Chemical Potential and Equilibrium

The chemical potential measures how a system's free energy changes when matter is added, and equating the chemical potentials of reactants and products pinpoints the position of chemical equilibrium.

Definition

Chemical potential is the partial molar Gibbs free energy of a species, and chemical equilibrium is the state in which the total Gibbs energy is minimized so that the weighted chemical potentials of reactants and products are equal.

Scope

This topic covers the chemical potential as the partial molar Gibbs energy, its dependence on temperature, pressure, and composition through activity and fugacity, and its role as the driving force for reaction and phase change. It develops the equilibrium condition for a reaction, the relation between the standard reaction Gibbs energy and the equilibrium constant, and the response of equilibrium to changes in conditions through Le Chatelier's principle and the van't Hoff equation. Calorimetric measurement of the underlying energetics is treated in a separate topic.

Core questions

• How does the chemical potential of a species depend on its activity or partial pressure?
• Why is equilibrium reached when the reaction Gibbs energy, not the standard Gibbs energy, is zero?
• How does the equilibrium constant depend on temperature through the van't Hoff equation?
• How does Le Chatelier's principle predict the response of equilibrium to disturbances?

Key concepts

• Chemical potential and partial molar quantities
• Activity, fugacity, and standard states
• Equilibrium constant and reaction quotient
• van't Hoff equation and temperature dependence
• Le Chatelier's principle

Key theories

Equilibrium constant from the reaction Gibbs energy

The reaction Gibbs energy is the slope of the total Gibbs energy along the reaction coordinate; setting it to zero gives the equilibrium condition and the relation between the standard reaction Gibbs energy and the equilibrium constant.

Temperature dependence via the van't Hoff equation

The variation of the equilibrium constant with temperature is governed by the standard reaction enthalpy, so exothermic equilibria shift toward products on cooling and endothermic ones on heating.

Clinical relevance

Chemical potential and equilibrium control the yield of industrial syntheses such as the Haber-Bosch process, the solubility and partitioning of drugs and pollutants, acid-base and complexation balances in solution, and the energetics of coupled reactions in metabolism.

History

Gibbs introduced the chemical potential in the 1870s; van't Hoff connected the equilibrium constant to thermodynamics through his isochore in the 1880s, and Lewis later introduced activity and fugacity to extend the treatment rigorously to real, non-ideal solutions and gases.

Key figures

• J. Willard Gibbs
• Jacobus Henricus van't Hoff
• Gilbert N. Lewis

Seminal works

• atkins2018
• levine2009

Frequently asked questions

Why is activity used instead of concentration in equilibrium expressions?

In non-ideal solutions and gases, molecules interact so that effective availability differs from nominal concentration or pressure; activity is the thermodynamically corrected quantity that restores the simple form of the equilibrium constant for real systems.

Does a catalyst change the equilibrium position?

No. A catalyst speeds the approach to equilibrium by lowering the activation barrier in both directions equally, but it leaves the equilibrium constant and the final equilibrium composition unchanged because these are set by thermodynamics, not kinetics.