Chemical potentials are what ultimately determines where electrons move. In the theory we present, the chemical potential is expressed in terms of reinterpretations of several well-known chemical concepts and physical quantities, including electronegativity, chemical hardness, changes in electronic repulsions within a molecule, and the sensitivity of core levels to changes in the electron density. One effect formalized (but not explored in this work) is the effect of pressure on the chemical potential. Conditions of high pressure are likely to significantly affect equilibration of electronegativity in chemical reactions, as also suggested elsewhere. At the zero-temperature limit, an expression of the Fermi level emerges that, we think, helps to connect several central chemical concepts to a plethora of material properties, theories and phenomena predominantly explored in condensed matter physics.