A solution is saturated with gas to yield a steady concentration of . If is added to this solution u — Ionic Equilibrium Chemistry Question
Question
A solution is saturated with $H_2S$ gas to yield a steady concentration of $0.1 \text{ M } H_2S$. If $HCl$ is added to this solution until the $[H^+]$ is exactly $0.2 \text{ M}$, calculate the final $[S^{2-}]$ concentration. Given $K_1 = 1.0 \times 10^{-7}$ and $K_2 = 1.2 \times 10^{-13}$ for $H_2S$. If the answer is $y \times 10^{-20} \text{ M}$, enter $y$.
💡 Solution & Explanation
For a diprotic acid, the overall dissociation constant $K_{eq} = K_1 \times K_2 = 1.0 \times 10^{-7} \times 1.2 \times 10^{-13} = 1.2 \times 10^{-20}$. The expression is $K_{eq} = \frac{[H^+]^2[S^{2-}]}{[H_2S]}$. Rearranging for $[S^{2-}]$, we get $[S^{2-}] = \frac{K_{eq}[H_2S]}{[H^+]^2}$. Plugging in the values: $[S^{2-}] = \frac{1.2 \times 10^{-20} \times 0.1}{(0.2)^2} = \frac{1.2 \times 10^{-21}}{0.04} = 30 \times 10^{-21} = 3 \times 10^{-20} \text{ M}$. Thus, $y = 3$.