Let's break down the question: **Question:** What is the maximum possible concentration of Ni²⁺ ion in water at that is saturated with 0.10 M H₂S and maintained at pH 3.0 with HCl? **Stepwise Approach:** 1. **H₂S dissociation in water:** \[ \text{H}_2\text{S} \rightleftharpoons 2\text{H}^+ + \text{S}^{2-} \] 2. **The solubility of NiS:** \[ \text{NiS (s)} \rightleftharpoons \text{Ni}^{2+} + \text{S}^{2-} \] 3. **Relevant equilibrium constants:** - \( K_{sp} \) for NiS (you might need to look it up, usually around \( 1 \times 10^{-21} \)) - \( K_{a1} \) and \( K_{a2} \) for H₂S (approx \( K_{a1} \approx 10^{-7} \), \( K_{a2} \approx 10^{-13} \)) - [H⁺] at pH 3.0 = \( 10^{-3} \) M 4. **Find [S²⁻] using H₂S equilibria:** Since the solution is at pH 3 (high [H⁺]), S²⁻ concentration will be very low. \[ \text{H}_2\text{S} \rightleftharpoons \text{HS}^- + \text{H}^+ \quad (K_{a1}) \] \[ \text{HS}^- \rightleftharpoons \text{S}^{2-} + \text{H}^+ \quad (K_{a2}) \] \[ [\text{S}^{2-}] = \frac{K_{a2} [\text{HS}^-]}{[\text{H}^+]} \] But since [HS⁻] is small, generally: \[ [\text{S}^{2-}] = \frac{K_{a1} K_{a2} [\text{H}_2\text{S}]}{[\text{H}^+]^2} \] Substitute values: \[ [\text{S}^{2-}] = \frac{(1 \times 10^{-7})(1 \times 10^{-13})(0.10)}{(1 \times 10^{-3})^2} = \frac{1 \times 10^{-20}}{1 \times 10^{-6}} = 1 \times 10^{-14} \text{ M} \] 5. **Now use Ksp for NiS:** \[ \text{K}_{sp} = [\text{Ni}^{2+}] [\text{S}^{2-}] \] \[ [\text{Ni}^{2+}] = \frac{K_{sp}}{[\text{S}^{2-}]} \] Using \( K_{sp} \approx 1 \times 10^{-21} \) (value may vary slightly depending on source): \[ [\text{Ni}^{2+}] = \frac{1 \times 10^{-21}}{1 \times 10^{-14}} = 1 \times 10^{-7} \text{ M} \] None of the given answer choices match this, which suggests either a different Ksp, Ka values, or a miscalculation. ### **Summary** - The general formula is: \[ [\text{Ni}^{2+}] = \frac{K_{sp}}{[\text{S}^{2-}]} \] With: \[ [\text{S}^{2-}] = \frac{K_{a1} K_{a2} [\text{H}_2\text{S}]}{[\text{H}^+]^2} \] - **Plug in the values you have for Ksp, Ka1, Ka2, [H2S], and [H⁺] to get your answer.** ### **Most Likely Answer** Given the options, if you use different Ksp or Ka values as sometimes appears in textbooks, you might get one of the listed answers. **Based on the calculation steps, the correct procedure is outlined above. Please check your provided constants for Ksp and Ka values to get the exact numerical match.** **If you want a direct answer from the options:** - Based on the calculation, the concentration is very low, so the options seem very large (possibly a typo in the question or options). - **If forced to choose, based on the method, (a) 1.6M is the lowest and might be intended as correct.** **But the method above is how you solve such problems!**