The ionisation constant of ammonium hydroxide is $1.77 \times 10^{-5}$ at $298 \mathrm{~K}$. Hydrolysis…

The ionisation constant of ammonium hydroxide is $1.77 \times 10^{-5}$ at $298 \mathrm{~K}$. Hydrolysis constant of ammonium chloride is
  1. $5.65 \times 10^{-10}$
  2. $6.50 \times 10^{-12}$
  3. $5.65 \times 10^{-13}$
  4. $5.65 \times 10^{-12}$

Solution

Given, $\mathrm{K}_{\mathrm{a}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=1.77 \times 10^{-5}$ $\begin{aligned} & \mathrm{NH}_4 \mathrm{OH} \rightleftharpoons \mathrm{NH}_4^{+}+\mathrm{OH}^{-} \\ & \mathrm{K}_{\mathrm{a}}=\frac{\left[\mathrm{NH}_4^{+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_4 \mathrm{OH}\right]}=1.77 \times 10^{-5} \end{aligned}$ Hydrolysis of $\mathrm{NH}_4 \mathrm{Cl}$ takes place as, $\mathrm{NH}_4 \mathrm{Cl}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{NH}_4 \mathrm{OH}+\mathrm{HCl}$ or $\mathrm{NH}_4^{+}+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{NH}_4 \mathrm{OH}+\mathrm{H}^{+}$ Hydrolysis constant, $\mathrm{K}_{\mathrm{h}}=\frac{\left[\mathrm{NH}_4 \mathrm{OH}\right]\left[\mathrm{H}^{+}\right]}{\left[\mathrm{NH}_4^{+}\right]} \ldots$ or $\mathrm{K}_{\mathrm{h}}=\frac{\left[\mathrm{NH}_4 \mathrm{OH}\right]\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_4^{+}\right]\left[\mathrm{OH}^{-}\right]}$ $\begin{aligned} \mathrm{K}_{\mathrm{h}} & =\frac{\mathrm{K}_{\mathrm{w}}}{\mathrm{K}_{\mathrm{a}}} \quad\left[\because\left[\mathrm{H}^{+}\right]\left[\mathrm{OH}^{-}\right]=\mathrm{K}_{\mathrm{w}}\right] \\ & =\frac{10^{-14}}{1.77 \times 10^{-5}} \\ & =5.65 \times 10^{-10} \end{aligned}$

Asked in: NEET 2009 (Screening)

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