Question

If `E_(1)^(@),E_(2)^(@)` and `E_(3)^(@)` are the standard electrode potential for `Fe//Fe^(2+),Fe^(2+),Fe^(2+)//Fe^(3+)` and `Fe//Fe^(3+)` electrodes respectively, derive a relation between `E_(1)^(@),E_(2)^(@) and E_(3)^(@)`.

Answer 1

`FetoFe^(2+)+2e^(-),DeltaG_(1)^(@)=2E_(1)^(@)F` . . . (i)
`Fe^(2+)toFe^(3+)+e^(-),-DeltaG_(2)^(@)=E_(2)^(@)F` . . (ii)
`Fe to Fe^(3+)+3e^(-),-DeltaG_(3)^(@)=3E_(3)^(@)F` . . . (iii)
Subracting eqn. (i) from eqn. (iii) , we get
`0 to Fe^(3+)-Fe^(2+)+e^(-),-DeltaG_(3)^(@)+DeltaG_(1)^(@)=F(3E_(3)^(@)-2E_(1)^(@))`
or `Fe^(2+) to Fe^(3+)+e^(-),-DeltaG_(3)^(@)+DeltaG_(1)^(@)=(3E_(3)^(@)-2E_(1)^(@))F` . . . (iv)
Comparing eqn. (ii) and (iv), we get
`-DeltaG_(2)^(@)=-DeltaG_(3)^(@)+DeltaG_(1)^(@)` [as eqns. (ii) and (iv) are same] ,brgt i.e., `E_(2)^(@)=F(3E_(3)^(@)-2E_(1)^(@))F` or `E_(2)^(@)=3E_(3)^(@)-2E_(1)^(@)` or `3E_(3)^(@)=E_(2)^(@)+2E_(1)^@`