In a saturated solution of the sparingly soluble strong electrolyte `AgIO_3` (molecular mass= 283) , the equilibrium which sets in is
` AgIO_3 (s) hArr Ag^(+) (aq) +IO_3^(-) (aq)`
If the solubility product constant ` K_(sp) " of " AgIO_3` at a given temperature is ` 1.0 xx 10^(-8) , ` what is the mass of `AgIO_3` contained in 100 mL of its saturated solution ?

Options

A. `28xx10^(-2) g`
B. `28.3xx10^(-3)g`
C. `1.0xx10^(-7)g`
D. `1.0xx10^(-4)g`

Answer

B

Explanation

`AgIO_(3(s)) to Ag_(3(s))^(+) + IO_(3(aq))^(-)`
Let the solubility of `AgIO_(3)` be S
`K_(sp)= [Ag^(+)][IO_(3)^(-)]`
`K_(sp)=SxxS`
or
`=(1.0xx10^(-4)x283)/1000 xx 100g//100ml=2.83xx10^(-3)g//100ml``S=sqrt(K_(sp))`
`S=sqrt(1.0xx10^(-8)) = 1.0xx10^(-4) mol//L= 1.0xx10^(-4)xx2.83mol//L`