Question

Derive an expression for the hydrolysis constant and degree of hydrolysis of salt of strong acid and weak base.

Answer 1

Let us consider the reactions between a strong acid, HCl, and a weak base, NH₄OH, to produce salt, NH₄Cl, and water.

\[\ce{HCl_{(aq)} + NH4OH_{(aq)} ⇌ NH4Cl_{(aq)} + H2O_{(l)}}\]

In aqueous solution NH₄Cl is completely dissociated as follows:

\[\ce{NH4Cl_{(aq)} -> NH^+_{4(aq)} + Cl^-_{( aq)}}\]

NH₄⁺ is a strong conjugate acid of the weak base NH₄OH and it has a tendency to react with OH^– from water to produce unionised NH₄OH shown below.

\[\ce{NH^+_{4(aq)} + H2O_{(l)} ⇌ NH4OH_{(aq)} + H^+_{( aq)}}\]

There is no such tendency shown by Cl^– and therefore [H⁺] > [OH^–] the solution is acidic and the pH is less than 7.

As discussed in the salt hydrolysis of a strong base and weak acid. In this case, also, we can establish a relationship between the K_a and K_b as K_h.K_b = K_w

Let us calculate the K_b value in terms of the degree of hydrolysis (h) and the concentration of salt K_h = h² C

[H⁺] = `sqrt("K"_"h"."C")`

[H⁺] = `sqrt("K"_"w"/"K"_"b"."C")`

pH = –log [H⁺]

= `-log ("K"_"w"/"K"_"b"."C")^(1/2)`

= `-1/2 log "K"_"w" - 1/2 log "C" + 1/2 log "K"_"b"`

pH = `7- 1/2 "pK"_"b" - 1/2 log "C"`