Two weak monobasic acids HA and HB having equal concentrations of 0.5 M are present in solution at 25oC having dissociation constants as 3.5×10−10 and 4.5×10−10 respectively. Calculate the pH of the solution at given temperature.
Mixture of two weak monoprotic acids HA and HB with concentration C1 and C2 and degree of dissociation α1 and α2
For HA :
HA(aq)⇌H+(aq)+A−(aq)
at t=0 C1 0 0
at t=teq C1−C1α1 (C1α1+C2α2) C1α1
For HB :
HB(aq)⇌H+(aq)+B−(aq)
at t=0 C2 0 0
at t=teq C2−C2α2 (C1α1+C2α2) C2α2
Dissociation constant for HA Ka1 :
Ka1=(C1α1+C2α2)(C1α1)C1(1−α1)
Dissociation constant for HB Ka2 :
Ka2=(C1α1+C2α2)(C2α2)C2(1−α2)
Since α1 and α2 are very small in comparison to unity for weak monoprotic acids.So 1−α1≈1 and 1−α2≈1.
C1Ka1+C2Ka2 = (C1α1+C2α2)2
[H+] = C1α1+C2α2 = √C1Ka1+C2Ka2