The specific conductivity of AgCl (aq) at `25^(@)C` is `1.26 xx 10^(-6)` and ionic conductivity of `Ag^(+)`(aq) and `Cl^(-)`(aq) and 76 S `cm^(2) " mol"^(-1)` respectively. Then the solubility product of AgCl at `25^(@)C`

Options

A. `8.3xx10^(-11)`
B. `8.3 xx 10^(-10)`
C. `9.3 xx 10^(-10)`
D. `9.3 xx 10^(-16)`

Answer

A

Explanation

`A^(oo) (AgCl) = 62 +76 = 138 S cm^(2) mol^(-1)` Since `AgCI` is a sparingly soluble salt, its saturated solution contain only very small amount of `Ag^(+)` and `Cl^(-)` ions, `A^(C) = A^(oo)`. Also concentration of `Ag^(+)` ion or `Cl^(-)` ion in saturated solution is same as solubility (s).
`rArr 138 =(1.26 xx 10^(-6) xx 1000)/(S), ( : A = (k.1000)/(C))`
`rArr S = 9.13 xx 10^(-6) rArr K_(sp) = S^(2) = 8.3 xx 10^(-11)`