Question

The solubility product of a salt having formula $M_{2} X_{3}$ is $2.2 \times 10^{-20}$. If the solubility of an another salt having formula $M_{2} X$ is twice the molar solubility of $M_{2} X_{3}$, the solubility product of $M_{2} X$ is

• A. $3 \times 10^{-12}$
• B. $9.16 \times 10^{-5}$
• C. $4.58 \times 10^{-5}$
• D. $2.76 \times 10^{-18}$

Answer 1

Answer: (A)

or $ 2.2 \times 10^{-20}=108\, s ^{5}$
$\therefore s=4.59 \times 10^{-5}$
For $M_{2} X$
$M_{2} X \rightleftharpoons \underset{2 s}{2} M^{+}+\underset{s}{X}^{2-}$
$K_{ sp }=(2 s)^{2} \cdot(s)$
$K_{ sp }=4 s^{3}$
$K_{ sp }=4\left(2 \times 4.59 \times 10^{-5}\right)^{3}$
$\left[\because\right.$ Solubility of $M_{2} X=2 \times$ solubility of $\left.M_{2} X_{3}\right]$
$=3 \times 10^{-12}$