RESPIRA TION 6 1 7 



of separation between the phases. What are to be regarded as the components 

 taking part in the equilibrium is not always easy to see. They may all be of the 

 same chemical compound, such as ice, water, and steam. In a gas phase, there 

 may be a number of different gases, but it remains one homogeneous phase. A 

 mixture of different solids, on the contrary, consists of as many phases as there 

 are substances present, as in the case of calcium carbonate and calcium oxide, 

 dealt with above. The components of the system are to be regarded as those 

 which are not mutually dependent on one another. Thus, in the calcium carbonate 

 case, if two of the phases are taken, the composition of the third is denned by the 

 equation : 



Suppose that we have a given mass of a gas, that is, one phase, we cannot define 

 its state by fixing one only of its independent variables, temperature, pressure, 

 and volume. The same volume, for example, may be obtained by 'changing 

 pressure and temperature inversely. But if two are fixed, then the third must 

 have a definite value; at any given values of temperature and pressure, a given 

 mass of gas can only occupy one particular volume. 



Next, suppose that we have two phases, say, water in contact with its vapour. 

 Here the condition is defined by giving one only of the variables a definite value. 

 If we fix the temperature, the pressure under which liquid and vapour can both 

 exist is determined also. 



Finally, suppose that we have ice also, that is, three phases. We find now 

 that it is impossible to change any one of the three variables without causing 

 disappearance of one of the phases. In other words, there is only one temperature 

 and one pressure at which ice, water, and steam can coexist together, the so-called 

 "triple-point." 



We see, then, that according to the number of phases present, a different 

 number of the variable factors requires fixing in order to define perfectly the state 

 of the system. This number is spoken of as that of the degrees of freedom, and a 

 system is said to be invariant, univariant, bivariant, or multivariant according 

 as the number of degrees of freedom is zero, one, two, or more than two. 



A point of importance is that, in the heterogeneous systems dealt with by the 

 phase rule, the state of equilibrium is independent of the amounts of the phases 

 present. 



Willard Gibbs formulated the phase rule, which may be most concisely put 

 thus : If P is the number of the phases, F that of the degrees of freedom, and C 

 the number of components, then, 



or, F = C + 2-P. 



The greater the number of phases, the fewer the degrees of freedom. 



In the case of water in contact with its vapour, we have two phases and one 

 component, so that the number of degrees of freedom is, 



1 + 2-2 = 1. 



In the calcium carbonate system there are two components, CaO and CaCO 3 (since 

 carbon dioxide is defined by CaCO 3 = CaO + CO 2 ), but three phases, gas (there can 

 only be one gas phase) and two solid phases. Thus, 



F = 2 + 2-3 = l. 



Both systems are univariant, possessing one degree of freedom only. To each 

 temperature, therefore, in both cases, there is one only definite pressure of vapour 

 or gas with which equilibrium is possible. 



In applying the phase rule to the case of haemoglobin and oxygen, we have 

 two solid phases, oxyhsemoglobin and haemoglobin, if we assume that oxyhaemoglobin 

 is a definite chemical compound. We have one gas phase, oxygen. The number 

 of components must be two, and therefore again : 



F=2 + 2-3 = l. 

 So that it seems that the system should behave like the calcium carbonate system, 



