Gibbs Energy of Reaction Taking Place in an Electrochemical Cell Notes Chapter 3 Electrochemistry Chemistry Class 12

Q-14 What is the Gibbs energy of reaction taking place in an electrochemical cell?
Electrical work done in one second is equal to electrical potential multiplied by total charge passed. If we want to obtain maximum work from a galvanic cell then charge has to be passed reversibly. The reversible work done by a galvanic cell is equal to decrease in its Gibbs energy and therefore, if the emf of the cell is E and nF is the amount of charge passed and ΔrG is the Gibbs energy of the reaction, then
Δ rG = – nFE(cell)
It may be remembered that E(cell) is an intensive parameter but ΔrG is an extensive thermodynamic property and the value depends on n. Thus, if we write the reaction
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
ΔrG = -2FE(cell)
but when we write the reaction
2 Zn (s) + 2Cu²⁺(aq) →2 Zn²⁺(aq)+2Cu(s)
ΔrG = -4FE(cell)
If the concentration of all the reacting species is unity, then E(cell) = (cell) EV and we have
ΔrG_ = –nFE^Ө (cell) …(1)
We have the relation
ΔrG_ = –RT ln K. … (2)
From equation (1) and (2)
–nFE^Ө (cell) = –RT ln K.
E^Ө (cell) = –RT/nF ln K.