Question

A $40ml$ sample of an aqueous solution of the methylamine at $25^{\circ }C$ is titrated with $0.15MHCl$ and the equivalence point is reached when $40ml$ of the acid have been added. The $pH$ at the equivalence point is
(Given : $K_a$ for $C{H}_{3}N{H}_3^{+}$is $4/3\times 10^{-11}$ ).

Answer 1

Answer: 6

$K_a=\frac{\left[C{H}_{3}N{H}_2\right]\left[H_3{O}^{+}\right]}{\left[C{H}_{3}N{H}_3^{+}\right]}$
$=\frac{\frac{6}{80}{h}^2}{(1-h)}\simeq \frac{6}{80}{h}^2$
$h=\sqrt{\frac{K_a\times 80}{60}}$
$\left[H_3{O}^{+}\right]=\frac{6}{80}h$
$\sqrt{K_a\times \frac{6}{80}}=\sqrt{\frac{4}{3}\times 10^{-11}\times \frac{6}{80}}$
$=\sqrt{10^{-12}}$
$\left[H_3{O}^{+}\right]=10^{-6}M$
$pH=6.0$