Question

The values of $ {{K}_{sp}} $ for $ CuS,A{{g}_{2}}S $ and $ HgS $ are $ {{10}^{-31}},~{{10}^{42}} $ and $ {{10}^{-54}} $ respectively. The correct order of their solubility in water is:

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

Answer 1

Answer: (D)

Solubility product $ ({{K}_{sp}}) $ of $ CuS={{10}^{-31}} $ liability of $ CuS=\sqrt{{{K}_{sp}}}=\sqrt{{{10}^{-31}}} $ $ =3.16\times {{10}^{-16}}mol/lit $ Similarly, solubility of $ A{{g}_{2}}S $ $ =\sqrt[3]{\frac{{{K}_{sp}}}{4}} $ $ (\because for\,A{{g}_{2}}S,4{{s}^{3}}={{K}_{sp}}) $ $ =\sqrt{\frac{{{10}^{-42}}}{4}} $ $ =6.3\times {{10}^{-15}}mol/litre $ Solubility of $ HgS=\sqrt{{{K}_{sp}}} $ $ =\sqrt{{{10}^{-54}}} $ $ ={{10}^{-27}}mol/lit $ Hence, the correct order of solubility is $ A{{g}_{2}}S>CuS>HgS $