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. `1.0 xx 10^(-4)g`
B. `28.3 xx 10^(-2)g`
C. `2.83 xx 10^(-3)g`
D. `1.0 xx 10^(-7)g`

Answer

C

Explanation

`AgIO_(3)hArr underset(s)(Ag^(+))+underset(s)(IO_(3)^(-))`
`K_(sp)=s^(2)`
or `s=sqrt(K_(sp))=sqrt(10^(-8))-10^(-4)mol L^(-1)`
`=10^(-4) xx 283 g L^(-1) =2.83 xx 10^(-2) g L^(-1)`
Thus 1000 mL of the saturated solution will contain `AgIO_(3)=2.83 xx 10^(-2)g`
`:. `100 mL of the saturated solution will contain `AgIO_(3)=2.83 xx10^(-3)g`