Question

The solubility of different sparingly soluble salts are given as under:
$\begin{array}{ccc}S.No.& FormulaType& Solubilityproduct\\ 1.& AB& 4.0\times {10}^{-20}\\ 2.& A_{2}B& 3.2\times {10}^{-11}\\ 3.& A{B}_3& 2.7\times {10}^{-31}\end{array}$
The correct increasing order of solubility is:

• A. $1,3,2$
• B. $2,1,3$
• C. $1,2,3$
• D. $3,1,2$

Answer 1

The correct option is A $1,3,2$

$K_{sp}=\left[A\right]\left[B\right]$ (solubility product)
1. For $AB$
$S=K_{sp}or\sqrt{4\times {10}^{-20}}\Rightarrow 2\times {10}^{-10}$

2. For $A_{2}B{K}_{sp}=(2S{)}^2\times S=4S^3$
$S={\left(\frac{K_{sp}}{4}\right)}^{1/3}$
$S={\left(\frac{3.2\times {10}^{-11}}{4}\right)}^{1/3}$
$S=(8\times {10}^{-12}{)}^{1/3}$
$S=2\times {10}^{-4}$

3. For $A{B}_3{K}_{sp}=S\times (3S{)}^3=27S^4$
$S={\left(\frac{K_{sp}}{27}\right)}^{1/4}$
$S={\left(\frac{2.7\times {10}^{-31}}{27}\right)}^{1/4}$
$S=({10}^{-32}{)}^{1/4}$
$S={10}^{-8}$
$Solubilityis1<3<2$.