Question

An aqueous solution contains $0.10\mathrm{M}{\mathrm{H}}_2\mathrm{S}$ and $0.20\mathrm{M}\mathrm{HCl}$. If the equilibrium constants for the formation of ${\mathrm{HS}}^{-}$ ions from ${\mathrm{H}}_2\mathrm{S}$ is $1.0\times {10}^{-7}$ and that of ${\mathrm{S}}^{2-}$ from ${\mathrm{HS}}^{-}$ ions is $1.2\times {10}^{-13}$ then the concentration of ${\mathrm{S}}^{2-}$ ions in an aqueous solution is :

• A. $3\times {10}^{-20}$
• B. $6\times {10}^{-21}$
• C. $5\times {10}^{-19}$
• D. $5\times {10}^{-8}$

Answer 1

The correct option is A

$3\times {10}^{-20}$

Explanation for the correct option:

(A) Formation of ${\mathrm{HS}}^{-}$ from ${\mathrm{H}}_2\mathrm{S}$,

${\mathrm{H}}_2\mathrm{S}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{HS}}^{-}\left(\mathrm{aq}\right)$

$K_{a_1}=\frac{\left[H{S}^{-}\right]\left[H^{+}\right]}{\left[H_{2}S\right]}$………………………………1

Formation of ${\mathrm{S}}^{2-}$ from ${\mathrm{HS}}^{-}$

${\mathrm{HS}}^{-}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{S}}^{2-}\left(\mathrm{aq}\right)$

$K_{a_2}=\frac{\left[H^{+}\right]\left[S^{2-}\right]}{\left[H{S}^{-}\right]}$………………………………..2

$\mathrm{K}={\mathrm{K}}_{{\mathrm{a}}_1}\times {\mathrm{K}}_{{\mathrm{a}}_2}$

$=$ $\frac{\left[H{S}^{-}\right]\left[H^{+}\right]}{\left[H_{2}S\right]}$$\times \frac{\left[H^{+}\right]\left[S^{2-}\right]}{\left[H{S}^{-}\right]}$

$=$$\frac{{\left[H^{+}\right]}^2\left[S^{2-}\right]}{\left[H_{2}S\right]}$

$\frac{{\left[H^{+}\right]}^2\left[S^{2-}\right]}{\left[H_{2}S\right]}$ $=$${10}^{-7}\times 1.2\times {10}^{-20}$

$\frac{{\left[H^{+}\right]}^2\left[S^{2-}\right]}{\left[H_{2}S\right]}$ $=$ $1.2\times {10}^{-20}$

${\mathrm{H}}_2\mathrm{S}\left(\mathrm{aq}\right)\rightleftharpoons 2{\mathrm{H}}^{+}\left(\mathrm{aq}\right)+{\mathrm{S}}^{2-}\left(\mathrm{aq}\right)$

Given, at t = 0; $\left[H^{+}\right]=0.2$ $\left[H_{2}S\right]=0.1$

$K=\frac{{\left[H^{+}\right]}^2\left[S^{2-}\right]}{\left[H_{2}S\right]}$$=\frac{{\left[0.2\right]}^2\times {\left[S^{2-}\right]}^{}}{\left[0.1\right]}$$=$

So, $\left[S^{2-}\right]=1.2\times {10}^{-20}\times 0.1\times {\left(0.2\right)}^2$

$=3\times {10}^{-20}$

Explanation for the incorrect options:

(B) From the above calculation, we can see that the calculated value is not equal to $6\times {10}^{-21}$.

(C) From the above calculation, we can see that the calculated value is not equal to $5\times {10}^{-19}$.

(D) From the above calculation, we can see that the calculated value is not equal to $5\times {10}^{-8}$.

Hence, option (A) is correct.