Question

In a hydrolysis of a salt of weak acid and strong base ${{A}^{-}}+{{H}_{2}}O\rightleftharpoons HA+O{{H}^{-}}$, the hydrolysis constant $({{K}_{h}})$is equal to:
A. $\dfrac{{{K}_{w}}}{{{K}_{a}}}$
B. $\dfrac{{{K}_{w}}}{{{K}_{b}}}$
C. $\sqrt{\dfrac{{{K}_{a}}}{C}}$
D. $\dfrac{{{K}_{w}}}{{{K}_{a}}\times {{K}_{b}}}$

Answer 1

Hint: Hydrolysis is the chemical breakdown of the substances by water. A solution of weak acid mix with a solution of strong base to produce the conjugate base of weak acid and the conjugate acid of strong base. The conjugate acid of the strong base is a weaker acid than water and has little effect on the acidity of the resulting solution.

Complete Step by Step Answer:
Consider the hydrolysis of weak acid and strong base.

Let us consider the general hydrolysis reaction of a salt of weak acid and strong base which can be written as:
${{A}^{-}}+{{H}_{2}}O\rightleftharpoons HA+O{{H}^{-}}$
This leads to the equilibrium constant expression
${{K}_{h}}=\dfrac{[HA][O{{H}^{-}}]}{[{{A}^{-}}][{{H}_{2}}O]}$

The concentration of water is very large and is regarded as practically constant.
${{K}_{h}}=\dfrac{[HA][O{{H}^{-}}]}{[{{A}^{-}}]}$
And ${{K}_{w}}=[{{H}^{+}}][O{{H}^{-}}]$

For the dissociation of a weak acid HA,
$HA\rightleftharpoons {{H}^{+}}+{{A}^{-}}$
The acid dissociation constant ${{K}_{a}}$is expressed as:
${{K}_{a}}=\dfrac{[{{H}^{+}}][{{A}^{-}}]}{[HA]}$
Then $\dfrac{{{K}_{w}}}{{{K}_{a}}}=\dfrac{[O{{H}^{-}}][HA]}{[{{A}^{-}}]}$=${{K}_{h}}$
Hence $\dfrac{{{K}_{w}}}{{{K}_{a}}}={{K}_{h}}$
Thus, Option (A) is correct.

Note: Solubility product is a type of equilibrium constant whose value depends on the temperature. It is denoted by ${{K}_{sp}}$. It usually increases with the increase in temperature because of the increased solubility. Remember that solubility and the solubility product are different from each other. Solubility of a substance in a solvent is the highest amount of solute that can be dissolved in a solvent whereas the solubility product is an equilibrium constant that gives the equilibrium between the solid solute and its ions that are dissolved in the solution