Question

$K_{sp}$ of $CuS,A{g}_{2}S,HgS$ are ${10}^{-31},{10}^{-44},{10}^{-54}$ respectively. Select the correct order for their solubility in water:

• A. $HgS>CuS>A{g}_{2}S$
• B. $HgS>A{g}_{2}S>CuS$
• C. $A{g}_{2}S>HgS>CuS$
• D. $A{g}_{2}S>CuS>HgS$

Answer 1

The correct option is D $A{g}_{2}S>CuS>HgS$

For $CuS$
$CuS\rightleftharpoons C{u}^{+2}+S^{2-}$
$K_{sp}=s_1^2\Rightarrow s_1=\sqrt{{10}^{-31}}\approx {10}^{-16}$

For $A{g}_{2}S$
$A{g}_{2}S\rightleftharpoons 2A{g}^{+}+S^{2-}$
$K_{sp}=4s_2^3\Rightarrow s_2=\sqrt[3]{3\frac{{10}^{-44}}{4}}\approx {10}^{-15}$

For $HgS$
$HgS\rightleftharpoons H{g}^{+2}+S^{2-}$
$K_{sp}=s_3^2\Rightarrow s_3=\sqrt{{10}^{-54}}\approx {10}^{-27}$

Thus the order of solubility $s_2>s_1>s_3$