Question

$Pb^{2 +} + SO_{4}^{2 -} \rightleftharpoons PbSO_{4}(s);K_{eq} = \frac{1}{K_{sp}} = \frac{1}{1.6 \times 10^{- 7}}$

$\frac{8.32 \times 10^{- 3}/200}{100/1000}\frac{10^{- 4}}{100/1000} $$$= 4 \times 10^{- 4} = 10^{- 3}$$

100% $0\left( 10^{- 3} - 4 \times 10^{- 4} \right) = 6 \times 10^{- 4}M$

Eqn. $xM\left( 6 \times 10^{- 4} + x \right)M$

As $\left\lbrack Pb^{2 +} \right\rbrack\left\lbrack SO_{4}^{2 -} \right\rbrack = K_{sp} \Rightarrow x.\left( 6 \times 10^{- 4} + x \right) = 1.6 \times 10^{- 7}$

$\Rightarrow x = 2 \times 10^{- 4}\text{ M}$

∴ Mass of lead un-precipitated = $\left( \frac{100 \times 2 \times 10^{- 4}}{1000} \right) \times 208 = 4.16 \times 10^{- 3}\text{ gm}$