Law of Chemical Equilibrium

According to this law, the ratio of product of concentration of products to the product of concentration of reactants, with each concentration term is raised to the power by its coefficient in overall balanced chemical equation, is a constant quantity at a given temperature and it is called equilibrium constant.

Derivation of law of chemical equilibrium

Let us consider for the following equilibrium

                              aA + bB ⇔ cC + dD

then, from Law of mass action

rate of forward reaction r₁ ∝ [A]^a [B]^b

or         r₁ = K_a [A]^a [B]^b and rate of reverse reaction r_­2 ∝ [C]^c [D]^d

            r₂ = K₂ [C]^c [D]^d

at equilibrium, r₁ = r₂

            ⇒ K₁ [A]^a[B]^b = K₂ [C]^c[D]^d

            ⇒ K₁/K₂ = [C]^c[D]^d/[A]^a[B]^b

K_c = K₁/K₂, an equilibrium constant in terms of active masses of reacting species.

                                          SO₂Cl_­2        ⇔       SO₂      +    Cl₂

            equilibrium conc.       a–x/V                    x/V               x/V (V is volume of container)

So,       [SO₂Cl₂] = a–x/V; [SO₂] = x/V = [Cl₂]

So,       K_c = (x/V)×(x/V)/(a–x/V) = x²/(a–x)V ⇒ K_c = x²/(a–x)×V