Question

What is ${{K}_{a}}$ of $ZnC{{l}_{2}}$?

Answer 1

Hint: When any acid or a base is added to a solution, it dissociates to some extent. This extent of dissociation when calculated for acids is called dissociation constant for an acid, denoted by ${{K}_{a}}$. The value for the base dissociation constant multiplied by acid dissociation constant is ${{K}_{a}}\times {{K}_{b}}=1\times {{10}^{-14}}$.

Complete answer:
The dissociation of any acid in the solution leads to formation of ions in a particular concentration. The concentration of the ions produced by the acid upon the concentration of the dissociated acid gives us dissociation constant for an acid, denoted by ${{K}_{a}}$.
$ZnC{{l}_{2}}$ is zinc chloride that acts as an acid, when dissolved in water undergoes a reaction to produce zinc hydroxide base, and hydrochloric acid. The reaction is, $ZnC{{l}_{2}}+2{{H}_{2}}O\rightleftharpoons Zn{{(OH)}_{2}}+2HCl$ , in ionic form this equation will be, $Z{{n}^{++}}+2{{H}_{2}}O\rightleftharpoons Zn{{(OH)}_{2}}+2{{H}^{+}}$ the dissociation constant for the acid zinc chloride will be calculated as,
${{K}_{a}}=\dfrac{[Zn{{(OH)}_{2}}][{{H}^{+}}]}{[Z{{n}^{++}}]}$
This ${{K}_{a}}$ is called a hydrolysis constant as zinc chloride is subjected to hydrolysis that produces the mentioned ions in the formula. The ${{K}_{a}}$ can also be expressed as assuming that the concentration of the $ZnC{{l}_{2}}$ solution is 0.001 M and the base dissociation constant ${{K}_{b}}$ for zinc hydroxide, we have,
$Zn{{(OH)}_{2}}\rightleftharpoons Z{{n}^{++}}+2O{{H}^{-}}$ , so dissociation constant for base will be,
${{K}_{b}}=\dfrac{[Z{{n}^{++}}]{{[O{{H}^{-}}]}^{2}}}{[Zn{{(OH)}_{2}}]}$
We have dissociation constant of water ${{K}_{w}}$as ${{K}_{w}}=[{{H}^{+}}][O{{H}^{-}}]$
Therefore the dissociation constant for acid will be, ${{K}_{a}}=\dfrac{{{K}_{w}}^{2}}{{{K}_{b}}}$
Hence, ${{K}_{a}}$ for $ZnC{{l}_{2}}$is ${{K}_{a}}=\dfrac{[Zn{{(OH)}_{2}}][{{H}^{+}}]}{[Z{{n}^{++}}]}$or ${{K}_{a}}=\dfrac{{{K}_{w}}^{2}}{{{K}_{b}}}$

Note:
By putting the values of dissociation constants of water and zinc hydroxide we can calculate the value of ${{K}_{a}}$ for $ZnC{{l}_{2}}$. For calculating these values it is important to know the concentration of the ionic species present in the solution. ${{K}_{a}}$ and ${{K}_{b}}$tells us the strength of acids and bases respectively through their dissociation.