A fuel cell is an energy conversion system that converts chemical energy directly to electrical energy without any intermediate steps. At the very elementary level, a fuel cell consists of two electrodes (designated as anode and cathode) where ionization of the chemical species fuel/oxidizer takes place. The two electrodes are separated by a membrane which permits only ions to move through it. The electrodes are loaded with catalyst (catalyst loading - grams per unit electrode surface area; mg/cm²) to facilitate the respective electrode reaction. The typical structure of a fuel cell is presented in the following figure. The figure to the left presents a positive ion (a specie that has lost electrons; hence positively charged) exchange membrane type fuel cell while the figure to the right presents a negative ion (a specie that has gained electrons; hence negatively charged) exchange membrane type fuel cell.

Fuel is supplied to the anode side of the fuel cell where it gets oxidized by loosing electron(s). Similarly, oxidizer is supplied to the cathode side where it gets reduced by accepting electrons. The fuel cell is maintained at temperatures at which the catalysts can oxidize the fuel / reduce the oxidizer. The membrane that separates the anode and the cathode permits only charged ions to pass through and depending on its construction, the membrane can permit either the positive ions to pass through from the anode to the cathode side or can permit the negative ions to pass through from the cathode to the anode side. In either case, electrons generated on the anode side move through the external circuit to the cathode side, doing electrical work.

In a positive ion exchange fuel cell, the positive ions generated on the anode move through the membrane to the cathode side and form product(s) by reacting with the reduced oxidizer and the electrons. Thus, the products will be formed on the cathode side as such the cathode side will have to be designed to carry away the products. A typical example of a positive ion exchange fuel cell is the Proton Exchange Membrane (PEM) fuel cell (PEMFC) wherein Hydrogen is used as the fuel and Oxygen is used as the oxidizer. Platinum is used as the catalyst on both the electrodes (with different loading intensity) of a PEM fuel cell. Operating at near ambient temperature, Hydrogen ions are formed on the anode side which then move through the membrane to the cathode side to react with reduced Oxygen and incoming electrons forming Water as the terminal product. A typical example of a negative ion exchange fuel cell is the Solid Oxide (SO) fuel cell (SOFC) wherein typically Hydrogen is used as the fuel and Oxygen is used as the oxidizer. Nickel is used as the catalyst on both the electrodes (with different loading intensity) of an SO fuel cell. Operating in the 500 to 1000 deg C temperature range, Oxygen ions are formed on the cathode side by accepting the incoming electrons and these ions then move through the membrane/electrolyte to the anode side to react with oxidized Hydrogen forming Water as the terminal product. The elementary construction and basic fuel/oxidizer ionization and flow for both PEMFC and SOFC are presented in the following figure.

As a fuel cell is supplied with fuel and oxidizer on the anode and cathode side respectively, electrons start to accumulate on the anode side resunting in the establishment of a gradient (difference in the concentration of electrons) of electrons across the electrodes. If the anode and cathode are not connected through an external circuit, the gradient continues to build upto a certain threshold magnitude. Once the threshold magnitude is attained with no current being drawn (when the circuit is open), no further accumulation of electrons takes place. This gradient of electrons establishes a driving potential OR voltage across the electrodes known as the Electro Motive Force (EMF) having units of volts. Thus, essentially, the EMF is the potential difference established across the anode and cathode when they are not electrically connected and hence no current is drawn. It is important to note that, as fuel and oxidizer are supplied continuously to the anode and cathode side, electron and hence negative charge build-up on the anode side takes place. If these electrons are not evacuated (as in open circuit mode) the negative charge continues to build resulting in increased resistance to further oxidation of fuel. At a sufficiently high negative charge, practically no further nett oxidation of fuel (and hence release of electrons) takes place as equilibrium sets in. At equilibrium, every forward reaction is accompanied by an equivalent reverse reaction, resulting in no nett change. Thus, even in the face of continuous and infinite supply of fuel and oxidizer, equilibrium restricts the electron build-up and hence the EMF to a finite value.
When the anode and cathode are electrically connected through and external circuit, it is the EMF (measured in volts) that drives the electrons from the anode to the cathode across the load. The EMF is thus, basically the work done (Joules) in moving a unit charge (Coulombs) across the applied load. If a single fuel molecule is oxidized releasing one electron, the EMF generated can mathematically be represented as;

If, on oxidation of a single fuel molecule, n electrons are released then the total charge correspond to ne^-. Similarly, oxidation of one mole of fuel molecules (Avogadro constant → N_A = 6.02214076 x 10²³ number of molecules) will result in a total charge of N_Ane^-. The product of Avogadro number and charge on an electron is basically the Faraday constant F (= N_Ae^-). Thus, the total charge will be nF. The expression for EMF developed when a mole of fuel is oxidized with each molecule releasing 2 electrons will be;

The maximum electrical work developed by a fuel cell under constant temperature and pressure conditions basically corresponds to the change in the Gibbs free energy dG; essentially dG = - W_el [Click HERE for the derivation]. The expression for the EMF thus takes the form;

• Faraday constant F → 96,485 Coulombs / mole
• Avogadro constant N_A → 6.02214076 x 10²³ per mole
• Charge on an electron e^- → 1.60217662 x 10^-19 coulombs