Chemical Potential - Overview

Overview

Particles tend to move from higher chemical potential to lower chemical potential. In this way, chemical potential is a generalization of "potentials" in physics such as gravitational potential. When a ball rolls down a hill, it is moving from a higher gravitational potential (higher elevation) to a lower gravitational potential (lower elevation). In the same way, as molecules move, react, dissolve, melt, etc., they will always tend naturally to go from a higher chemical potential to a lower one, changing the particle number, which is conjugate variable to chemical potential.

A simple example is a system of dilute molecules diffusing in a homogeneous environment (animation at right). In this system, the molecules tend to move from areas with high concentration to low concentration, until eventually the concentration is the same everywhere.

The microscopic explanation for this is based in kinetic theory and the random motion of molecules. However, it is simpler to describe the process in terms of chemical potentials: A molecule has a higher chemical potential in a higher-concentration area, and a lower chemical potential in a low concentration area. Movement of molecules from higher chemical potential to lower chemical potential is accompanied by a release of free energy. Therefore it is a spontaneous process.

Another example is a glass of liquid water with ice cubes in it. Above 0°C, an H₂O molecule in the liquid phase has a lower chemical potential than a water molecule in an ice cube (solid phase). When some ice melts H₂O molecules migrate from solid to liquid where their chemical potential is lower. Below 0°C, the molecules in ice have a lower chemical potential, so the ice cubes grow. At the temperature of the melting point, 0°C, the chemical potentials in water and ice are the same; the ice cubes neither grow nor shrink, and the system is in equilibrium.

A third example is illustrated by the chemical reaction of dissociation of a weak acid, such as acetic acid, HA, A=CH₃COO-.

HA H+ + A-

Vinegar contains acetic acid. When acid molecules dissociate, the concentration of the undissociated acid molecules (HA) decreases and the concentrations of the product ions (H+ and A-) increase. Thus the chemical potential of HA decreases and the sum of the chemical potentials of H+ and A- increases. When the sums of chemical potential of reactants and product are equal the system is at equilibrium and there is no tendency for the reaction to proceed in either the forward or backward direction. This explains why vinegar is acidic, because acetic acid dissociates to some extent, releasing hydrogen ions into the solution.

Chemical potentials are important in many aspects of equilibrium chemistry, including melting, boiling, evaporation, solubility, osmosis, partition coefficient, liquid-liquid extraction and chromatography. In each case there is a characteristic constant which is a function of the chemical potentials of the species at equilibrium.

In electrochemistry, ions do not always tend to go from higher to lower chemical potential, but they do always go from higher to lower electrochemical potential. The electrochemical potential completely characterizes all of the influences on an ion's motion, while the chemical potential includes everything except the electric force. (See below for more on this terminology.)