The conductivity of a saturated solution of a springly soluble salt, `MX_(2)` is found to be `4.0xx 10^(-6) Omega^(-1) cm^(-1)`. If `lamda_(m)^(oo) ((1)/(2) M^(2+)) = 50.0Omega^(-1) cm^(2) mol^(-1) and lamda_(m)^(oo) (X^(-)) = 50 Omega^(-1) cm^(2) mol^(-1)`, the solubility product of the salt is about

Answer

C

Explanation

`Lamda_(m)^(oo) (MX_(2))= Lamda_(m)^(oo) (M^(2+)) + 2Lamda_(m)^(oo) (X^(-)) = 2Lamda_(m)^(oo) ((1)/(2) M^(2+)) + 2 Lamda_(m)^(oo) (X^(-))`
`=(2 xx 50+2 xx 50) S cm^(2) mol^(-1)= 200 S cm^(2) mol^(-1)`
`c= (k)/(Lamda_(m)^(oo))= (4.0 xx 10^(-5)S cm^(-1))/(200S cm^(2) mol^(-1))= 2xx 10^(-7) mol cm^(-3) = 2 xx 10^(-4)` mol `dm^(-3)`
`K_(sp) = [M^(2+)] {2[X^(-)]}^(2)= (2 xx 10^(-4) mol dm^(-3)) (4 xx 10^(-4) mol dm^(-3))^(2)= 32 xx 10^(-12)`