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 concentrations of `M^(2+)` ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.
The solubility product `(K_(sp), mol^(3) dm^(-9))` of `MX_(2)` at 298 K based on the information available for the given concentration cell is `("take "2.303xxRxx298//F=0.059 V)` :

Options

A. `1xxx10^(-15)`
B. `4xx10^(-15)`
C. `1xx10^(-12)`
D. `4xx10^(-12)`

Answer

B

Explanation

`M|M^(2+)(aq)||underset(0.001M)(M^(2+(aq)|M)`
Anode: `MtoM^(2+)(aq)+2e^(-)`
cathode: `underline(M^(2+)(aq)+2e^(-)toM)`
`M^(2+)(aq)_(c)hArrM^(2+)(aq_(a)`
`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)="solubility"=s`
`K_(sp)=4s^(3)=4xx(10^(-5))^(3)=4xx10^(-15)`