Question

What is the $pH$ (nearest integer) of a solution made by dissolving $0.05$ litre ${NH}_3$ gas at $NTP$ and $0.27g$ ${NH}_{4}Cl$ in $50mL$ solution? $K_b$ for ${NH}_{4}OH=1.8\times {10}^{-5}$.

Answer 1

First, calculate the pKb of ammonia.

$p{K}_b=-log{K}_b=-log1.8\times {10}^{-5}=4.7447$

Now calculate the number of moles of ammonia present.

$\frac{0.05L}{22.4L}=2.232\times {10}^{-3}$ moles

Now calculate the number of moles of ammonium chloride.

$\frac{0.27g}{53.5g/mol}=5.047\times {10}^{-3}mol$

Now calculate the pOH of the buffer solution.

$pOH=p{K}_b+log\frac{\left[N{H}_{4}Cl\right]}{\left[N{H}_3\right]}=4.7447+log\frac{5.047}{2.232}=4.7447+0.354=5.099$

Hence, the pH of the buffer solution is $14-5.099=8.901\approx 9$.