Chemical Potential

The purpose of the first chapter was to give an overview of the book’s contents: the topics covered, results gained, limitations, and so on. The next seven chapters, starting with this one, give the groundwork on which the main conclusions are based. The intention is to assemble the needed ideas, taking advantage of the fact that an extensive literature exists in which the ideas are established, discussed, restricted, etc. What follows is thus an extract of selected essentials from other documents, rather than being a free-standing and self-contained development of the ideas. The reader is asked to relate the ideas as summarized here to the longer discussions in which they appear elsewhere. The total energy in a portion of material can be split in either of two ways: . . . Total energy = internal energy + external energy, or . . . . . . Total energy = free energy + bound energy . . . In symbols, . . . U + PV = total = G + TS . . . where U = internal energy of the portion; G = free energy of the portion, specifically the Gibbs free energy or enthalpy; P = pressure; V = volume of the portion; T = temperature; S = entropy of the portion. All the terms except the free energy, G, have independent definitions, so the equations just given define that quantity: . . . G = U + PV – TS (2.1) . . . The equation relates to whatever portion of material one has in view. We now suppose that the material has n components and that, in the portion considered, the masses of each are m1, m2, . . . , mn. Then we imagine increasing m1 by a small amount δm1 while keeping P, T, and m2, m3, . . , ,mn constant. Let the consequent change in G be δG: then the limit of the ratio δG/δm1 as δm1 → 0 is the quantity of interest, henceforth written μ1; it is the chemical potential of component 1 in the material at its current pressure, temperature, and composition.