Question

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

• A. 4.3
• B. 5.15
• C. 7
• D. 8.75

Answer 1

The correct option is B 5.15

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