Equation of dissociation of hydrocyanic acid, HCN will be given as:
HCN < ---------> H+ + CN–
Let α is the degree of ionization of HCN
Initial concentration:
[HCN] = 0.2
[H+] = 0
[CN–] = 0
Equilibrium concentration:
[HCN] = 0.2 (1 – α)
H+] = 0.2 α
[CN–] = 0.2 α
Ka = [H+] [CN–] / [HCN]
4.9 x 10-10 = (0.2 α) (0.2 α) / 0.2 (1 – α)
As, 1 – α ≈ 1
Therefore, 4.9 x 10-10 = (0.2 α) 2
α = (4.9 x 10-10 / 0.2)1/2
= 4.95 x 10-5
Hence, percent ionization = 0.00495 %