`M_(2)SO_(4) (M^(o+)` is a monovalent metal ion) has a `K_(sp)` of `3.2 xx 10^(-6)`at `298 K`. The maximum concentration of `SO_(4)^(2-)` ion that could be attained in a saturated solution of this solid at `298 K` is

Options

A. `3xx10^(-3) M`
B. `7xx 10^(-2) M`
C. `2.89 xx 10^(-4) M`
D. `2xx10^(-2)M`

Answer

D

Explanation

The maximum concentration of `SO_(4)^(2-)` will be same as the solubility of `M_(2)SO_(4)`.
If solubility is x mol `L^(-1)`.
`M_(2)SO_(4) hArr 2M^(+)+SO_(4)^(2-)`
`K_(sp)=[M^(+)]^(2)[SO_(4)^(2-)]=4x^(3)`
`x=(K_(sp)//4)^(1//3)`
`[SO_(4)^(2-)]=x=((K_(sp))/(4))^(1//3)`
`=((3.2xx10^(-5))/(4))^(1//3)=2xx10^(-2)M`