Published on *PNG 520: Phase Behavior of Natural Gas and Condensate Fluids* (https://www.e-education.psu.edu/png520)

We have just seen that the chemical potential is a thermodynamic property which is related to *all* thermodynamic properties with units of energy. Its most useful definition is given in terms of constant pressure and temperature:

$${\mu}_{i}={\left(\frac{\partial G}{\partial {n}_{i}}\right)}_{P,T,{n}_{i}\ne {n}_{1}}={\overline{G}}_{i}$$

This constitutes the working definition of chemical potential, the one that relates it to the partial molar quantity concept studied before.

Although the mathematical definition of chemical potential can be stated clearly, its “physical” meaning is not as easy to grasp. It is much easier to understand the physical implications of “pressure,” “temperature,” and “internal energy” than it is to undestand the physical interpretation of “chemical potential.” Given equation (15.24), and recognizing Gibbs free energy (G) as the capacity of a system to do work, we may write the following *formal* definition of chemical potential:

The **chemical potential** of a component in a given phase is the rate of increase of the capacity of the phase to do work per unit addition of the substance to the phase, at constant temperature and pressure.

We may also quote the definition that J.W. Gibbs provided for it:

If to any homogeneous mass, we suppose an infinitesimal quantity of any substance to be added, the mass remaining homogeneous and its entropy and volume remaining unchanged, the increase of energy of the mass divided by the quantity of the substance added is the potential for that substance in the mass considered.

This definition is closely related to the mathematical definition given in (15.20).

$${\mu}_{i}={\left(\frac{\partial U}{\partial {n}_{i}}\right)}_{S,V,{n}_{i}\ne {n}_{1}}$$

To understand the physical implications of the chemical potential of a species, we have to recall that for any thermodynamic process to be carried out, a driving force must be causing it. For instance, a pressure gradient is the driving force that causes the bulk movement of fluids from one point to the other, and a temperature gradient provides the potential difference needed for heat to flow. We also know that if we have a higher concentration of solute in a homogeneous system, it will diffuse to the zones of lower concentration. Here, the chemical potential is responsible for the diffusion of species within two points in space, or even its exchange between two different phases, without the presence of either pressure or temperature gradients. The *chemical potential* is the* potential* describing the ability of species to move from one phase to another.