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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 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)`

A

`1xx10^(-15)`

B

`4xx10^(-15)`

C

`1xx10^(-12)`

D

`4xx10^(-12)`

Text Solution

Verified by Experts

The correct Answer is:
B
The given concentration cell is
`M|M^(2+)("Saturated"=C_(1))||M^(2+)(0.001M=C_(2))|M`
EMF of concentration cell is ltBrgt `E_(cell)=(2.303RT)/(F)"log"(C_(2))/(C_(1))=(0.059)/(n)"log"(C_(2))/(C_(1))`
`therefore0.059=(0.059)/(nF)"log"(C_(2))/(C_(1))=(0.059)/(n)"log"(C_(2))/(C_(1))`
`therefore0.059=(0.059)/(2)"log"(0.001)/(2)`
or `2="log"(10^(-3))/(C_(1))" or "log10^(-3)-logC_(1)=2`
or `-3-logC_(1)=2" or "logC_(2)=-5`
or `C_(1)=10^(-5)M`
For the salt `MX_(2)`,
`underset(S)(MX_(2))hArr underset(S)(M^(2+))+underset(2S)^(2X^(-))`
`K_(sp)=S(2S)^(2)=4S^(3)=4xx(10^(-5))^(3)`
`=4xx10^(-15)`
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