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The electrochemical cell shown below is ...

The electrochemical cell shown below is a concentration cell.
`M|M^(2+)` (saturated solution of a sparingly soluble salt, `MX_2` || `M^(2+)` (0.001 mol `dm^(-3)`) |M
The emf of the cell depends on the difference in concentration of `M^(2+)` ions at the two electrode The emf of the cell at 298 is 0.059 V
The solubility product `(K_(sp) , mol^(3) dm^(-9)) ` of `MX_2 ` at 298 based on the information available the given concentraiton cell is (take ` 2.303 xx R xx 298 // F = 0.059 V`)

A

` 1 xx 10^(-15)`

B

`4 xx 10^(-15)`

C

`1 xx 10^(-12)`

D

`4 xx 10^(-12)`

Text Solution

Verified by Experts

The correct Answer is:
B

`0.059 = (-0.059)/(2) log ""([M^(+2)])/(10^(-3)) , S = [M^(+2)] M xx 2 = 10^(-2) xx 10^(-3) = 10^(-5)`
` K_(gp) = [M^(+2)] [X^(-)]^(2) = (10^(-5)) (2 xx 10^(-5))^(2) = 4 xx 10^(-15)`
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