Question

Derive the relation of EMF of cell with G and H.​

Answer 1

Answer:

One is to realise that (reversible ideal case) ΔG=Wnon-exp (non-expansion). Therefore, in an ideal chemical cell, if the potential difference between the electrodes is E, to move one mole electrons across the external circuit will be FE, which must be equal to the decrease in gibbs free energy of the system. Hence for n mole electrons transferred at the same potential, Wnon-exp=ΔG=−nFE.

The fact that ΔG=Wnon-exp can be derived as under:

$:dSdUWnon-exp=δqT=δq+Wnon-exp+Wexp=dU−Wexp−δq=dU+pdV−TdS=dH−TdS=dG(reversible case)(const. p and T)$

Another approach is to use

μelectrochemical=μchemical+zFϕ,

where ϕ is the electric potential at the point, z is the charge on the species. Using this and$anddGT,P=∑i=1nμidni,$   we get the required equation for z=1 for an electron, and considering the electrochemical potential of both the electrodes. I am unsure of a rigorous derivation for the electrochemical potential but Wikipedia has some basics on it.