Question

The solubility product of a salt, having general formula $M{X}_2$, in water is $4\times {10}^{-12}$. The concentration of $M^{2+}$ ions in the aqueous solution of the salt (in terms of solubility) is:

• A. $2.0\times {10}^{-6}M$
• B. $1.0\times {10}^{-4}M$
• C. $1.6\times {10}^{-4}M$
• D. $4.0\times {10}^{-10}M$

Answer 1

Answer: (B)

$1.0\times {10}^{-4}M$

The ionization of $M{X}_2$ is as shown below.
$M{X}_2\rightleftharpoons M^{2+}+2X^{-}$

The expression for the solubility product is, $K_{sp}=\left[M^{2+}\right][X^{-}{]}^2$.
But $\left[M^{2+}\right]=s$ and $\left[X^{-}\right]=2s$.

$K_{sp}=4\times {10}^{-12}$.

Substitute values in the expression for the solubility product.

$4\times {10}^{-12}=s(2s{)}^2=4s^3=4\times {10}^{-12}$.

Hence, the solubility $s=1.0\times {10}^{-4}M$.