# Law Of Mass Action Or Law Of Chemical Equilibrium

The concentration of reactants and products, at equilibrium, are constant at a given temperature. Do the equilibrium concentrations of these substances have any relation? Can equilibrium constant be expressed in other terms?Let’s try to answer these questions.

Consider the following simple reversible reaction where A and B are reactants, C and D are the products.

A + B  $⇌$ C + D

A mixture of products and reactants at the equilibrium state is called equilibrium mixture. From experimental studies, it is observed that the concentration of chemical equilibrium mixtures has a relation. It can be represented by equilibrium equation and is given as follows:

$K_c$ = $\frac{[C][D]}{[A][B]}$

Kis called the equilibrium constant. The concentration of A at equilibrium is represented as [A] (similarly for B, C, and D), the stoichiometric coefficients of the reactants and products are 1. Now, what if the coefficients are different? Will the equation change? Well, it is experimentally observed that the equation does depend on the coefficients and is given by the law of chemical equilibrium.

The product of concentrations of the products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentrations of the reactants raised to their individual stoichiometric coefficients has a constant value (equilibrium constant) at a given temperature. This is known as the equilibrium law or law of chemical equilibrium or law of mass action.

For a balanced reaction of the type,

a A + b B $⇌$   c C + d D

According to the law of mass action, the constant value obtained by relating equilibrium concentrations of reactants and products is called equilibrium constant. For the forward reaction, this is given by

$K_c$ = $\frac{[C]^c[D]^d}{[A]^a[B]^b}$

The equilibrium constant for the reverse reaction is the inverse of forward reaction and is given by:

$K’_c$ = $\frac{1}{K_c}$ = $\frac{[C]^c[D]^d}{[A]^a[B]^b}$

If the coefficients of the chemical equation are multiplied by a factor ‘n’ then the equilibrium constant is raised by the power ‘n’ i.e. the constant becomes $K_c^n$.

 Equilibrium Constant Representation Expressed in terms of: Expressed as: Kc Concentrations of reactants and products $\frac{[C]^c[D]^d}{[A]^a[B]^b}$ Kp Partial pressures of reactants and products. (only for the substances which are in gaseous state) $\frac{p_{C}^{c}p_{D}^{d}}{p_{A}^{a}p_{B}^{b}}$ Kx Mole fractions of reactants and products $\frac{[X_C]^c[X_D]^d}{[X_A]^a[X_B]^b}$

### Relation between Kc, Kp and Kx:

$K_p$ = $K_c (RT)^{∆n_g}$

$K_x$ = $K_p (RT)^{∆n_g}$

Where,

$∆n_g$ = moles of gaseous products – moles of gaseous reactants.

Kc is the equilibrium constant expressed regarding concentration, similarly Kp is shown regarding partial pressures of the substances and K x is expressed regarding mole fraction.

For more insight on applications of the equilibrium constant to predict the nature of reactions download Byju’s- the learning app.

#### Practise This Question

For the reaction PCl5 (g)  PCl3 (g) + Cl2 (g) if we start with only a moles of PCl5
PCl5PCl3Cl2(g)Moles t=0a00Moles At Eq.a(1α)aαaα
α is called the degree of dissociation - True or false?