Question

The molar solubility in $\left(mol{L}^{-1}\right)$ of a sparingly soluble salt $M{X}_4$​ is ${}^{\prime }{s}^{\prime }$.The molar solubility product is $K_{sp}$. ${}^{\prime }{s}^{\prime }$ is given in terms of $K_{sp}$ by the relation:

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

Answer 1

The correct option is B $s={\left(\frac{K_{sp}}{256}\right)}^{\frac{1}{5}}$

The expression for the dissociation of the salt is, $M{X}_4\left(aq\right)\rightleftharpoons M^{4+}+4X^{-}$
$s4s$

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

Thus the expression for solubility becomes,
$s^5=\left(\frac{K_{sp}}{256}\right)$
$\Rightarrow s={\left(\frac{K_{sp}}{256}\right)}^{\frac{1}{5}}$