A solution is 0.010 M in Zn^2+ and saturated with H2S ([H2S] = 0.10 M). Use K_a1K_a2 = 1.0x10^-21 for H2S and K_sp(ZnS) = 3.0x10^-23. The highest pH at which no ZnS precipitates is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ia032

A solution is 0.010 M in $Zn X^{2 +}$ and saturated with $H X_{2} S$ ( $[H X_{2} S] = 0.10$ M). Use $K_{a 1} K_{a 2} = 1.0 \times 1 0^{- 21}$ for $H X_{2} S$ and $K_{s p} (ZnS) = 3.0 \times 1 0^{- 23}$ . The highest pH at which no $ZnS$ precipitates is

No precipitation requires

[Zn X^{2 +}] [S X^{2 -}] \leq K_{s p}

. With

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

[H X^{+}]^{2} \geq K_{a 1} K_{a 2} [H X_{2} S] [Zn X^{2 +}] / K_{s p} = 0.0333

, so

[H X^{+}] \geq 0.1826

M and pH

\leq 0.74

. Forgetting the square root gives 1.48.