Question

Which is the correct alternate for hydrolysis constant of $N{H_4}CN$ ?
A. $\sqrt {\dfrac{{{K_w}}}{{{K_a}}}} $
B. $\dfrac{{{K_w}}}{{{K_a} \times {K_b}}}$
C. $\sqrt {\dfrac{{{K_w}}}{c}} $
D. $\dfrac{{{K_a}}}{{{K_b}}}$

Answer 1

Hint: The hydrolysis constant is the rate constant for a hydrolysis reaction. In general, the hydrolysis constant for any reaction equals the product of the hydronium ion concentration, the base concentration, and the acid concentration. Here we will individually break the reactions into acid-base bases and compute the hydrolysis constant.

Complete Step by Step Solution:
Both cationic and anionic hydrolysis occur in weak acid and base salts. It produces a weak base during cationic hydrolysis and a weak acid during anionic hydrolysis.
$N{H_4}CN$ is a salt which is formed from weak basic and weak acid.
Additionally, we are aware that neutralisation is the opposite of salt hydrolysis.
$N{H_4}OH + HCN \rightleftarrows N{H_4}CN + {H_2}O$
On hydrolysis, breaking the reaction into two forms i.e., acidic and basic we get,
$N{H_4}OH \rightleftarrows NH_4^ + + O{H^ - }$

The equilibrium constant for the above reaction can be written as
${K_b} = \dfrac{{[NH_4^ + ][O{H^ - }]}}{{[N{H_4}OH]}}$ …(1)
Similarly for acidic reaction
$HCN \rightleftarrows {H^ + } + C{N^ - }$

The equilibrium constant for the above reaction can be written as
${K_a} = \dfrac{{[{H^ + }][C{N^ - }]}}{{[HCN]}}$ …(2)
Also, the ${K_w}$ is defined as multiplication of concentration of ${H^ + }$ and $O{H^ - }$
On hydrolysis of $N{H_4}CN$
$N{H_4}CN \rightleftarrows NH_4^ + + C{N^ - }$
$NH_4^ + + {H_2}O \rightleftarrows N{H_4}OH + {H^ + }$ …(3)
$C{N^ - } + {H_2}O \rightleftarrows HCN + O{H^ - }$ …(4)

On adding equation 3 and 4 we get,
$NH_4^ + + C{N^ - } + {H_2}O \rightleftarrows N{H_4}OH + HCN$
Now hydrolysis constant of above reaction is given by,
${K_h} = \dfrac{{[N{H_4}OH][HCN]}}{{[NH_4^ + ][C{N^ - }]}}$
${K_h} = \dfrac{{{K_w}}}{{{K_a} \times {K_b}}}$
Hence the hydrolysis constant of $N{H_4}CN$ is given by ${K_h} = \dfrac{{{K_w}}}{{{K_a} \times {K_b}}}$
So, option B is correct.

Note: The ionisation constant serves as a measure for the acid's strength; the higher the Ka value, the more hydrogen ions are released per mole of solution and the strength of the acid. When determining whether a species will donate or accept protons at a particular pH level, ${K_a}$ , ${K_a}$ are the most useful parameters. They describe how much an acid or base has ionised.