Law of Mass Action

The law of mass action was introduced by Cato Guldberg and Peter Wage in 1864. This law states that the rate of a chemical reaction at a given temperature and time is directly proportional to the product of the active masses of the reactants or directly proportional to the product of the molar concentrations of the reactants each raised to a power equal to the corresponding stoichiometric coefficient that appears in the balanced chemical equation.

The active mass is the mass of the reactant that takes part in the chemical reaction. It is expressed as the molar concentration of a substance per unit volume of it. It is expressed in mol dm^-3.

The law of mass action is applicable to all irreversible reactions. The chemical reactions that take place in an open container or where precipitate is formed are irreversible chemical reactions. In reversible reactions, the law of mass action applies to both the forward and backward reactions.

Mathematical Expression of the Law of Mass Action

Let us take a chemical reaction wherein A and B are reacting with each other

A + B → Products

Now, as per the law of mass action, the rate of reaction 'R' is given below;

R ∝ A B

For a general reaction such as aA + bB → Products, the rate of reaction according to the law of Mass Action is as follows;

aA + bB → Products

R ∝ A^a B^b

How to derive the law of mass action

Let us consider a reversible reaction at equilibrium as shown below;

aA + bB ⇌ cC + dD

Now, as per the law of mass action, the forward reaction will be directly proportional to the concentration of actives masses of A and B

R_f ∝ [A]^a [B]^b

or

R_f = K_f [A]^a [B]^b, where K_f is the rate constant of the forward reaction

Similarly, the backward reaction rate is given below;

Rb ∝ [C]^c [D]^d

Or

R^b= K_b[C]^c [D]^d, where R^b is the rate constant of backward reaction

Now, as this reaction is at equilibrium, so forward and backward reactions are occurring at the same speed.

So, R_f = R_b

Or

K_f [A]^a [B]^b = K_b[C]^c [D]^d

So, K_f / K_b = [C]^c [D]^d / [A]^a [B]^b

Or, K_c = [C]^c [D]^d / [A]^a [B]^b, where K_c is known as the equilibrium constant.

So, we can say that in the law of mass action equation, Kc (equilibrium constant) refers to the ratio of the product of the concentrations of products to the product of the concentrations of the reactants at the equilibrium and where their concentrations are raised to their stoichiometric coefficients in the balanced chemical equation.

Equilibrium Constant expression in terms of partial pressure or for gaseous reactions

What is Partial Pressure?

The pressure exerted by a gas in a mixture of gases when it occupies the same volume alone is called partial pressure. Each gas in a mixture of gases exerts pressure. The total pressure exerted by the mixture of gases is the sum of the partial pressures of all the gaseous components.

Let us take a chemical reaction where reactants (A and B) are gases or in the gaseous state and products (C and D) are also in the gaseous state and partial pressures of reactants and products are given. Here, we don't have the molar concentration, so, we can calculate the equilibrium based on the partial pressure as described below;

a A + b B ⇌ c C + d D

We cannot determine Kc (equilibrium constant) here as we don't have molar concentration. So, here, the equilibrium constant becomes Kp, where p represents partial pressure.

Now, Kp = [P^C]^c [p^D]^d / [p^A]^a [p^B]^b

Where, P^C, P^D, P^A and P^B are partial pressures of C, D, A and B respectively.

Concentration Quotient

It refers to the ratio of the product of the equilibrium concentration of the products to that of the product of the equilibrium concentrations of the reactants at a given temperature and when each concentration term is raised to the power equal to the stoichiometric coefficients of the respective reactant or product in the balanced chemical equation. It is denoted by Qc and is also known as concentration ratio.

At equilibrium, the concentration quotient is equal to the equilibrium constant Kc.

The concentration quotient plays an important role in predicting the direction in which the net reaction is proceeding when the concentrations or partial pressures of reactants and products are given.

For example;

If Qc > Kc, the backward reaction is occurring, towards the reactants.

If Qc < Kc, the forward reaction is taking place, in the direction of products.

If Qc = Kc, the reaction is in the equilibrium state, no net reaction taking place as the rate of the forward reaction is the same as the backward reaction.