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Solubility Product

The solubilit...

Question

The solubility of $P b {S O}_{4}$ in water is $0.038 g$ $L^{- 1}$ at $25^{o} C$ . Calculate its solubility at the same temperature.

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Solution

Solubility $(S)$ of $P b {S O}_{4}$ in $m o l L^{- 1}$
$= \frac{0.038}{M o l m a s s o f P b {S O}_{4}} = \frac{0.038}{303} = 1.254 \times 10^{- 4}$
The equilibrium is
$P b {S O}_{4} ⇌ {P b}^{2 +} + {S O}_{4}^{2 -}$
So, $K_{s} = [{P b}^{2 +}] [{S O}_{4}^{2 -}] = S \times S = S^{2}$
or $K_{s} = 1.254 \times 10^{- 4} \times 1.254 \times 10^{- 4} = 1.573 \times 10^{- 8}$

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