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

Answer

C

Explanation

`{:("AgIO"_(3),hArr,"Ag"^(+),+,"IO"_(3)^(-)),(,,S,,S):}`
`K_(sp)=S^(2) or S=sqrt(K_(sp))=sqrt(10^(-8))=10^(-4) "mol" L^(-1)`
`=10^(-4)xx283 g L^(-1) = 2.83 xx 10^(-2) g L ^(-1)`
Thus, 1000 mL of the saturated solution will contain `AgIO_(3)=2.83xx10^(-2)g`
`:. 100 ` m L of the saturated solution will contain
`AgIO_(3)=2.83xx10^(-3)g`.