Question

A saturated aqueous solution of sparingly soluble salt $A{B}_3$ has the vapour pressure $0.08mm$ lesser than the vapour pressure $17.33mm$ of solvent at ${25}^{o}C$. The solubility product of $A{B}_3$ is ?

Answer 1

Relative lowering of vapour pressure,

$\frac{P_o-P}{P_o}=X$ or $X=\frac{.08}{17.33}=4.6\times {10}^{-3}$

$M=\frac{1000\times X}{(1-X)\left(M{w}_{solvent}\right)}=\frac{1000\times 4.6\times {10}^{-3}}{18}$ (As the $(1-X)$ is very less so we neglected it)

$Molarity=.25M$

Now the solubility product for type $A{B}_3$ salt,

$K_{sp}=4S^3=4\times {.25}^3=6.25\times {10}^{-2}$