Chemical potential is a thermodynamics concept familiar to many, not only in materials science but also in physics, chemistry, chemical engineering, and biology. It is a central concept in thermodynamics of materials because all of the thermodynamic properties of a material at a given temperature and pressure can be obtained from knowledge of its chemical potential. Under the most common thermodynamic condition of constant temperature and pressure, chemical potential determines the stability of substances, such as chemical species, compounds, and solutions, and their tendency to chemically react to form new substances, to transform to new physical states, or to migrate from one spatial location to another.
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Chemical potential is considered by many to be one of the most confusing and difficult concepts to grasp, although there appears to be no confusion about temperature, pressure, and electric potential. Chemical potential has been underappreciated and underutilized in applications of thermodynamics to materials science and engineering. One of the reasons for this is the widespread use of molar Gibbs free energy, partial molar Gibbs free energy, or simply Gibbs energy or Gibbs free energy but with the unit of J/mol. Adding to the confusion is the occasional use of Gibbs potential in place of Gibbs energy or Gibbs free energy, even when it refers to the Gibbs free energy of an entire system rather than on a per mole basis. Another reason why chemical potential is underappreciated is the surprising lack of a unique unit associated with such a quantity of central importance in the thermodynamics of materials.
Josiah Willard Gibbs formally introduced the concept of chemical potential approximately 140 years ago in his foundational article.1 Gibbs not only established the mathematical beauty of thermodynamics by formulating the fundamental equation of thermodynamics of a system but also introduced the concept of chemical potential, which he originally called the intrinsic potential. The establishment of the fundamental equation and introduction of chemical potential marked the birth of chemical thermodynamics and made it possible to apply thermodynamics to materials science and engineering.
The definition of chemical potential based on Equation 4 should be significantly easier to comprehend for most people, particularly for beginners in thermodynamics, than using derivatives or rate of increase in an energy function with respect to the addition of a substance, as is often the case. For example, in most textbooks, the chemical potential of a given species i is defined as the rate of increase in the internal energy of the system with respect to the increase in the number of moles of species i under constant entropy, constant volume, and constant number of moles for all species except species i. Alternatively, it is defined as the rate of increase in the Gibbs free energy of the system with respect to the increase in the number of moles of species i under constant temperature, constant pressure, and constant number of moles for all species except species i.
For those that do think about energy, most if not all the attention that energy gets from chemists is devoted to heating, cooling, separations, electrochemistry, pumping and reluctantly, to calculations related to thermodynamics (e.g., Gibbs Free Energy). The attention is not in minimizing or considering where energy comes from or if it matters what form is used, it's just a given that we need to heat or cool or shove electrons into the reaction to make or break bonds. In reflecting on my own training as a chemist, I never was asked to convert any heating, cooling, pumping or electrochemical requirements to a cost for electricity, steam or some other utility. That may be done in chemical engineering, but not in chemistry. 2ff7e9595c
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