LawsIntegrated First-Order Rate Laws

All integrated first order rate laws All integrated first order rate laws take the following general form:take the following general form:

ln[A] = -kt + [A]ln[A] = -kt + [A]oo

Items to note:Items to note:

1) The equation shows how the 1) The equation shows how the concentration of A depends on timeconcentration of A depends on time

Integrated First-Order Rate LawsIntegrated First-Order Rate Lawsln[A] = -kt + ln[A]ln[A] = -kt + ln[A]oo

2) The above equation is of the form 2) The above equation is of the form y=mx + by=mx + b, , where a plot of where a plot of yy vs. vs. xx is a straight line with slope is a straight line with slope mm and intercept and intercept bb..

In the above rate law:In the above rate law:

y=ln[A] x=ty=ln[A] x=t m=-k b=ln[A] m=-k b=ln[A]oo

As a result, plotting ln[A] vs. time always gives a As a result, plotting ln[A] vs. time always gives a straight line. (This fact is often used to test straight line. (This fact is often used to test whether a reaction is 1whether a reaction is 1stst order or not) order or not)3) The integrated rate law for a 13) The integrated rate law for a 1stst order reaction order reaction can also be written as:can also be written as:

ln([A]ln([A]oo/[A]) = kt/[A]) = kt

Half-LifeHalf-LifeThe time required for a reactant to reach The time required for a reactant to reach half of its original concentration is called half of its original concentration is called the the half-lifehalf-life of a reactant and is designated of a reactant and is designated with the symbol twith the symbol t1/21/2..

The general equation for the half-life of a The general equation for the half-life of a first order reaction is first order reaction is

tt1/21/2 =0.693/k =0.693/k

(Half-life does not depend on concentration)(Half-life does not depend on concentration)

Second-Order Rate LawsSecond-Order Rate Laws

The integrated second order rate law The integrated second order rate law has the form: has the form:

1/[A] = kt + 1/[A]1/[A] = kt + 1/[A]oo

Note:Note:

1) A plot of 1/[A] vs. time produces a 1) A plot of 1/[A] vs. time produces a straight line with a slope=k.straight line with a slope=k.

2) The half-life equation for a 22) The half-life equation for a 2ndnd order reaction is: torder reaction is: t1/21/2 = 1/k[A] = 1/k[A]oo

Zero-Order Rate LawsZero-Order Rate LawsThe rate law for a zero order reaction is:The rate law for a zero order reaction is:

rate = krate = kThe integrated rate law for a zero order The integrated rate law for a zero order reaction isreaction is

[A] = -kt + [A][A] = -kt + [A]oo

Note:Note:1) A plot of [A] vs. time results is a straight 1) A plot of [A] vs. time results is a straight lineline2) the half life equation is:2) the half life equation is:

tt1/21/2 = [A] = [A]00/2k/2k

Example Problem 16-10 p. 674Example Problem 16-10 p. 674

Complete homework problems Complete homework problems 33,35,39, and 41.33,35,39, and 41.

Complete the supplemental problems Complete the supplemental problems given out in class today.given out in class today.