Question

Determine the pH of a $0.05M$ aqueous solution of ammonium sulphate, $k_b$ of ammonia is $2\times 10^{-5}$ ?

• A. 4.30
• B. 5.15
• C. 7.0
• D. 8.75

Answer 1

Answer: (B)

The hydrolysis reaction is
$N{H}_4^{+}+H_{2}O\rightleftharpoons N{H}_{4}OH+H^{+}$
$K_h=\frac{\left[N{H}_{4}OH\right]\left[H^{+}\right]}{\left[N{H}_4\right]}=\frac{K_w}{K_5}=5\times 10^{-10}$
$5\times 10^{-10}=\frac{{\left[H^{+}\right]}^2}{c}\left\{\because \left[N{H}_{4}OH\right]=\left[H^{-}\right]\right\}$
$\left[H^{+}\right]=\sqrt{5\times 10^{-10}\times 2\times 0.05}$
$\left[H^{+}\right]=7\times 10^{-6}\Rightarrow pH=5.15$