The concept of free energy is covered in the course on Chemical Thermodynamics.
One of the principal reasons to study electrochemistry centers around the fact that, when a chemical reaction is conducted electrochemically, we have the best chance of making use of all of the available free energy (ΔG) from that chemical reaction.
The relationship between free energy and Eo is: ΔG = -nFEo
Gibbs free energy.