Question

The molar solubility (in $mol{L}^{-1})$ of a sparingly soluble salt $M{X}_4$ is ${}^{\prime }{S}^{\prime }$. The corresponding solubility product is ${}^{\prime }{K}_{sp}^{\prime }$. ${}^{\prime }{S}^{\prime }$ in term of ${}^{\prime }{K}_{sp}^{\prime }$ is given by the relation:

• A. $S={\left(\frac{K_{sp}}{128}\right)}^{1/4}$
• B. $S={\left(\frac{K_{sp}}{256}\right)}^{1/5}$
• C. $S=(\frac{256}{K_{sp}}{)}^{1/15}$
• D. $S=(\frac{128}{K_{sp}}{)}^{1/4}$

Answer 1

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

$M{X}_4\left(s\right)+aq\leftrightharpoons \underset{S}{M^{+4}\left(aq\right)}+\underset{4S}{4X^{-}\left(aq\right)}$

The molar solubility (in mol/ L) of a sparingly soluble salt $M{X}_4$ is ′$S$′.

The corresponding solubility product is ′$K_{sp}$′. ′S in term of ′$K_{sp}$′ is given by the relation:

$K_{sp}=\left[M^{4+}\right][X^{-}{]}^4$

$K_{sp}=S(4S{)}^4=256S^5$

Hence, the molar solubility is,

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

Hence, option B is correct.