Law of mass action

The law of mass action correlates the rate of a chemical reaction and the concentration of the reactants. C.M. Guldberg and P. Waage

(1864-67) suggested this relationship. This law states that, at a constant temperature and pressure, the rate of a chemical reaction is directly proportional to the product of the molar concentration of the reactants each raised to a power equal to the corresponding stoichiometric coefficient, which appears in the balanced chemical equation.

For a reaction,

According to the law of mass action,

Rate of reaction [A]^a[B]^b

or Rate of reaction = K[A]^a [B]^b

where 'K' is a proportionality constant known as 'rate constant'.

It must be noted here that the law of mass action is valid for an individual single-step reaction.

Consider a reversible reaction,

aA + bB

cC + dD

Then, according to the law of mass action,

Rate of the forward reaction, R_f [A]^a [B]^b

or Rate of the forward reaction, R_f = k_f [A]^a [B]^b

Similarly,

Rate of the backward reaction, R_b [C]^c [D]^d

or Rate of the backward reaction, R_b = k_b[C]^c [D]^d

At equilibrium, the two rates become equal, i.e.,

Rate of the forward reaction = Rate of the backward reaction

So, at equilibrium

k_f [A]^a [B]^b = k_b [C]^c [D]^d

The above equation is the law of chemical equilibrium. This law states:

'For a reversible reaction at equilibrium, the ratio of the product of the concentrations of the products to the product of the concentrations of the reactants each raised to a power equal to the corresponding stoichiometric coefficient in the balanced chemical equation at a constant temperature is constant. This constant is called equilibrium constant'.

For a homogeneous chemical equilibrium, when the concentration of the reactants and products is expressed in moles per litre unit, the equilibrium constant is written as K_c and is given by,

Further, if the reaction is a homogeneous gas phase reaction then the molar concentration of a substance is directly proportional to its partial pressure 'p' at constant temperature. In that case, the equilibrium constant is expressed in terms of partial pressure of the reactants and products. Such an equilibrium constant is denoted by K_p. Then similar to the above equation one can write

K_c and K_p are different forms of the equilibrium constant of a reaction.