The solubility product of `BaSO_4 ` at 298 K is ` 1.08 xx 10^(-10) ` . What is the minimum concentration of ` SO_4^(2-)` ions required to precipitate `BaSO_4` from a 0.01 M solution of `BaCl_2`

Explanation

`[Ba^(2+)]= [BaCl_(2)]= 0.01 mol L^(-1)`
`K_(sp)` for `BaSO_(4)` is given by
`K_(sp)= [Ba^(2=)] [SO_(4)^(2-)]`
The precipitation will occur when the ionic product `[Ba^(2+)] [SO_(4)^(2-)]` exceeds the solubility products. At equilibrium,
`[SO_(4)^(2-)] = (K_(sp))/([Ba^(2+)])= (1.08 xx 10^(-10))/(0.01)= 1.08 xx 10^(-8) mol L^(-1)`
Hence, in order to precipitate `BaSO_(4)` from the given solution of `BaCl_(2)`, the concentration of `SO_(4)^(2-)` ions must be greater than `1.08 xx 10^(-8) mol L^(-1)`