Since chemical equations written in terms of species and biochemical equations written in terms of sums of species, at a specified pH, are matrix equations, it is of interest to apply these methods to electrochemical equations. The transport of electrons from one electrode to another is coupled to a chemical reaction system, and this coupling is expressed by an additional conservation equation for the system. Matrix methods can also be applied to electrochemical reactions at a specified pH. When the pH is fixed, the Gibbs energy G is not minimized equilibrium, and it is necessary to use a Legendre transform to define a transformed Gibbs energy G’that is minimized at equilibrium. This leads to a transformed enthalpy H’ and a transformed entropy S’and requires cell reactions and half-cell reactions to be written in such a way that it is immediately evident that the pH is held constant.