Question

The molar solubility (in mol $L^{-1})$ of a sparingly soluble salt $M{X}_4$ is 's'. The corresponding solubility product is $K_{sp}$. $s$ can be given in terms of $K_{sp}$ by the relation:

• A. $s={\left[\frac{K_{sp}}{256}\right]}^{\frac{1}{5}}$
• B. $s=[128K_{sp}{]}^{\frac{1}{4}}$
• C. $s=[26K_{sp}{]}^{\frac{1}{5}}$
• D. $s={\left[\frac{K_{sp}}{128}\right]}^{\frac{1}{4}}$

Answer 1

The correct option is A $s={\left[\frac{K_{sp}}{256}\right]}^{\frac{1}{5}}$

The expression for the dissociation of the salt is, $M{X}_4\left(aq\right)\rightleftharpoons {\underset{s}{M}}^{4+}+\underset{4s}{4}{X}^4$

The expression for the solubility product is, $K_{sp}=\left[M^{3+}\right][X^{-}{]}^4=s(4s{)}^4=256s^5$

Thus the expression for solubility becomes $s=[\frac{K_{sp}}{256}{]}^{\frac{1}{5}}$.