In the first dissociation of H2A:
molarity H2A(aq)↔ (HA)^-(aq) + H^+(aq)
initial 0.05 m 0 m 0 m
change -x +x +x
equilibrium 0.05-x x x
we can neglect X in [H2A] as it so small compared to the 0.05
so by substitution in Ka equation:
Ka1 = [HA][H] / [H2A]
2.2x10^-6 = X^2/0.05
X = √(2.2x10^-6)*(0.05)= 1.1x10^-7
X= 3.32x10^-4 m
∴ [H2A] = 0.05 - 3.32x10^-4 = 0.0497 m
[HA] = 3.32x10^-4 m
[H] = 3.32x10^-4 m
the second dissociation of H2A: when ka2 = 8.2x10^-9
HA-(aq) ↔ A^2- (aq) + H+(aq)
at equilibrium 3.32x10^-4 y 3.32x10^-4
Ka2 = [H+][A^2-] / [HA]
8.2x10^-9 = Y(3.32x10^-4)/(3.32x10^-4)
∴y = 8.2x10^-9 m
∴[A] = 8.2x10^-9 m
PH= -㏒[H+]
= -㏒(3.32x10^-4)= 3.479
[A]=8.2x10^-9 m
[H2A] = 0.0497 ≈ 0.05 m