Q6(b). Hydrolysis constant and degree of hydrolysis of a weak base–strong acid salt

Salt BHCl (for example NH₄Cl) of initial concentration C mol L⁻¹; h = fraction hydrolysed. Cl⁻ is the conjugate base of a strong acid and does not react.

BH⁺ + H₂O ⇌ B + H₃O⁺

tabularl c c c & BH⁺ & B & H₃O⁺ initial & C & 0 & 0 equilibrium & C(1-h) & Ch & Ch tabular

Kₕ=([B][H₃O⁺])/([BH⁺])=((Ch)(Ch))/(C(1-h))=(Ch²)/(1-h)

Relation with K_b

Multiply numerator and denominator by [OH⁻]:

Kₕ=([B][H₃O⁺][OH⁻])/([BH⁺][OH⁻])=(K_w)/(K_b) (K_b=([BH⁺][OH⁻])/([B]))

Degree of hydrolysis and pH

• From (i) and (ii): (Ch²)/(1-h)=(K_w)/(K_b), a quadratic in h.
• For a weak base K_b is small, so h≪1 and 1-h≈1: Kₕ=Ch² ⇒ h=√((Kₕ)/(C))=√((K_w)/(K_bC)).
• [H₃O⁺]=Ch=√(KₕC)=√((K_wC)/(K_b)), so pH=12(pK_w-pK_b-log C).
• h increases on dilution (h∝ C^(-1/2)) and with temperature (since K_w increases).

for 0.1 M NH₄Cl, K_b=1.8×10⁻⁵: Kₕ=5.6×10⁻¹⁰, h=7.5×10⁻⁵, pH =5.13.