What is the minimum pH required to prevent the precipitation of ZnS in a solution that is $0.01 M Z n C l_{2}$ and saturated with $0.10 M H_{2} S ?$ $[G i v e n K_{s p} = 10^{- 21}, K_{a_{1}} \times K_{a_{2}} = 10^{- 20}]$

Question

What is the minimum pH required to prevent the precipitation of ZnS in a solution that is

0.01 M Z n C l_{2}

and saturated with

0.10 M H_{2} S ?

[G i v e n K_{s p} = 10^{- 21}, K_{a_{1}} \times K_{a_{2}} = 10^{- 20}]

(A) 0 (B) 1 (C) 2 (D) 4

Tardigrade Admin · Accepted Answer

Z n S ⇌ Z n^{2 +} + S^{2 -}

K_{s p} = [Z n^{2 +}] [S^{2 -}]

Z n C l_{2} \to Z n^{2 +} + 2 C l^{-}

[S^{2 -}] = \frac{K_{s p}}{[Z n^{2 +}]} = \frac{10^{- 21}}{(0.01)}

\Rightarrow [S^{2 -}] = 10^{- 19}

K a_{1} . K a_{2} = \frac{{[H^{+}]}^{2} [S^{2 -}]}{[H_{2} S]}

Where,

K_{a_{1}} = \frac{[H S^{-}] [H^{+}]}{[H_{2} S]}

K_{a_{2}} = \frac{[H^{+}] [S^{2 -}]}{[H S^{-}]}

So,

10^{- 20} = \frac{{[H^{+}]}^{2} [S^{2 -}]}{[H_{2} S]} = \frac{{[H^{+}]}^{2} (10^{- 19})}{(0.1)}

\Rightarrow [H^{+}] = 0.1

\Rightarrow p H = - log [H^{+}] = 1

Q. What is the minimum pH required to prevent the precipitation of ZnS in a solution that is 0.01 M ZnCl2 and saturated with 0.10 M H2S ? Given Ksp=10-21, Ka1×Ka2=10-20