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

Hint: 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 $M{{X}_{2}}$ = $3.2\times {{10}^{-14}}$
\[\begin{align}
  & {{K}_{sp}}=\left( S \right)\text{ }{{\left( 2S \right)}^{2}}=4{{S}^{3}} \\
 & 4{{S}^{3}}=3.2\times {{10}^{-14}} \\
 & S=2\times {{10}^{-5}} \\
\end{align}\]
- Solubility product of the first salt ${{M}_{3}}X$ is as follows
- Solubility constant of the ${{M}_{3}}X$ = $2.7\times {{10}^{-15}}$
\[{{M}_{3}}X\to \underset{3S}{\mathop{3{{M}^{+}}}}\,+\underset{S}{\mathop{{{X}^{3-}}}}\,\]
\[\begin{align}
  & {{K}_{sp}}=\left( S \right)\text{ }{{\left( 3S \right)}^{3}}=27{{S}^{4}} \\
 & 27{{S}^{4}}=2.7\times {{10}^{-15}} \\
 & S=1\times {{10}^{-4}}M \\
\end{align}\]
- 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.