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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)^(@). |
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Answer» Solution :`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)^@` |
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