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^(-12)`

Answer

B

Explanation

`M|underset((K_(sp) =?))(M^(+)(sat.))"||"M^(2+) (0.001M)`
emf of concentration cell,
`E_(cell) = (-0.059)/(n)log. ([M^(+2)]_(a))/([M^(+2)]_(c))`
`0.059 = (0.059)/(2)log. ([0.001])/([M^(+2)]_(a))`
`[M^(+2)]_(a) = 10^(5) = S` (solubility of salt in saturated solution)
`underset((S))(MX_(2))rarr underset((S))(M^(+2)) +underset((2S))(2x^(-)(aq))`
`K_(sp) = 4S^(3) = 4 xx (10^(-5))^(3) = 4 xx 10^(-15)`