The electrochemical cell shown below is a concentration cell. `M|M^(2+)(` saturated solution of sparingly soluble salt, `MX_(2))||M^(2+)(0.001 mol dm^(-3))|M`
The `emf` of the cell depends on the difference in the concentration of `M^(2+)` ions at the two electrodes. The `emf` of the cell at `298` is `0.059V`.
The solubility product `(K_(sp),mol^(3) dm^(-9))` of `MX_(2)` at 298 based on the information available the given concentration cell is `(` Take `2.303xxRxx298//F=0.059V)`

Options

A. `1xx10^(-15)`
B. `4xx10^(-15)`
C. 1xx10^-12`
D. `4xx10^9

Explanation

`Mto M^(+2)` (salt): (oxidation half cell)
`M^(+2)(0.001)toM :` (Reduction half cell)
Reaction is `M+M^(+2)(0.001)to M^(+2)` (S: solubility )+M
`E=E^(@)-0.059/n'log .S/(0.001) implies E^(@)=0`
`-2=logs. S/(10^(-3))implies S=10^(-5)`
`K_(SP)=4s^(3)=4xx10^(-15)`