Calculate the concentration in a saturated () solution to which enough has been added to produce a s — Ionic Equilibrium Chemistry Question
Question
Calculate the $[S^{2-}]$ concentration in a saturated ($0.1 \text{ M}$) $H_2S$ solution to which enough $HCl$ has been added to produce a steady $[H^+]$ of $2 \times 10^{-4} \text{ M}$. (Given $K_1 = 10^{-7}, K_2 = 10^{-14}$ for $H_2S$)
Answer: A
💡 Solution & Explanation
For a diprotic acid like $H_2S$, the overall dissociation constant is $K = K_1 \times K_2 = \frac{[H^+]^2[S^{2-}]}{[H_2S]}$. Rearranging for $[S^{2-}]$, we get $[S^{2-}] = \frac{K_1 K_2 [H_2S]}{[H^+]^2}$. Substituting the known values: $[S^{2-}] = \frac{10^{-7} \times 10^{-14} \times 0.1}{(2 \times 10^{-4})^2} = \frac{10^{-22}}{4 \times 10^{-8}} = 0.25 \times 10^{-14} = 2.5 \times 10^{-15} \text{ M}$.
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