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The solubility product of a sparingly soluble $A B_2$ salt is $2.56 \times 10^{-4} \mathrm{M}^3$ at $25^{\circ} \mathrm{C}$. The $K_f$ of water is $1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. The depression in freezing point of a standard solution of $A B_2$ is
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0.216 K
Let, solubility of $A B_2$ (1:2 type electrolyte) is pure water $=5 \mathrm{~mol} \mathrm{~L}^{-1}=5 \mathrm{M}$
$\Rightarrow K_{\mathrm{sp}}=4 S^3=2.56 \times 10^{-4} \mathrm{M}^3$ (given)
$\therefore S=0.04 \mathrm{M}=0.04 \mathrm{~m}$ (molal) under standard condition of the solution.
Depression of freezing point,
$\Delta T_f=K_f \times m \times i=1.8 \times 0.04 \times 3=0.216 \mathrm{~K}$
$\left[\because\right.$ Assuming complete dissociation of $A B_2$,
van't Hoff factor, $i=3]$
$\Rightarrow K_{\mathrm{sp}}=4 S^3=2.56 \times 10^{-4} \mathrm{M}^3$ (given)
$\therefore S=0.04 \mathrm{M}=0.04 \mathrm{~m}$ (molal) under standard condition of the solution.
Depression of freezing point,
$\Delta T_f=K_f \times m \times i=1.8 \times 0.04 \times 3=0.216 \mathrm{~K}$
$\left[\because\right.$ Assuming complete dissociation of $A B_2$,
van't Hoff factor, $i=3]$
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