question_answer 27)

The values of\[{{K}_{sp}}\] of two sparingly soluble Salt \[Ni{{(OH)}_{2}}\] and\[AgCN\]are \[2\times {{10}^{-15}}\]and \[6\times {{10}^{-17}}\]respectively. Which salt is more soluble? Explain.  

Answer:

\[\underset{{{s}_{1}}}{\mathop{AgCN}}\,\to \underset{{{s}_{1}}}{\mathop{A{{g}^{+}}}}\,+\underset{{{s}_{1}}}{\mathop{C{{N}^{-}}}}\,\] \[{{K}_{sp}}=s_{1}^{2}\] \[{{s}_{1}}=\sqrt{{{K}_{sp}}}=\sqrt{6\times {{10}^{-17}}}\] \[=7.8\times {{10}^{-9}}M\] \[\underset{{{s}_{2}}}{\mathop{Ni{{(OH)}_{2}}}}\,\to \underset{{{s}_{2}}}{\mathop{N{{i}^{2+}}}}\,+\underset{2{{s}_{2}}}{\mathop{2O{{H}^{-}}}}\,\] \[{{K}_{sp}}=[N{{i}^{2+}}]{{[O{{H}^{-}}]}^{2}}\] \[={{s}_{2}}{{(2{{s}_{2}})}^{2}}=4s_{2}^{3}\] \[^{{{s}_{2}}={{\left( \frac{2\times {{10}^{-15}}}{4} \right)}^{1/3}}}\] \[=7.93\times {{10}^{-6}}M\] Thus, \[Ni{{(OH)}_{2}}\] is more soluble.