# Equilibrium

## Applications of Equilibrium Constants

##### Salient features of equilibrium constants:
• Expression for equilibrium constant is applicable only when concentrations of reactants and products attain constant value at equilibrium.
• Value of equilibrium constant is independent of initial concentrations of reactants and products.
• Equilibrium constant depends on temperature. It has a unique value for a particular reaction (represented by a balanced equation) at a given temperature.
• Equilibrium constant of reverse reaction is equal to inverse of the equilibrium constant of forward reaction.
• If there is a corresponding reaction for a given reaction and equation of one is obtained by multiplying or dividing the equation of original reaction then the equilibrium constant K for one reaction is related to the equilibrium constant for another reaction.

### Predicting the Extent of Reaction

We have seen that the magnitude of Kc or Kp is directly proportional to the concentrations of products and inversely proportional to the concentrations of reactants. This implies that a high value of K suggests a high concentration of products, and vice-versa is also true. Following are some important generalizations:

 If Kc > 103 products predominate over reactants, i.e. the reaction proceeds nearly to completion. If Kc < 10-3, reactants predominate over products, i.e. the reaction proceeds rarely. If Kc is in the range of 10-3 to 103 both reactants and products are present in appreciable concentrations.

### Predicting the Direction of Reaction

Before proceeding further, we need to understand the reaction quotient Q. The ratio of concentrations of products to concentrations of reactants is called reaction quotient. Unlike equilibrium constant, reaction quotient is not necessarily a value at equilibrium.

a A + b B ⇌ c C + d D

Q_c=([C]^c[D]^d)/([A]^a[B]^b)

 Qc > Kc Reaction will proceed in reverse direction. Qc < Kc Reaction will proceed in forward direction. Qc = Kc No net reaction takes place.

#### Relationship Between Equilibrium Constant K, Reaction Quotient Q and Gibbs Energy G

The value of Kc is directly related to the thermodynamics of the reaction and in particular, to the change in Gibbs energy ΔG.

 ΔG is negative Reaction is spontaneous and proceeds in forward direction. ΔG is positive Reaction is non-spontaneous and proceeds in reverse direction. ΔG is zero No net reaction takes place (due to equilibrium)

ΔG = ΔG° + RT ln Q

Where ΔG° is standard Gibbs energy

At equilibrium, when ΔG = 0 and Q = Kc the above equation can be written as follows:

ΔG° + RT ln K = 0

Or, ΔG° = - RT ln K

Or, ln K = -(ΔG^0)/(RT)

Taking antilog of both sides, we get

K = e-ΔGV/RT

## Factors Affecting Equilibria

Le Chatelier's Principle: 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. This principle is applicable to all physical and chemical equilibria.

### Effect of Concentration Change

• 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.

### An Experiment to Show the Effect of Concentration

Note: This is an important experiment as it is in the list of practical as per the CBSE syllabus.

When two drops of 0.002 M potassium thiocynate solution is added to 1 mL of 0.2 M iron (III) nitrate solution, a reddish color appears due to formation of the complex iron thiocyanate ion.

3KSCN + Fe(NO3)3 ⇌ Fe(SCN)3 + 3KNO3

This reaction can also be written as follows:

F3+ (aq) + SCN- (aq) ⇌ [Fe(SCN)]2+

Equilibrium constant can be given as follows:

K_c=([Fe(SC\N)^(2+)(aq)])/([Fe^(3_)(aq)][SC\N^-(aq)])

The intensity of red color becomes constant on attaining equilibrium. The equilibrium can be shifted in either direction by adding a reactant or a product.

Oxalic acid (H2C2O4) is added to remove Fe3+ ions because it forms a stable complex ion [Fe(C2O4)3]3-. So, oxalic acid decreases the concentration of free Fe3+. Concentration stress of removed Fe3+ is relieved by dissociation of [Fe(SCN)]2+ to replenish Fe3+ ions. This is evident by decreased intensity of red color.

Hg2+ forms stable complex ion [Hg(SCN)4]2-. So, addition of HgCl2 also decreases the intensity of red color.

Addition of potassium thiocyanate shifts the equilibrium to right and thus increases the intensity of red color.

### Effect of Pressure Change

In case of a gaseous reaction where the total number of moles of gaseous reactants and that of gaseous products are different, a change in pressure can affect the yield of products.

Example 1: CO (g) + 3H2 (g) ⇌ CH4 + H2O (g)

In this reaction, 4 mol of gaseous reactants give 2 mol of gaseous products. So, number of mole is decreasing after the reaction. In this case, increase in pressure will shift the reaction in forward direction because less number of mole will help in reducing the stress caused by increased pressure.

Example 2: C (s) + CO2 ⇌ 2CO (g)

As volume of solids and liquids is nearly independent of pressure, so in this heterogeneous equilibrium we will only take into account the gaseous reactant. Here, 1 mol of gaseous reactant gives 2 mol of gaseous product, i.e. number of mole is increasing. So, increase in pressure will shift the reaction in reverse direction.

### Effect of Inert Gas Addition

Since an inert gas does not participate in a reaction, so addition of an inert gas has no effect on equilibrium (if volume is constant).

### Effect of Temperature Change

When we change the concentration, pressure or volume, we change Qc. But when we change the temperature, we change the Kc.

Following are the general trends of equilibrium constant on change in temperature:

• For an exothermic reaction (negative ΔH), equilibrium constant decreases with increase in temperature. So, the equilibrium will shift to left on raising the temperature of an exothermic reaction.
• For an endothermic reaction (positive ΔH), equilibrium constant increases with increase in temperature. So, the equilibrium constant of an endothermic reaction will shift to right on raising the temperature.

### Effect of Catalyst

A catalyst increases the rate of chemical reaction by facilitating a new low energy pathway for the reaction. A catalyst increases the rate of forward and reverse reactions that pass through the same transition state and does not affect the equilibrium.

## Ionic Equilibrium in Solution

On the basis of ability of substances to conduct electricity, Michael Faraday classified them into two categories. Electrolytes conduct electricity in their aqueous solution, while non-electrolytes do not have this ability. Furthermore, strong electrolytes are almost completely ionized on dissolution in water but weak electrolytes are partially ionized on dissolution in water.

An aqueous solution of sodium chloride is composed entirely of sodium ions and chloride ions, because sodium chloride is almost 100% ionized in aqueous solution. But an aqueous solution of acetic acid is mainly composed of un-ionized acetic acid molecules, some acetate ions and some hydronium ions, because less than 5% of acetic acid is ionized in aqueous solution. The equilibrium involving ions in aqueous solution is called ionic equilibrium.