Question

Solubility product constant (Ksp​) of salts of types MX, $M{{X}_{2}}$ ​ 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 (in mole $d{{m}^{-3}}$ ) of the salts at temperature, T, are in the order ____
A. MX >$M{{X}_{2}}$ ​> ${{M}_{3}}X$
B. ${{M}_{3}}X$ >$M{{X}_{2}}$ ​> MX
C. $M{{X}_{2}}$ ​> ${{M}_{3}}X$ > MX
D. MX >${{M}_{3}}X$> $M{{X}_{2}}$

Answer 1

The relation between solubility of the compound with its solubility product is as follows.
$S=\sqrt{{{K}_{sp}}}$
Here, S = solubility of the compound
${{K}_{sp}}$ = solubility product of the compound

Complete answer:
- In the question it is asked to write the solubilities of the three given slats in the proper order by using the given data.
- The solubility constant of the given salts at temperature T are $4.0\times {{10}^{-8}}$ , $3.2\times {{10}^{-14}}$ and $2.7\times {{10}^{-15}}$.
- We have to calculate the solubility product of the given salts and they are as follows.
- Solubility product of the first slat MX is as follows.
$MX\to \underset{S}{\mathop{{{M}^{+}}}}\,+\underset{S}{\mathop{{{X}^{-}}}}\,$
Solubility of the MX=$\sqrt{{{K}_{sp}}}=\sqrt{4\times {{10}^{-8}}}=2\times {{10}^{-4~}}M$
- Solubility product of the first slat $M{{X}_{2}}$ is as follows.
$M{{X}_{2}}\to \underset{S}{\mathop{{{M}^{+}}}}\,+\underset{2S}{\mathop{2{{X}^{-}}}}\,$
- Solubility constant of the $M{{X}_{2}}$ = $3.2\times {{10}^{-14}}$

& {{K}_{sp}}=\left( S \right)\text{ }{{\left( 2S \right)}^{2}}=4{{S}^{3}} \\\ & 4{{S}^{3}}=3.2\times {{10}^{-14}} \\\ & S=2\times {{10}^{-5}} \\\ \end{aligned}$$ \- Solubility product of the first salt ${{M}_{3}}X$ is as follows \- Solubility constant of the ${{M}_{3}}X$ = $2.7\times {{10}^{-15}}$ $${{M}_{3}}X\to \underset{3S}{\mathop{3{{M}^{+}}}}\,+\underset{S}{\mathop{{{X}^{3-}}}}\,$$ $$\begin{aligned} & {{K}_{sp}}=\left( S \right)\text{ }{{\left( 3S \right)}^{3}}=27{{S}^{4}} \\\ & 27{{S}^{4}}=2.7\times {{10}^{-15}} \\\ & S=1\times {{10}^{-4}}M \\\ \end{aligned}$$ \- Therefore, the solubilities of the three given salts are $2\times {{10}^{-4~}},2\times {{10}^{-5}}$ and $1\times {{10}^{-5}}$ . \- So, solubilities (in mole $d{{m}^{-3}}$ ) of the salts at temperature, T, are in the order of MX >${{M}_{3}}X$ > $M{{X}_{2}}$ . **The correct option is D.** **Note:** We should calculate the solubilities of the given salts by using the relation between the solubility and solubility constant. Without solubility constant we cannot calculate the solubility of the respective salts.