Broad Definition: Electrochemistry is chemistry, but where electrically-charged particles are mobile.
Narrower definition: electrochemistry is a chemical reaction in which the electrochemical step (the moving of an electron or hole) is the rate-limiting step. This way, the chemical reaction can be driven forwards or backwards by supplying a source of sink of electrons. This is very useful, on so many levels.
Here are the four guiding principles for all of electrochemistry.
1. Chemical Thermodynamics. Electrochemistry is simply thermodynamics, but the electron is counted as a chemical species: add the electrochemical potential to all of the chemical potentials. If you can do thermodynamics, you can do electrochemistry too.
2. Charge Neutrality. Adding the chemical potential of an electron adds another constraint—charge balance. Charge neutrality must be conserved, so for every electron liberated, it must be consumed by another reaction. No extra electrons nor deficits allowed! Therefore, electrochemical reactions are *always* coupled oxidation and reduction= “redox” reactions. If you’re sitting in a seminar in which the words “redox” or “oxygen fugacity” have just floated by, pay attention, and simply follow the electrons. It’s the geochemistry equivalent of mass/energy/momentum balance.
3. Mass Balance. As in thermodynamics, mass balance plays an important role. The charge taken up by the sum of all oxidation reactions has to equal the charge taken up by the reduction reactions. For simplicity in Earth science contexts, we’ll do our best to assume that only one oxidation reaction and one reduction reaction dominates. Remember by rule 2 charge neutrality—that a set of oxidation and reduction reactions must dominate together! The challenge in application will be to determine which set of reactions dominates setting the local equilibrium for the local system, and which sub-systems are forced to respond. Chemically—who leads and who follows? But even asking this simple question can get complicated. Hopefully for most systems of interest, only one set of redox reactions dominates setting the environment, and everything else simply responds. As always, my general philosophy is to start simple and only get complicated if I am forced to do so by reality.
4. Kinetics. Electrochemical thermodynamics tells us whether or not a redox reaction is energetically favored, and addresses whether a reaction has the ability to proceed. But kinetics tells us how quickly it will happen—and therefore whether or not the reaction will actually really occur in a real system. Again in the interest of binary simplicity in Earth science contexts I like to think of kinetics as either very fast (kinetic limitations unimportant: hey we have geologic time!) or zero (very slow—as in diffusion-limited solid state reactions even over geologic time.)
Given these four considerations—each is worth at least one undergrad and one grad level course all by itself—we are set up to do all Earth electrochemistry. The rest is just data and examples.