Question
For the cell Zn/Zn2+ (aq) || Cu2+(aq) | Cu, derive the relation between E°cell and Kc at 298 k.
Solution
Gibbs energy of the reaction given by:
= – nFE(cell)
thus the reaction
Zn(s) + Cu2+(aq)---> Zn2+(aq) + Cu(s)
= – 2FE(cell)
but when we write the reaction
2 Zn (s) + 2 Cu2+----->2 Zn2+(aq) + 2Cu(s)
= – 4FE(cell)
If the concentration of all the reacting species is unity, then
E(cell) =
and we have
= – nF
Thus, from the measurement of we can obtain an important thermodynamic quantity, , standard Gibbs energy of the reaction.
From the latter we can calculate equilibrium constant by the equation:
= –RT ln Kc
