Chemical and Ionic Equilibrium 2 Question 13
13. Solubility product constant ( $K_{\text {sp }}$ ) of salts of types $M X, M X_{2}$ and $M_{3} X$ at temperature ’ $T$ ’ are $4.0 \times 10^{-8}, 3.2 \times 10^{-14}$ and $2.7 \times 10^{-15}$, respectively. Solubilities $\left(\mathrm{mol} \mathrm{dm}^{-3}\right)$ of the salts at temperature ’ $T$ ’ are in the order
$(2008,3 \mathrm{M})$
(a) $M X>M X_{2}>M_{3} X$
(b) $M_{3} X>M X_{2}>M X$
(c) $M X_{2}>M_{3} X>M X$
(d) $M X>M_{3} X>M X_{2}$
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Solution:
- $M X$ :
$$ K_{\text {sp }}=S^{2}=4 \times 10^{-8} $$
$\Rightarrow \quad S=2 \times 10^{-4}$
$M X_{2}: \quad K_{\text {sp }}=4 S^{3}=3.2 \times 10^{-14} \Rightarrow S=2 \times 10^{-5}$
$M_{3} X: \quad K_{\text {sp }}=27 S^{4}=2.7 \times 10^{-15} \Rightarrow S=10^{-4}$
Order of solubility is $\quad M X>M_{3} X>M X_{2}$
