Solubility of a salt is defined as the maximum amount of a salt which can be dissolved in…

Solubility of a salt is defined as the maximum amount of a salt which can be dissolved in a given amount of solvent at a particular temperature. Unit of solubility is mole per litre of solution. The solubility of a salt of weak acid with strong base (CH₃COOAg) in acidic buffer can be calculated as
\[\begin{array}{l} \begin{array}{l} \mathrm{CH}_{3} \mathrm{COOAg} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{Ag}^{+}(\mathrm{aq}) \\ \mathrm{S}-\mathrm{X} \\ \mathrm{CH}_{3} \mathrm{COO}^{-}(\mathrm{aq})+\mathrm{H}^{+} \rightleftharpoons \mathrm{S}=\text { Solubility of salt } \\ (\mathrm{S}-\mathrm{X}) \quad \mathrm{CH}_{3} \mathrm{COOH} \end{array}\\ \text { Dissociation constant of weak acid }\\ \left(\mathrm{K}_{\mathrm{a}}\right)=\frac{(\mathrm{S}-\mathrm{X})\left[\mathrm{H}^{+}\right]}{\mathrm{X}} \end{array}\]
 
The solubility of CaCO₃ is 7 mg/L. Calculate the solubility product of BaCO₃ from this information and from the fact that when Na₂CO₃ is added slowly to a solution containing equimolar concentration of Ca²⁺ and Ba²⁺, no precipitate is formed until 90% of Ba²⁺ has been precipitated as BaCO₃.