Equilibriums

Introduction INTRODUCTION When a liquid evaporates in a closed container

molecules with relatively higher kinetic energy escape the liquid surface into the vapour phase strike the liquid surface and are retained in the liquid phase .it gives rise to constant vapour pressure because of an equilibrium in which the number of molecules leaving the liquid equal the number returning to liquid from the vapour. We say that the system has reached an EQUILBIRUM STATE.

The mixture of reactants and products is called equilibrium mixture .

The stage where there is no change in the concentrations is called a dynamic equilibrium.

Equilibriums involving ions are called ionic equilibrium.

Equilibriums in physical processes The most famous examples of physical equilibrium is the

phase transformation processes.That is given below:- solid liquid⇋ liquid gas⇋ solid gas⇋

The Concept of Equilibrium As a system approaches

equilibrium, both the forward and reverse reactions are occurring.

At equilibrium, the forward and reverse reactions are proceeding at the same rate.

A System at Equilibrium Once equilibrium is

achieved, the amount of each reactant and product remains constant.

Here NO2 and N2O4 has reached equilibrium.

Depicting EquilibriumIn a system at equilibrium, both the forward and reverse reactions are being carried out; as a result, we write its equation with a double arrow

Here the partial pressures of the above gases are also equal.

N2O4 (g) 2 NO2 (g)⇋

Equilibrium

Equilibriums involving dissolution of solid or gases in liquids Solids in liquids:-When no more solute can be dissolved in the solution it is called a

saturated solution.That is, sugar(solution) sugar(solid)⇋And also the rate of dissolution of sugar = rate of crystallization of

sugar.

The ratio of radioactive molecules to the nonradioactive molecules in the solution increases till attains a constant value.

Gases in liquids and henry’s law There is a certain equilibrium between the

molecules of the gaseous state and molecules of the liquid state.

Carbon dioxide(gas) carbon dioxide(in solution)⇋Henry’s law:-states that the mass of a gas dissolved in a

given mass of a solvent at any temperature is proportional to the pressure of the gas above the solvent.

The amount decreases with the increase in temperature.

(1) for solid ⇋liquid equilibrium , there is only one temperature(melting point) at 1 atm (1.013 bar) at which the two phases can coexist. If there is no exchange of heat with the surroundings , the mass of the two phases remains constant.

(2) For liquid vapour equilibirum the vapour pressure is constant ⇋at a given temperature.

(3) for dissolution of solids in liquids, the solubility is constant at a given temperature.

(4) For dissolution of gases in liquids, the concentration of a gas in liquid is proportional to the pressure of the gas over the liquid.

General characteristics of equilibria involving physical processes Equilibrium is only possible only in a closed system at a given

temperature. Both the opposing processes occur at the same rate and there

is a dynamic but a stable condition. When equilibrium is attained for a physical process, it is characterized by constant value of one of its parameters at a given temperature The magnitude of such quantities at any stage indicates the extent to which the physical process has proceeded before reaching equilibrium.

Dynamic equilibrium General case of an equilibrium reaction:- A+B C+D⇋With the passage of time, there is accumulation of the

products C and D and depletion of the reactants A and B. This leads to a decrease in the rate of forward reaction and an increase in the rate of the reaction.

Finally, the two reactions occur at the same rate and the system reaches a state of equilibrium.

Law of chemical equilibrium and equilibrium constant We know that for a reversible reaction:- A+B C+D⇋These reactants and products are balanced and hence we

can relate them by a equilibrium equation.

Where Kc is called the equilibrium constant and the expression on the right side is called equilibrium constant expression

At a given temperature the product of concentrations of the reactions products raised to the respective stoichiometric coefficient in the balanced chemical equation divided the by the product of concentrations of the reactants raised to their individual stoichiometric coefficients has a constant value . This is known as law of chemical equilibirum.

Equilibirum constant for a general reaction can be written as:- a A+b B ⇋ c C+ d D

Equilibirum constant for the reverse reaction is the inverse of the equilibrium constant in the forward direction

What Does the Value of K Mean? If K >> 1, the reaction is

product-favored; product predominates at equilibrium.

If the reverse takes place than the former predominates.

What Does the Value of K Mean? If K >> 1, the reaction is

product-favored; product predominates at equilibrium.

• If K << 1, the reaction is reactant-favored; reactant predominates at equilibrium.

The range of equilibrium constants

small K large Kintermediate K

Homogeneous equilibria In an homogeneous system the reactants and the

products are in the same phase(solution phase) .

and also we can say in the next reaction that the ions are equal

Equilibrium constant in gaseous systems We know that

So, Here p is the pressure in Pascal's ,”n”is the number of moles and

volume is in cubic metre. And T is the temperature in Kelvin.If c is the concentration in mol/L and p is in bar. then

Here R=0.0831 bar litre/mol K

Heterogeneous equilibria Equilibrium in a system having more than one phase is

called heterogeneous equilibrium.

Example :- the equilibrium between water vapour and liquid water in a closed container is an example of heterogeneous equilibrium.

Applications of equilibrium constants Expression for equilibrium constant is applicable only when

concentrations of the reactants and products have attained constant value at equilibirum state.

The value of equilibrium constant is independent of initial concentrations of the reactants and products.

Equilibrium constant is temperature dependent having one unique value for a particular reaction is represented by a balanced equation at a given temperature

The equilibrium constant for a reverse reaction is equal to the inverse of the equilibrium constant for the forward reaction

Predicting the extent of the reaction The magnitude of equilibirum constants (kc and kp) is

directly proportional to the concentrations of the products. and inversely proportional to the concentrations of the reactants.

If Kc is very large then the reaction proceeds nearly to completion.

If Kc is very small then the reaction proceeds rarely.

Predicting the direction of the reaction The equilibrium constant helps in predicting the direction in

which a given reaction will proceed at any stage. For this purpose we calculate the reaction quotient Q.

It is denoted with Qc with molar concentrations.

If Qc >kc then the reaction will proceed in the direction of

reactants( reverse reaction) If Qc < kc the reaction will proceed in the direction of products

(forward reaction) If both are equal then the mixture has attained equilibriums

If Qc >kc net reaction goes from left to right If Qc < kc net reaction goes from right to left If Qc = kc no net reaction occurs

Calculating equilibrium concentrations Write the balanced chemical equation for the reaction. Under the equation make the ICE table.(a)The initial concentrations(b)The change in concentrations on going to equilibrium(c)Equilibrium concentrationSubstitute the equilibrium concentrations into the

equilibirum equation and solve for x. if you are to solve a quadratic equation choose the

mathematical solution that makes chemical sense.• Calculate the equilibirum concentrations form the

calculated value of x.• Check the results by substituting them into the

equilibrium equation.

Relationship between equilibrium constant (K), reaction quotient (Q) and Gibbs energy (G) If, ∆G is negative then the reaction is spontaneous and proceeds in the

forward direction. If ,∆G is positive then the reaction is considered non-spontaneous ,

instead as reverse reaction would have negative ∆G , the products of the forward reaction shall be converted to reactants.

If , ∆G = 0 reaction has achieved equilibrium, and at this point, there is no longer any free energy left to drive the reaction.

A mathematical expression of this thermodynamic view can be written as:-

At equilibrium ∆G =0 and Q = Kc

Then the equation becomes:-

Which is equal to :

Therefore:- Taking antilog on both sides we get :-

Factors affecting equilibria Le Chateliers’s principle:- it

states that a change in any of the factors that determine the equilibrium conditions of a system will cause the system to change in such a manner so as to reduce or to counteract the effect of the change.

Effect of concentration changeThe chatelier’s principle predicts that:- The concentration stress of an added reactant/product is relieved by net

reaction in the direction that consumes the added substance. The concentration stress of a removed reactant/product is relieved by net

reaction in the direction that replenishes the removed substance. Or in other words

“ When the concentration of any reaction or products in a reaction at equilibrium is changed , the composition of the equilibrium mixture changes so as to minimize the effect of concentration changes”.

Effect of temperature changes In general temperature depends on the ∆H for the reaction:- The equilibrium constant for an exothermic reaction decreases as the

temperature increases in this case ∆H is negative The equilibrium constant for an endothermic reaction increases as

temperature increases and in this case ∆H is positive. Raising the temperature shifts the equilibrium to left and decreases its

concentration

EFFECT OF INERT GAS ADDITION If the volume is kept constant and an inert gas such as

argon is added which does not take part in the reaction, the equilibrium remains undisturbed. It is because the addition of an inert gas at constant volume does not change the partial pressures or the molar concentrations of the substance involved in the reaction.

The reaction quotient changes only if the added gas is a reactant or product involved in the reaction

EFFECT OF CATALYST A catalyst increases the rate of the chemical reaction by making available a

new low energy pathway for the conversion of reactants to products. It increases the rate of forward and reverse reactions that pass through the

same transition state and does not affect equilibrium. Catalyst lowers the activation energy for the forward and reverse reactions

by exactly the same amount. Catalyst does not affect the equilibrium composition of a reaction mixture. It

does not appear in the balanced chemical equation or in the equilibrium constant expression.

If a reaction has an exceedingly small K, a catalyst would be of little help.

ACIDS BASES AND SALTS Acid + base salt +water.⇒This reaction is called neutralization reaction.

Dielectric constant:-the ability of a polar solvent to dissociate in water is called dielectric constant.

It is a measure relative permeability.

Separation of ions in water is called ionization or dissociation. When ions of water are separated it is known as hydration.

Organic acids like acetic acid and formic acid cannot ionize . They can only be partially ionized. That is (<5%)

Arrhenius concept of acids and bases According to Arrhenius theory:-“acids are substances that dissociate in water to give H+

(aq) and bases are substances that produce hydroxyl ions OH-(aq)”.

HX→ H+ +X-

or

HX+H2O→H3O+ + X-

Water forms bond with hydrogen ion to form Hydronium ion. It has the shape of

trigonal bipyramidal.

The Brönsted Lowry theory of acids and bases According to Brönsted Lowry theory, “acid is a

substance that is capable of donating a hydrogen ion and bases are substances capable of accepting hydrogen ions.”

In short acids are proton donors and bases are proton acceptors.

Lewis acids and bases According to Lewis:- “He defined acids as

a species which accepts electron pair base which donates and electron pair”.

In Lewis concepts acids do not have a proton at all.

In bases a lone pair is provided in such cases

BF3 does not have a proton but still acts as an acid and reacts with NH3 by accepting its lone pair of electrons.

IONIZATION OF ACIDS AND BASES Always the stronger acid donates a proton to the stronger base. Strong acids dissociate very easily in water resulting in a

formation of a weak base. So always strong acids have weak conjugate bases

Examples are perchloric acid, hydroiodic acid, nitric acid etc:- Weak acids have very strong conjugate bases Examples are hydrofluoric acid, acetic acid.

Ionization constant and ionic product In pure water one water molecule donates proton and acts as

an acid and another water molecules accepts a proton and acts as a base at the same time . The following equilibrium exists as:-

The dissociation can be represented as:-

The concentration of water is omitted from the denominator as water is a pure liquid and its concentration remains constant. Water is incorporated within the equilibrium constant to give a new constant Kw which is called the ionic product of water.

W can distinguish acidic, basic and neutral solutions by the relative values of and concentrations:-

Acidic:-

Basic:- Neutral:-

Ionization constants of weak acids General formula for dissociation of weak acids is given by the

formula:-

Ka is called the dissociation or the ionization constant. At a given temperature T, Ka is a measure of the strength of an

acid HX that is larger the value of Ka the stronger is the acid. It is a dimensionless quantity with all species of concentrations 1M.

The pH scale for hydrogen ion concentration has been extended to other species and quantities.

Steps to evaluate pH for weak electrolytes:-A. The species present before dissociation are identified as Brönsted Lowry acids/bases.B. Balanced equations for possible reactions i.e with a species acting both as acid as

well as a base are written.C. The reaction with higher ionization constant is identified as the primary reaction

Whilst the other is a subsidiary reaction.D. Enlist in a tabular form the following values of each of the species in the primary

reaction.

(i) Initial concentration (ii) (ii)change in concentrations into equilibriums in terms of α, degree of ionization.

(iii)Equilibrium concentration.

E. Substitute equilibrium concentrations into equilibrium constant equation for principal reaction and solve for α.

F. Calculate pH by the formula pH=-log(H+)

Acid and Base Strength Strong acids are

completely dissociated in water.Their conjugate bases are

quite weak. Weak acids only

dissociate partially in water.Their conjugate bases are

weak bases.

Acid and Base StrengthIn any acid-base reaction, the equilibrium will favor the reaction that moves the proton to the stronger base.

HCl(aq) + H2O(l) H3O+(aq) + Cl−(aq)

H2O is a much stronger base than Cl−, so the equilibrium lies so far to the right K is not measured (K>>1).

Ionization of weak bases The equilibrium constant for base ionization is called

base ionization constant and is represented by Kb.

Alternatively if c = initial concentration of base and α = degree of ionization of base that is the extent to which the base ionizes then equilibirum constant can be written as:-

Relation between Ka and Kb The equilibrium constant for a net reaction obtained after adding two or

more reactions equal the product of the equilibrium constants for individual reactions.

In case of a conjugate acid base pair:-

Therefore :-

Di-and polybasic acids and di-and polyacidic bases Some acids like oxalic acid, sulphuric acid , phosphoric acid

have more than one ionizable proton per molecule of the acid. Such acids are called polybasic or polyprotic acids.

Dibasic acids are those acids which have more than 2 ionizable protons and a tribasic acid has more than 3 ionizable protons.

Higher order ionization constants are smaller than the lower order ionization constants.

Hence it is difficult to remove a positively charged proton from a negative ion due to electrostatic forces.

Polyprotic Acids often acid molecules have more than one ionizable H –

these are called polyprotic acids the ionizable H’s may have different acid strengths or be equal 1 H = monoprotic, 2 H = diprotic, 3 H = triprotic

HCl = monoprotic, H2SO4 = diprotic, H3PO4 = triprotic polyprotic acids ionize in steps

each ionizable Hydrogen removed sequentially removing of the first Hydrogen automatically makes

removal of the second Hydrogen harder. H2SO4 is a stronger acid than HSO4

Extent of dissociation of an acid depends on the strength and polarity of the H-A bond.

Strength of the H-A bond decreases as the energy required to break the bond decreases. That is HA becomes a stronger acid.

As the size of A increases down a group in the periodic table H-A bond strength decreases and so the acid strength increases.

As electronegativity of A increases, the strength of the acid also increases.

General Trends in AcidityThe stronger an acid is at donating H+, the

weaker the conjugate base is at accepting H+

Higher the oxidation number of an acid , stronger is the oxyacidH2SO4 > H2SO3 ; HNO3 > HNO2

Cations are stronger than acids than neutral molecule and neutral acids are stronger than anions.H3O+ > H2O > OH- ; NH4

+ > NH3 > NH2-

Bases have an opposite trend.

Common ion effect Reducing the concentration of hydrogen ions is called

the common ion effect It can be defined as a shift of the equilibrium on adding

a substance that provides more of an ionic species already present in the dissociation equilibrium.

Common ion effect is based on the chatelier’s principle.

Hydrolysis of salts and the pH of their solutions Salts are formed by the reactions between acids and

bases in definite proportions which afterwards undergo ionization in water.

The cations and anions formed on ionization of salts either exist as hydrated ions in aqueous solution or interact with water to reform corresponding acids/bases. The later process of interaction between water and cations or anions or both of the salts is called hydrolysis.

We can say that the degree of hydrolysis is independent of concentration of solution and pH of such solutions is determined by their pK values.

The pH of solution can be greater to 7 , if the difference is positive and it will be less than 7 if the difference is negative.

)

Buffer solutions The solutions which resist change in pH on dilution or with the

addition of small amount of acid or alkali are called buffer solutions.

Buffer solutions are prepared from the knowledge of pKa and pKb of base and controlling the ratio of salt and acid or salt and base.

Solubility equilibria of sparingly soluble salts. Solubility of salts depends on lattice enthalpy of the

salts and the solvation enthalpy of the ions in the solution.

For a salt to dissolve in a solvent the strong forces of attraction between its ions must be overcome by the ion-solvent interactions.

The solvation enthalpy of ions is referred to as solvation which is always negative that is energy released in the process of solvation.

The amount of solvation enthalpy depends on the nature of the solvent.

In case of non polar solvent, solvation enthalpy is small and hence not sufficient to overcome the lattice enthalpy of the salt.

Salt does not dissolve in a non polar solvent. As a general rule:- For a salt to be able to dissolve in a

particular solvent its solvation enthalpy must be greater than its lattice enthalpy so that the latter may be overcome by former.

Solubility of salts depend on its temperature.

Solubility product constant Solubility product constant is denoted by Ksp . A solid salt has the formula of :- with molar

solubility S in equilibrium with its saturated solution may be represented by the equation:-

Where

Solubility product constant is given by :-

Therefore,The term Ksp in the equation is given by Qsp when the

concentration of one or more species is not the concentration under equilibrium. Obviously then Ksp = Qsp but otherwise it gives the direction of the process of precipitation or dissolution.

Common ion effect of solubility of ionic salts If we increase the concentration of any one of the ions , it should combine

with the ion of its opposite charge and some of the salt will be precipitated once again.

Similarly if the concentration of one of the ions is decreased more salt will dissolve to increase the concentration of both the ions where it will be again precipitated.

The solubility of salts of weak acids like phosphates increases at lower pH. This is because at lower pH the concentration of the anion decreases due to

protonation. This inturn will increase the solubility of the salt. Protonation:- protonation is the process is the addition of a proton (H+)

to an atom molecule , or  ion, forming the conjugate acid