An aqueous solution contains 0 . 10M H _ 2 S and 0 . 20MHCl . If...

$\begin{cases}HCl & \to & {H}^{+} & + & {Cl}^{-} \\ & & \left(0 . 2 + x + y\right) & & 0 . 2\end{cases}$$</p><p>$\begin{cases}{H}_{2}S & ⇌ & {H}^{+} & + & {HS}^{-} \\ \left(0 . 1 - x\right) & & \left(0 . 2 + x + y\right) & & \left(x - y\right)\end{cases}; {K}_{{a}_{1}} = {10}^{- 7}$</p><p>$\begin{cases}{HS}^{-} & \to & {H}^{+} & + & {S}^{2 -} \\ \left(x - y\right) & & \left(0 . 2 + x + y\right) & & \left(y\right)\end{cases}; {K}_{{a}_{2}} = 1 . 2 \times {10}^{- 13}$</p><p> </p><p>\left[{H}^{+}\right] = \left(0 . 2 + x + y\right)M = 0 . 2M$

${K}_{{a}_{1}} = \dfrac{\left[{H}^{+}\right]\left[{HS}^{-}\right]}{\left[{H}_{2}S\right]} = \dfrac{0 . 2 \times \left[{HS}^{-}\right]}{0 . 1 - x} = \dfrac{0 . 2\left[{HS}^{-}\right]}{0 . 1}$ ($x =$negligible)

\left[{HS}^{-}\right] = \dfrac{{K}_{{a}_{1}} \times 0 . 1}{0 . 2} = \dfrac{1}{2} \times {10}^{- 7}$</p><p>${K}_{{a}_{2}} = \dfrac{\left[{H}^{+}\right]\left[{S}^{2 -}\right]}{\left[{HS}^{-}\right]} = \dfrac{\left[0 . 2M\right]\left[{S}^{2 -}\right]}{\dfrac{1}{2} \times {10}^{- 7}}$</p><p>\left[{S}^{2 -}\right] = \dfrac{{K}_{{a}_{2}} \times \dfrac{1}{2} \times {10}^{- 7}}{0 . 2} = \dfrac{1 . 2 \times {10}^{- 13} \times \dfrac{1}{2} \times {10}^{- 7}}{0 . 2} = 3 \times {10}^{- 20}M$