pH OF Weak Acids and Bases:

Weak acids and bases are not completely ionised; an equilibrium is found to have been established between ions and unionised molecule. Let us consider a weak acid of basicity 'n'.

                       AH_n  ↔  A^n-  +   nH⁺

            i  = 0    -C        0          0

            t_eq      C(1-α)   Cα       nCα

            [H⁺] = nCα;  .·. pH = -log₁₀ [nCα]                ...... (i)

For monobasic and,  n=1

            pH = -log₁₀ [Cα]                                       ...... (ii)

Dissociation constant of acid K_a may be calculated as

            K_a = [A^n-][H⁺]ⁿ/[AH_n] = [Cα][nCα]ⁿ/[C(1-α)]

            =  α [nCα]ⁿ/(1-α)           For weak acids, α« 1

                                                  .·. (1-α) = 1

            = α[nCα ]ⁿ/(1-α)

               nCK_a = nCα [nCα ]ⁿ

            = [nCα ]⁽ⁿ⁺¹⁾

            = [nCα ] = [nCK_a]^1/(n+1)

               = [H⁺] = [nCK_a]^1/(n+1)

            .·. pH = -1/(n+1) log₁₀(nCK_a)              ...... (iii)

            For monobasic acid, n = 1

            pH = -log√CK_α                                ....... (iv)

            Since K_a = α[nCα]ⁿ

            ka/α = (nCα)ⁿ

            [nCα ] = [K_α/α]^1/n = [H⁺]

            pH = -1/n log₁₀(K_α/α)                          ..... (v)

            For n = 1       pH = -log₁₀(K_α/α)          ..... (vi)