Consider two Group IV metal ions X²⁺ and Y²⁺. A solution containing 0.01 M X²⁺ and 0.01 M Y²⁺ is saturated with H₂S. The pH at which the metal sulphide YS will form as a precipitate is ____ . (Nearest integer) (Given: Ksp(XS) = 1 × 10⁻²² at 25°C, Ksp(YS) = 4 × 10⁻¹⁶ at 25°C, [H₂S] = 0.1 M in solution, Ka₁ × Ka₂ (H₂S) = 1.0 × 10⁻²¹, log 2 = 0.30, log 3 = 0.48, log 5 = 0.70)

Consider two Group IV metal ions X2 plus and Y2 plus saturated with H2S pH of precipitation question

Q. Consider two Group IV metal ions X²⁺ and Y²⁺.

A solution containing 0.01 M X²⁺ and 0.01 M Y²⁺ is saturated with H₂S. The pH at which the metal sulphide YS will form as a precipitate is ____ . (Nearest integer)

(Given: K_sp(XS) = 1 × 10⁻²² at 25°C, K_sp(YS) = 4 × 10⁻¹⁶ at 25°C, [H₂S] = 0.1 M in solution, K_a1 × K_a2 (H₂S) = 1.0 × 10⁻²¹, log 2 = 0.30, log 3 = 0.48, log 5 = 0.70)

Correct Answer: 4

Explanation

For precipitation of YS:

\[ K_{sp} = [Y^{2+}][S^{2-}] \]

\[ 4 \times 10^{-16} = (0.01)\,[S^{2-}] \]

\[ [S^{2-}] = \mathbf{4 \times 10^{-14}} \]

From dissociation of H₂S:

\[ H_2S \rightleftharpoons 2H^+ + S^{2-} \]

\[ K_{a1}K_{a2} = \frac{[H^+]^2 [S^{2-}]}{[H_2S]} \]

\[ 1.0 \times 10^{-21} = \frac{[H^+]^2 \times 4 \times 10^{-14}}{0.1} \]

\[ [H^+]^2 = \mathbf{2.5 \times 10^{-9}} \]

\[ [H^+] = \mathbf{5 \times 10^{-5}} \]

\[ \text{pH} = -\log(5 \times 10^{-5}) \]

\[ \text{pH} = -(\log 5 - 5) \]

\[ \text{pH} = 5 - 0.70 = \mathbf{4.3} \]

Nearest integer value of pH = 4

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