An acidified solution of 0 . 05   M   Zn 2 + is saturated with 0 . 1   M   H 2 S . What…

For $\mathrm{ZnS}$

${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{ZnS}\right)=\left[{\mathrm{Zn}}^{2+}\right]\times \left[{\mathrm{S}}^{2-}\right]=1.25\times {10}^{-22}$

$=0.05\times \left[{\mathrm{S}}^{2-}\right]=1.25\times {10}^{-22}$

$\left[{\mathrm{S}}^{2-}\right]=25\times {10}^{-22}$

For ${\mathrm{H}}_2\mathrm{S}$

$\underset{0.1\mathrm{M}}{{\text{H}}_2\text{S}}\rightleftharpoons 2{\text{H}}^{+}+\underset{25\times {10}^{-22}}{{\text{S}}^{2-}}$

${\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{H}}^{\text{'}}\right]\left[{\mathrm{S}}^{2-}\right]}{\left[{\mathrm{H}}_2\mathrm{S}\right]}=1\times {10}^{-21}$

$=\frac{{\left[{\mathrm{H}}^{+}\right]}^2\times 25\times {10}^{-22}}{0.1}=1\times {10}^{-21}$

${\left[{\mathrm{H}}^{+}\right]}^2=\frac{1}{25}$

$\left[{\mathrm{H}}^{+}\right]=\frac{1}{5}$

$\left[{\mathrm{H}}^{+}\right]=0.2 \mathrm{M}$