Question

The solubility product of a salt having general formula $M{X}_3,$ in water is $9\times {10}^{-12}$. The concentration $\left({\text{mol L}}^{-1}\right)$ of $M^{3+}$ ions in the aqueous solution of the salt is:

• A. $1\times {10}^{-3}{\text{mol L}}^{-1}$
• B. $1.6\times {10}^{-4}{\text{mol L}}^{-1}$
• C. $2\times {10}^{-4}{\text{mol L}}^{-1}$
• D. $3\times {10}^{-4}{\text{mol L}}^{-1}$

Answer 1

The correct option is A $1\times {10}^{-3}{\text{mol L}}^{-1}$

The dissociation equation is:
$\begin{array}{ccccc}M{X}_3\left(s\right)& \rightleftharpoons & M^{3+}\left(aq\right)& +& 3X^{-}\left(aq\right)\\ 1& & 0& & 0\\ 1-s& & s& & 3s\end{array}$
where $s$ is solubility.
The solubility product is given by:
$K_{sp}=\left[M^{3+}\right][X^{-}{]}^3$
$K_{sp}=s\times (3s{)}^3=9s^4$
$K_{sp}=9s^4=9\times {10}^{-12}$
$s^4={10}^{-12}$
$s=\left[M^{3+}\right]={10}^{-3}{\text{mol L}}^{-1}$