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. `1.0xx10^(-4)`
B. `28.3xx10^(-2)`g
C. `2.83xx10^(-3)g`
D. `1.0xx10^(-7)g`

Answer

C

Explanation

Let s=Solubility
`AgIO_(3)hArrAg^(+)+IO_(3)^(-)`
`K_(sp)=[Ag^(+)][IO_(3)^(-)]=sxxs=s^(2)`
Given `K_(sp)=1xx10^(-8)`
`:.s=sqrt(K_(sp))=sqrt(1xx10^(-8))`
`1.0xx10^(-4)mol//L=1.0xx10^(-4)xx283g//L`
(`:.` Molecular mass of `AgIO_(3)=283`)
`=(1.0xx10^(-4)xx283xx100)/(1000)g//100mL`
`=2.83xx10^(-3)g//100mL`