question_answer 154)

  A sparingly soluble salt having general formula \[{{A}_{x}}{{B}_{y}}\]and molar solubility s is in equilibrium with its saturated solution. Derive a relationship between the solubility and solubility product for such salt.

Answer:

  \[\underset{s}{\mathop{{{A}_{x}}{{B}_{y}}}}\,\to \underset{xs}{\mathop{x{{A}^{y+}}}}\,+\underset{ys}{\mathop{y{{B}^{x-}}}}\,\] Solubility product \[{{K}_{sp}}={{[{{A}^{y+}}]}^{x}}{{[{{B}^{x-}}]}^{y}}\] \[={{[xs]}^{x}}{{[ys]}^{y}}\] \[={{x}^{x}}{{y}^{y}}{{x}^{x+y}}\]