A cell is to be constructed to show a redox change `:`
`Cr+2Cr^(3+)hArr3Cr^(2+)`. The number of cells with different `E^(c-)` an `n` but same value of `DeltaG^(c-)` can be made `(` Given `E^(c-)._(Cr^(3+)|Cr^(2+))=-0.40V,E^(c-)._(Cr^(3+)|Cr)=-0.74V,` adn `E^(c-)._(Cr^(2+)|Cr)=-0.91V)`

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

For `I` :
`{:(Cr|Cr^(3+)||Cr^(3+),Cr^(2+)|Pt),(CrrarrCr^(3+)+3e,E^(@)=+0.74V),(3Cr^(3+)+3erarr3Cr^(2+),E^(@)=-0.40V):}/(Cr+2Cr^(3+)rarr3Cr^(2+)(n=3))`
`E^(@) = 0.74 - 0.40 = 0.34 V`
`DeltaG^(@) = 3 xx 0.34 xx F = 1.02 F`
For (II)
`{:(Cr|Cr^(2+)||Cr^(3+)|Cr),(3Crrarr3Cr^(3+)+6e,E^(@)=0.91V),(2Cr^(3+)+6erarr2Cr,E^(@)=-0.74V):}/(Cr+2Cr^(3+)rarr3Cr^(2+)(n=6))`
For `E^(@) = 0.91 - 0.74 = 0.17 V`
`DeltaG^(@) = 0.17 xx 6 xx F = 1.02 F`
For (III)
`{:(Cr|Cr^(2+)||Cr^(3+)|Cr^(2+)|Pt),(CrrarrCr^(2+)+2e,E^(@)=0.91V),(2Cr^(3+)+2erarr2Cr^(2+),E^(@)=-0.40V):}/(Cr+2Cr^(3+)rarr3Cr^(2+)(n=2))`
`E^(@) = 0.91 - 0.40 = 0.51 V`
`:. DeltaG^(@) = 2 xx 0.51 xx F = 1.02F`