In a saturated solution of the spatingly soluble strong electrolyte `AgIO_(3)` (molecular mass `=283`) the equilibrium which sets in is
`AgIO_(3) (s)hArrAg^(+)(aq)+IO_(3)^(-)(aq)`
If the solubility product constant `K_(SP)` of `AgIO_(3)` at a given temperature is `1.0xx10^(-8)`, what is the mass of `AgIO_(3)` cotained in `100 mL` of its saturated solution?

Options

A. `28.3xx10^(-2) g`
B. `28.3xx10^(-3) g`
C. `1.0xx10^(-7) g`
D. `1.0xx10^(-4) g`

Answer

B

Explanation

`AgIO_(3)(S)hArrAg_((aq))^(+)+IO_(3(aq))^(-)`
Let the solubility of `AgIO_(3)` be `S`
`K_(SP)=[Ag^(+)][IO_(3)^(-)]`
`1.0xx10^(-8)=S^(2)`
`S=10^(-4)mol//litre`
`= (10^(-4)xx283)/(1000)xx100=283xx10^(-5)`
`=2.83xx10^(-3) g//100mL`