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. `1 xx 10^(-15)`
B. `4 xx 10^(-15)`
C. `1 xx 10^(-12)`
D. `1 xx 10^(-12)`

Answer

B

Explanation

`0.059 = 0 - (0.059)/(2)log.([M^(++)])/(0.001)`
`([M^(++)])/(0.001) = 10^(-2)`
`[M^(++)] = 10^(-5) = s`
`K_(sp) = 4s^(3) = 4 xx (10^(-5))^(3)`
`=4 xx 10^(-15)`