Question

Vapour pressure of a saturated solution of a sparingly soluble salt, $A_2{B}_2$, is $31.8$ mm of Hg at ${40}^o$C. If vapour pressure of pure water is $31.9$ mm of Hg at ${40}^o$C. Calculate $K_{sp}$ of $A_2{B}_2$ at ${40}^o$C.

Answer 1

Let stability of $A_2{B}_2$ be $5$ moles/litre

$A_2{B}_2\rightleftharpoons 2A^{+}+2B^{-}$

$2s$ $2s$

$K_{sp}=(2s{)}^2\times (2s{)}^2=16\times s^4$

Now, $\frac{P^o-P}{P}=\frac{n}{N}=\frac{4}{55.56}$

$\Rightarrow \frac{31.9-31.8}{31.8}=\frac{4s}{55.56}\Rightarrow S=0.043$ moles/litre

$\therefore K_{sp}=16\times (0.043{)}^4=5.47\times {10}^{-5}$