Question

The solubility product of a salt having general formula $M{X}_2,$ in water is $4\times {10}^{-12}$. The concentration $\left(mol{L}^{-1}\right)$ of $M^{2+}$ ions in the aqueous solution of the salt is:

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

Answer 1

The correct option is B $1.0\times {10}^{-4}$

The dissociation equation is$M{X}_2\left(s\right)\rightleftharpoons M^{2+}\left(aq\right)+2X^{-}\left(aq\right)1001-ss2s$
s is solubility.
The solubility product is given by
$K_{sp}=\left[M^{2+}\right][X^{-}{]}^2$
$K_{sp}=s\times (2s{)}^2=4s^3$
$K_{sp}=4s^3=4\times {10}^{-12}$
$s^3={10}^{-12}$
$s=\left[M^{2+}\right]={10}^{-4}mol{L}^{-1}$