The solubility product of BaSO _ 4 is 1 × 10 ^ - 10 at 298K . The...

For the insoluble salt barium sulphate, sulphate ion added is the common ion. Due to the common ion effect the solubility of barium sulphate decreases. Let us assume solubility of barium sulphate is $S$.

${BaSO}_{4}\left(s\right) ⇌ \mathop{{Ba}^{2 +}}_{S}\left(aq\right) + \mathop{{SO}_{4}^{2 -}}_{S + 0 . 1}\left(aq\right)$
$\mathop{{K}_{2}{SO}_{4}}_{0 . 1 - 0 . 1} ⟶ \mathop{{K}^{+}}_{0 . 1}\left(aq\right) + \mathop{{SO}_{4}^{2 -}}_{0 . 1}\left(aq\right)$
${K}_{SP} = \left[{Ba}^{2 +}\right]\left[{SO}_{4}^{2 -}\right]$
$1 \times {10}^{- 10} = S ( S + 0 . 1 )$
$≃ 0 . 1S$
$S = {10}^{- 9}M = 233 \times {10}^{- 9}{gL}^{- 1}$