No. 582] SIGNIFICANCE OF INTERNAL CONDITIONS 349 



3. The Phase Rule 

 One other principle of physical chemistry finds frequent 

 application in biology, and that is the phase rule devel- 

 oped by Gibbs. The phase rule defines the condition of 

 equilibrium existing in a system by the relation between 

 the number of coexisting phases and components. "Ac- 

 cording to it a system made up of n components in n -f 2 

 phases can only exist when pressure, temperature and 

 composition have definite fixed values; a system of n 

 components in w + 1 phases can exist so long as only 

 one of the factors varies and a system of n components 

 in n phases can exist while two of the factors vary. In 

 other words, the degree of freedom is expressed by the 

 equation 



p + F = C + 2, or F = C + 2 — P, 



where P designates the number of phases, C the number 

 of components, and F the degree of freedom. ' ' 39 In other 

 words, F represents the number of conditions which may 

 be varied without causing one of the phases to disappear. 



An example of the phase rule, based upon the proper- 

 ties of a familiar substance, is that of ice, liquid water and 

 water vapor existing together in a closed vessel from 

 which the air has been exhausted. Ice, liquid water and 

 water vapor each constitute a phase of the system, and 

 there is but one component or substance— water— present. 

 Here, one component exists in three different phases. 

 We have, then, n components and n -f- 2 phases. The es- 

 sential conditions for the existence of the system are 

 temperature and pressure of the water vapor. In the 

 notation quoted above, P = 3, C = 1. Hence, F = 1 + 2 

 — 3 = 0. Neither of the conditions — temperature or 

 pressure— of the system can be changed without causing 

 one of the phases to disappear. There is no degree of 

 freedom, or, as it is sometimes expressed, the system is a 



