The most amazing thing about electrochemical cells is that by separating the oxidation and reduction reaction into different compartments, we now have the ability to directly measure the free energy of the reaction by measuring the electrical potential.
The potential or voltage or EMF or whatever you prefer to call it is a measure of the free energy of the reaction. This is because the difference in free energy between the reactant and the products directly corresponds to the electrical potential of the cell.
When looking at chemical reactions, we often talked about the difference in free energy between the reactants and products. This was either \(\Delta G\) at whatever conditions existed currently or if it was given at standard conditions, we had \(\Delta G^\circ \).
Previously, we discussed this in terms only of spontaneity. However, \(\Delta G\) has another interpretation. It corresponds to the maximum reversible work we can extract from this chemical reaction. While previously you may have dealt with the concept of "work" in the context of pressure-volume work, the "work" we are interested in now is electrical work.
Electrical work is defined as charge times potential (\(w = q \cdot \mathcal{E}\) ). This will give us an energy. The total work would be the charge that is run through the cell (coulombs, C) times the potential (volts, V) of the cell. Note that a coulomb·volt is equivalent to a joule (1 V·C = 1 J). For a reaction, we are typically interested in the work (or energy) per mole of reaction. This is how we defined \(\Delta G\) with units of kJ mol-1. Looking at this, we get
\[{\rm work} = \Delta G = -n F \mathcal{E}\]
Here \(\Delta G\) is not for the standard conditions, but for the conditions now. So the potential \(E\) is not the standard potential but the potential now. \(n\) is the number of electrons per mole reaction as the equation is written. \(F\) converts between mole of electrons and charge in coulombs. Note: the energy you get is still per mole, but it is per mole reaction (not per mole of electrons).
With this relation, we can now convert directly between differences in free energy and differences in electrical potential!
Cell Potential and Electrical Work© 2013 mccord/vandenbout/labrake