Question

A saturated solution of a sparingly soluble metal chloride $MC{l}_2$ has a vapour pressure of 31.78mm of Hg at ${30}^{\circ }C$, while aqueous tension of water at ${30}^{\circ }C$ is 31.82mm of Hg. The solubility product of salt is:

• A. $3.1\times {10}^{-5}$
• B. $4.1\times {10}^{-5}$
• C. $5.1\times {10}^{-5}$
• D. $6.1\times {10}^{-5}$

Answer 1

The correct option is C $5.1\times {10}^{-5}$

$Loweringinvapourpressure=molefractionofsolute$

$\frac{P_A^0-P_s}{P_A^0}=\frac{3S}{3S+55.56}$

$forMCl,thesolubilityisas$

$MC{l}_2\rightleftharpoons {\underset{S}{M}}^{+2}+{\underset{2S}{2Cl}}^{-}$

Since the solution is very dilute 3S + 55.56 $\square$ 55.56

$\frac{31.82-31.78}{31.82}=\frac{3S}{55.56}$

$\therefore S=2.328\times {10}^{-2}$

Thus, the $K_{sp}=S\times (2S{)}^2$

$=(2.33\times {10}^{-2})(2\times 2.33\times {10}^{-2}{)}^2$

$=5.1\times {10}^{-5}$