Cell Potential, Electrical Work, and Free Energy

The work that can be accomplished when electrons are transferred through a wire depends on the "push" (the thermodynamic driving force) behind the electrons.  This driving force (the emf) is defined in terms of a potential difference (in volts) between two points in the circuit.

emf=potential difference (V) = work (J) / charge (C)

The term "work" is viewed from the point of view of the system.  Work flowing out of the system is a minus sign and when a cell produces a current, the cell potential is positive and the current can be used to do work.  Thus, cell potential and work (w) have opposite signs.

E = -w (work) / q (charge)

and wmax = -qEmax

However, because current must always flow to obtain work and when current flows energy is wasted, the maximum work is not obtained.  In any real, spontaneous process some energy is always wasted--the actual work realized is always less than the calculated maximum.  So the actual work done is:

w = -qE

where E represents the actual potential difference at which the current flowed and q is the quantity of charge in coulombs transferred.  The faraday is the charge on 1 mole of electrons and is abbreviated F.  It has the value of 96,485 coulombs of charge per mole of electrons.  Thus q equals the number of moles of electrons times the charge per mole of electrons:

q = nF

When we want to relate the potential to free energy, we see that the change in free energy equals the maximum useful work obtainable from that process:

ΔG = -nFE

which states that the maximum cell potential is directly related to the free energy difference between the reactants and the products in the cell.