100 mL of 0.020 M ZnCl2 is mixed with 100 mL of a solution of hydrochloric acid saturated with H2S, such that after mixing [H2S] = 0.10 M. Given K_sp(ZnS) = 2.0x 10^-22 and the overall constant K_a1K_a2 = 1.1x 10^-21 for H2S 2H+ + S^2-, what is the pH of the mixture at which ZnS just begins to precipitate (ZnS precipitates only if the pH is above this value)?

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia160

$100 mL$ of $0.020 M$ $ZnCl X_{2}$ is mixed with $100 mL$ of a solution of hydrochloric acid saturated with $H X_{2} S$ , such that after mixing $[H X_{2} S] = 0.10 M$ . Given $K_{s p} (ZnS) = 2.0 \times 1 0^{- 22}$ and the overall constant $K_{a 1} K_{a 2} = 1.1 \times 1 0^{- 21}$ for $H X_{2} S 2 H X^{+} + S X^{2 -}$ , what is the pH of the mixture at which ZnS just begins to precipitate (ZnS precipitates only if the pH is above this value)?

After mixing

[Zn X^{2 +}] = 0.010 M

. Precipitation begins when

[S X^{2 -}] = K_{s p} / [Zn X^{2 +}] = 2.0 \times 1 0^{- 20} M

[S X^{2 -}] = K_{a 1} K_{a 2} [H X_{2} S] / [H X^{+}]^{2}

, so

[H X^{+}]^{2} = 1.1 \times 1 0^{- 21} \times 0.10/2.0 \times 1 0^{- 20} = 5.50 \times 1 0^{- 3}

[H X^{+}] = 0.0742 M

and

pH = 1.13