Define law of mass action

P. Waage and C.M. Guldberg derived a relationship in 1864 to determine the concentration and composition of reactants and products, which is named as law of mass action. According to law of mass action the product of active masses of reactants is directly proportional to the rate of that particular reaction. The term active masses represents the concentration of reactions in moles per dm³, thus the rate of reaction directly depends upon the concentration of reactants. This law can be explained by taking a general example of a reaction with two reactants and products. An example is given as follows

In above equation A and B represent the reactants of a reaction, while C and D represent the products. The Square brackets [] around reactants and products indicates the concentration of these substances.

As the law of mass action states that the rate of a forward reaction is directly proportional to the concentration of reactants given in moles per dm³, thereby the rate of forward reaction for equation 1 can be written as follow

R_f α [A] [B]

R_f = k_f [A] [B]

Where R_f represents the rate of forward reaction, [A] and [B] are molar concentrations of reactants and k_f is proportionality constant for this reaction.

Similarly, rate of reverse reaction for equation 1 can be written as follow

R_r α [C] [D]

R_r = k_r [C] [D]

Where R_r is the rate of reverse reaction, k_r is the proportionality constant and [C] and [D] are molar concentrations of reactants for a reverse or backward reaction.

At the stage of equilibrium the rate of forward reaction is always equal to the rate of reverse reaction.

R_f = R_r

Putting the values of R_f and R_r

k_f [A] [B] =k_r [C] [D]

By rearranging above equation

Ratio of two rate constants is equal to equilibrium constant K_c, thus above equation can be written as follows

It can also be written as

For a balanced chemical equation rate constant can be written as follows

Where a, b, c and d are number of moles of reactants (A & B) and products (C & D) and are known as coefficients of balanced chemical reaction.

Equilibrium constant have no units as concentrations of all the reactants and products are given in number of moles per dm³, thus it cancels out with each other.