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Chemistry 1876

On the Equilibrium of Heterogeneous Substances

J. Willard Gibbs

Minimize free energy, and you can predict every phase, mixture and chemical equilibrium.

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In depth · the introduction

Why does water freeze at one fixed temperature, why does sugar dissolve only so far, why does a battery push exactly so many volts? Gibbs found the single bookkeeping rule behind all of it.

The big idea

Every chemical situation — ice melting, sugar dissolving, iron rusting — is drifting toward a balance. Gibbs showed there is one quantity, now called free energy, that a system lowers as far as it possibly can; when it can sink no further, the system is at equilibrium and stops changing.

Out of that one idea he pulled a startlingly simple counting law, the phase rule. For a pure substance, the number of conditions you are still free to change — temperature, pressure — equals the number of ingredients minus the number of phases present, plus two. It tells you, before any experiment, how much freedom a mixture has.

How it came about

Josiah Willard Gibbs was a soft-spoken Yale professor who rarely left New Haven. Between 1875 and 1878 he published a 300-page memoir in a little-read Connecticut journal, written in spare, forbidding mathematics. Almost no one read it.

James Clerk Maxwell in England was one of the very few who saw its depth. He carved a plaster model of Gibbs's “thermodynamic surface” and mailed it across the Atlantic to Yale. The work stayed buried until it was translated into German (1892) and French (1899) — only then did chemists realize that a quiet American had written the foundation of their science.

Why it mattered

Before Gibbs, much of chemistry was recipes and rules of thumb. He turned it into a predictive science: given temperatures, pressures and amounts, you could now calculate which way a reaction will go, how far it will run, and which phases can sit together — without endless trial and error. Steelmaking, semiconductor growth, drug formulation and the chemistry of rocks all run on his equations.

A way to picture it

Imagine a landscape of hills and valleys, where every possible state of a chemical system is a spot on the terrain and the “height” is its free energy. Left alone, the system rolls downhill and settles in the lowest valley it can reach — that is equilibrium. Change the temperature or pressure and you tilt the whole landscape, so the lowest valley moves: below 0 °C the ice valley wins, above it the liquid valley does. Gibbs handed us the map and the rule for how it tilts.

Interactive pressure–temperature phase diagram of water: choose a solid, liquid or vapour region, a melting/boiling/sublimation line, or the triple point, and see how many phases coexist and how many degrees of freedom F = C − P + 2 remain.

Where it sits

Carnot (1824) and Clausius had built thermodynamics for heat engines; Gibbs carried it into chemistry. He stands beside Boltzmann (1877), who at the very same time was giving entropy its molecular meaning; decades later Gibbs himself wrote the textbook of statistical mechanics that fused the two strands. The free energy he defined is the G that every chemistry student now meets as “ΔG.”

The original document
Original source text
J. Willard Gibbs · Transactions of the Connecticut Academy of Arts and Sciences, vol. III (1875–78): 108–248, 343–524
Die Energie der Welt ist constant. Die Entropie der Welt strebt einem Maximum zu.
The two sentences from Clausius that Gibbs set as the motto at the head of the memoir: “The energy of the world is constant. The entropy of the world tends toward a maximum.” The whole work is an answer to the question they pose — what configuration does matter settle into when its entropy can rise no further.
The criterion of equilibrium
Gibbs takes the two laws of thermodynamics as his only premises. For an isolated system he states the condition for equilibrium: among all variations that conserve the energy, the entropy is a maximum (equivalently, at fixed temperature and pressure the appropriate free energy is a minimum). Every later result is squeezed out of this single principle.
The fundamental equation and the potentials
He writes the energy of a homogeneous mass as a function of its entropy, volume and the masses of its independent components, and introduces for each component a quantity he calls its potential — what is now the chemical potential. Two phases in contact are in equilibrium only when their temperature, their pressure and the potential of every component are equal.
On coexistent phases
In this part Gibbs gives the modern thermodynamic meaning of the word phase, and by counting the equalities that must hold among r coexistent phases of n components he obtains the rule for the number of their independent variations — the phase rule, F = C − P + 2.
[ … ]
The memoir runs on to dilute solutions and osmotic pressure, the conditions of chemical reaction, electrochemical equilibrium, and the thermodynamics of surfaces and adsorption — a single framework for equilibria across phases, mixtures, reactions and interfaces.
New Haven, Connecticut · 1875–1878