The irreversible processes which occur in a binary electrolyte solution are described by a new formalism which uses observable variables. This is based on (i) the relationship of the electrochemical potential of ion constituents to the chemical potential of the electrolyte; (ii) the notion of observable electric potential measured with reversible electrodes; and (iii) the thermodynamics of irreversible processes. The electric potential, the electric charge density, and the Nernst-Planck-Poisson formalism are reviewed in this work. The properties of the new formalism are evidenced by applying it to MgCl2-H2O solutions.