294 Wells & Foote — One Hundred Years of Chemistry. 



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 sys- 

 tem composed of ice, water and water-vapor, there are 

 three phases and one- component and therefore 



F = l + 2 — 3 = 



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 sys- 

 tem can only exist in equilibrium at one fixed tempera- 

 ture, with a fixed value for its vapor-pressure. 



For instance, if the system is heated above the fixed 

 temperature, ice disappears and if the pressure is raised, 

 vapor is condensed. If this same system of water alone 

 contains but two phases, for instance, liquid and vapor, 

 F = 1 + 2 — 2 == 1, or there is one degree of freedom. 

 In such a system, one physical condition such as tempera- 

 ture can be varied independently, but only one, without 

 destroying a phase. For instance, the temperature may 

 be raised or lowered, but for every value of temperature 

 there is a corresponding value for the vapor pressure. 

 One is a function of the other. If both values are varied 

 independently, one phase will disappear, either vapor 

 condensing entirely to water or the reverse. Finally if 

 the system consists of one phase only, as water vapor, 

 F = 2, or the system is divariant, which means that at 

 any given temperature it is possible for vapor to exist at 

 varying pressures. 



The illustration which has been given relates to physi- 

 cal equilibrium, but the rule is applicable to cases involv- 

 ing chemical changes as well. In comparing the 

 phase-rule with the law of mass action, it will be noticed 

 that both have to do with equilibrium. The great advan- 

 tage of the former is that it is entirely independent of the 

 molecular condition of the substances in the different 

 phases. For instance, it makes no difference so "far as 

 the application of the rule is concerned, whether a sub- 

 stance in solution is dissociated, undissociated or com- 

 bined with the solvent. In any case, the solution 

 constitutes one phase. On the other hand, the rule is 

 purely qualitative, giving information only as to whether 

 a given change in conditions is possible. The law of 

 mass action is a quantitative expression so that when the 



