Question

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

• A. $s={\left(256K_{sp}\right)}^{1/3}$
• B. $s={\left(128K_{sp}\right)}^{1/4}$
• C. $s={\left(K_{sp}/128\right)}^{1/4}$
• D. $s={\left(K_{sp}/256\right)}^{1/5}$

Answer 1

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

$M{X}_4\rightleftharpoons M^{+}+4X^{-}$

If solubility is $s$, then:

$K_{sp}=\left[M^{+}\right]{\left[X^{-}\right]}^4=\left(s\right)\times {\left(4s\right)}^4=256s^5$

$s={\left(K_{sp}/256\right)}^{1/5}$

Hence, option D is correct.