Thermodynamics Of Voltaic Cell

Voltaic cells are used for spontaneous reactions. These reactions release energy which is then used for electrical work. The electrical work depends two factors

i) Total charge flowing between electrodes.

ii) Difference in electrode potential between two electrodes (E⁰).

If the cell yields an emf and supplies a quantity of electricity, then electrical work is done by the cell as W = QE. Here Q is charge and E is emf / cell potential. So we define work as “the product of charge and cell potential”.

∆G = W = QE

∆G = W = -QE e.q. 10.1

When energy is released then work is done by the system (negative).

The unit of charge is coulomb and emf if volt so,

W = coulomb x volt

The charge is due to flow of electrons and charge on one electron is 1.602 x10^-19 C. If one mole of electron will flow, then charge will be = 1.602 x10^-19 x 6.02x10^-23 = 9.6485 x 10⁴ C/mol.

Or 96485 c/mol of e^- = 1 Ferrate or 1F

Simply, charge on n moles for redox runs, Q= nF (Total charge). So, putting value of Q in e.q.10.1 we got

∆G = W = -nFE

and ∆G⁰ = W = -nFE⁰ e.q.10.2

Above is the relation between Gibbs free energy and cell potential. We also know that

∆G⁰ = -RTlnK e.q.10.3

LHS of e.q.10.2 and 10.3 is same so,

-nFE⁰ = - RTlnK