Question

An aqueous solution of a metal bromide $M{Br}_2$ $\left(0.05M\right)$ is saturated with $H_{2}S$. The minimum $pH$ at which $MS$ will precipitate is $X$ ($K_{sp}$ for $MS=6.0\times {10}^{-21}$). Value of nearest integer to X is _______.

[Concentration of saturated $H_{2}S=0.1M$; $K_1={10}^{-7}$ and $K_2=1.3\times {10}^{-13}$ for $H_{2}S$.]

Answer 1

For the precipitation of $MS$ from a solution of $M{Br}_2$ by passing $H_{2}S$
$K_{{sp}_{MS}}=\left[M^{2+}\right]\left[S^{2-}\right]$
or $6\times {10}^{-21}=\left[0.05\right]\left[S^{2-}\right]$
or $\left[S^{2-}\right]=1.2\times {10}^{-19}M$
i.e., precipitation of $MS$ will start when $H_{2}S$ provides
$1.2\times {10}^{-19}M$ ion of $S^{2-}$
For $H_{2}S$
$H_{2}S\rightleftharpoons 2H^{+}+S^{2-}$
$K=K_1\times K_2=\frac{\left[H^{+}\right]\left[S^{2-}\right]}{\left[H_{2}S\right]}$
or ${10}^{-7}\times 1.3\times {10}^{-13}=\frac{\left[H^{+}\right][1.2\times {10}^{-19}]}{0.1}$
or $\left[H^{+}\right]=1.04\times {10}^{-1}$
$\therefore$ $pH=0.9826$