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

Answer

B

Explanation

The cell reaction is :
`M^(2+)(0.001 M) hArr M(S)" "( :' n=2)`
`Q=S/0.001`
`E^(@)=0`
`E=0-0.059/2"log"S/0.001`
`0.059=-0.059/2"log"(S/0.001)`
`-2="log"S/10^(-3)`
`S=10^(-5)`
`K_(sp)=4S^(3)`
`=4xx(10^(-5))^(3)`
`=4xx10^(-15)`