In a saturated solution of the sparingly soluble strong electrolyte `AglO_(3) (s) hArr Ag^(+)(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)` contained 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

Let s =solubility
`AgIO_(3) hArr underset(s)(Ag^(**)) ** underset(s)(IO_(3))`
`K_(sp)=[Ag^(+)][IO_(3)^(-)]=sxxs=s^(2)`
Given `K_(sp)=1xx10^(-8)`
`therefore s= sqrt(K_(sp))=sqrt(1xx10^(-8))`
`=1.0xx10^(-4) "mol"//"lit"=1.0xx10^(-4)xx283`g/lit
`(because` Molecular mass of `Ag IO_(3)=283)`
`=(1.0xx10^(-4)xx283xx100)/(1000)gm//100ml`
`=2.83xx10^(-3)gm//100ml`