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Question: The solubility product of \({{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}}\) is \(1.08 \times {10^{ ...

The solubility product of A2X3{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} is 1.08×10−231.08 \times {10^{ - 23}}. Its solubility will be
A.1×10−31 \times {10^{ - 3}}
B.1×10−61 \times {10^{ - 6}}
C.1×10−41 \times {10^{ - 4}}
D.1×10−51 \times {10^{ - 5}}

Explanation

Solution

We know that the solubility product of any salt at any temperature is the product of the molar concentration of its constituent ions. The concentration of ions is raised to the number of ions produced on dissociation of one molecule of the salt.solubility product is calculated for those salts which are sparingly soluble.

Complete step-by-step answer: We know that the solubility product of any salt at any temperature is the product of the molar concentration of its constituent ions. The concentration of ions is raised to the number of ions produced on dissociation of one molecule of the salt
We know that the solubility of a salt at any temperature is calculated from its solubility product.
The salt A2X3{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} dissociates as follows:
A2X3⇌2A3++3X2−{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} \rightleftharpoons 2{{\text{A}}^{3 + }} + 3{{\text{X}}^{2 - }}
The solubility product of the salt A2X3{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} is given as follows:
KSP=[A3+]2[X2−]3{{\text{K}}_{{\text{SP}}}} = {[{{\text{A}}^{3 + }}]^2}{[{{\text{X}}^{2 - }}]^3}
Where KSP{{\text{K}}_{{\text{SP}}}} is the solubility product.
Let the concentration of the A3+{{\text{A}}^{3 + }} ion and X2−{{\text{X}}^{2 - }} ion be s. Thus,
A2X3⇌2A3++3X2−{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} \rightleftharpoons 2{{\text{A}}^{3 + }} + 3{{\text{X}}^{2 - }}
 (2s)2 (3s)3{\text{ }}{\left( {2s} \right)^2}{\text{ }}{\left( {3s} \right)^3}
Thus, the equation for the solubility product is as follows:
KSP=(2s)2(3s)3{{\text{K}}_{{\text{SP}}}} = {\left( {2s} \right)^2}{\left( {3s} \right)^3}
⇒1.08×10−23=4s2×27s3\Rightarrow 1.08 \times {10^{ - 23}} = 4{s^2} \times 27{s^3}
⇒1.08×10−23=108s5\Rightarrow 1.08 \times {10^{ - 23}} = 108{s^5}
⇒s5=1.08×10−23108\Rightarrow {s^5} = \dfrac{{1.08 \times {{10}^{ - 23}}}}{{108}}
⇒s5=10−25\Rightarrow {s^5} = {10^{ - 25}}
∴s=10−5\therefore s = {10^{ - 5}}
Thus, the solubility of A2X3{{\text{A}}_{\text{2}}}{{\text{X}}_{\text{3}}} is 1×10−51 \times {10^{ - 5}}.

Thus, the correct option is (D) 1×10−51 \times {10^{ - 5}}.

Note: The solubility product is calculated using the concentration of the ions in which the salt has dissociated. Solubility factor depends on various factors such as temperature, pressure and nature of the electrolyte. The concentration of ions is affected by these factors and thus, the solubility product gets affected.