Question

The molar solubility $\left(moll{t}^{-1}\right)$ of a sparingly soluble salt $M{X}_4$ is `s`. The corresponding solubility product is $K_{sp}$. Then `s`can be given in terms of $k_{sp}$ by the relation :

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

Answer 1

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

The ionization of $M{X}_4$ is as shown below.
$M{X}_4\rightleftharpoons M^{4+}+4X^{-}$
The expression for the solubility product is, $K_{sp}=\left[M^{4+}\right][X^{-}{]}^4$.
But $\left[M^{4+}\right]=s$ and $\left[X^{-}\right]=4s$
Substitute values in the expression for the solubility product.
$K_{sp}=s(4s{)}^{4}256s^5$.
Hence $s=(\frac{K_{sp}}{256}{)}^{\frac{1}{5}}$.