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|M_(aq)^(2+)||M_(aq)^(2+)(10^(-3)M)|M`
Anode`: M rarr M^(2+)(aq)+2e^(-)`
Cathode `: M^(2+)(aq)+2e^(-) rarr M`

`E_(cell)=0-(0.059)/(2)log{(M^(2+)(aq)_(a))/(10^(-3))}`
`0.059=-(0.059)/(2)log[(M^(2+)(aq)_(a))/(10^(-3))}`
`-2=log[(M^(2+)(aq)_(a))/(10^(-3))]`
`10^(-2)xx10^(-3)=M^(2+)(aq)_(a)=solubility =s`

`K_(sp)=4s^(3)=4xx(10^(-5))^(3)=4xx10^(-15)`