Question

The solubility product of a sparingly soluble salt \[A{X_2}\] is \[3.2 \times {10^{ - 11}}\] . Its solubility (moles/litre) is:
A) \[3.1 \times {10^{ - 4}}\]
B) \[2 \times {10^{ - 4}}\]
C) \[4 \times {10^{ - 4}}\]
D) \[5.6 \times {10^{ - 6}}\]

Answer 1

Hint:‌ To solve this question, we must first understand the concept of solubility and solubility product. Then we need to assess the correct reaction of the given compound and use the appropriate formula for solubility including solubility product and then only we can conclude the correct answer.

 Complete step by step solution:
Before we move forward with the solution of this given question, let us first understand some basic concepts:
Solubility: is the property of a solid, liquid or gaseous chemical substance called solute to dissolve in a solid, liquid or gaseous solvent. The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature, pressure and presence of other chemicals of the solution.
Solubility Product: We can say that it is a kind of equilibrium constant and its value depends on temperature. Represented as ${K_{sp}}$ and usually it increases with an increase in temperature due to increased solubility.
Step 1: In this step we will write the Reaction of the compound given in the question:
$A{X_2}\,\, \to \,\,{A^{ + 2}}\,\, + \,\,2{X^ - }$
Let the solubility of the salt be $'s'$ .
Therefore, for the above reaction:
Solubility of, $A{X_2}\,\, \to \,\,1 - s$ , ${A^{ + 2}} \to \,\,s$ , $2{X^ - } \to \,\,2s$
Hence, the solubility product ${K_{sp}}$ is $s \times {(2s)^2} = \,\,4{s^3}$
Step 2: In this step we will calculate the required solubility:
$\because \,\,{K_{sp}} = \,\,4{s^3}$
$\therefore \,\,3.2 \times {10^{ - 11}}\,\, = \,\,4{s^3}$
$ \Rightarrow {s^3}\,\, = \,\,\frac{{3.2 \times {{10}^{ - 11}}}}{4}$
$
 \Rightarrow \,\,\,{s^3}\,\, = \,\,8 \times {10^{ - 12}} \\
 \Rightarrow \,\,s\,\, = \,\sqrt[3]{{8 \times {{10}^{ - 12}}}} \\
$
$s = \,\,2 \times {10^{ - 4}}$
So, clearly we can conclude that the correct answer is Option B.

Note: The solubility of a substance in a solvent is the total amount of the solute that can be dissolved in the solvent at equilibrium. On the other hand, the solubility product constant is an equilibrium constant that provides insight into the equilibrium between the solid solute and its constituent ions that are dissociated across the solution.