The Phase Rule.—In 1876 Willard Gibbs of Yale published a paper in the Proceedings of the Connecticut Academy of Science on the “Equilibrium of Heterogeneous Substances,” and two years later he published an abstract of the article in the Journal (16, 441, 1878). He had discovered a new law of nature of momentous importance and wide application which is called the “Phase-Rule” and is expressed by a very simple formula.
The application of this great discovery to chemical theory was delayed for ten years, partly, perhaps, because it was not sufficiently brought to the attention of chemists, but largely it appears because it was not at first understood, since its presentation was entirely mathematical.
It was Rooseboom, a Dutch chemist, who first applied the phase-rule. It soon attracted profound attention, and the name of Willard Gibbs attained world-wide fame among chemists. When Nernst, who is perhaps the most eminent physical chemist of the present time, was delivering the Silliman Memorial Lectures at Yale a few years ago, he took occasion to place a wreath on the grave of Willard Gibbs in recognition of his achievements.
To understand the rule, it is necessary to define the three terms, introduced by Gibbs, phase, degrees of freedom and component.
By the first term, is meant the parts of any system of substances which are mechanically separable. For instance, water in contact with its vapor has two phases, while a solution of salt and water is composed of but one. The degrees of freedom are the number of physical conditions, including pressure, temperature and concentration, which can be varied independently in a system without destroying a phase. The exact definition of a component is not so simple, but in general, the components of a system are the integral parts of which it is composed. Any system made up of the compound H2O, for instance, whether as ice, water or vapor, contains but one component, while a solution of salt and water contains two. Letting P, F, and C stand for the three terms, the phase-rule is simply
F = C + 2 − P
that is, the number of degrees of freedom in a system in equilibrium equals the number of components, plus two, minus the number of phases. The rule can be easily understood by means of a simple illustration. In a system composed of ice, water and water vapor, there are three phases and one component and therefore
F = 1 + 2 − 3 = 0
Such a system has no degrees of freedom. This means that no physical condition, pressure or temperature can be varied without destroying a phase, so that such a system can only exist in equilibrium at one fixed temperature, with a fixed value for its vapor-pressure.
