EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 163 



The foregoing considerations appear sufficient to justify the defi- 

 nition of an ideal gas-mixture which we have chosen. It is of course 

 immaterial whether we regard the definition as expressed by equation 

 (273), or by (279), or by any other fundamental equation which can 

 be derived from these. 



The fundamental equations for an ideal gas-mixture corresponding 

 to (255), (265), and (271) may easily be derived from these equations 

 by using inversely the substitutions given on page 156. They are 



) log X- 



& l1 ll 



(292) 



- 2^1 ^i + a.m,) tlogt + ^a.m.t log )- ( 293 > 



The components to which the fundamental equations (273), (279), 

 (291), (292), (293) refer, may themselves be gas-mixtures. We may 

 for example apply the fundamental equations of a binary gas-mixture 

 to a mixture of hydrogen and air, or to any ternary gas-mixture in 

 which the proportion of two of the components is fixed. In fact, 

 the form of equation (279) which applies to a gas-mixture of any 

 particular number of components may easily be reduced, when the 

 proportions of some of these components are fixed, to the form which 

 applies to a gas-mixture of a smaller number of components. The 

 necessary substitutions will be analogous to those given on page 156. 

 But the components must be entirely different from one another with 

 respect to the gases of which they are formed by mixture. We 

 cannot, for example, apply equation (279) to a gas-mixture in which 

 the components are oxygen and air. It would indeed be easy to 

 form a fundamental equation for such a gas-mixture with reference 

 to the designated gases as components. Such an equation might be 

 derived from (279) by the proper substitutions, But the result would 

 be an equation of more complexity than (279). A chemical compound, 

 however, with respect to Dalton's law, and with respect to all the 

 equations which have been given, is to be regarded as entirely 

 different from its components. Thus, a mixture of hydrogen, oxygen, 

 and vapor of water is to be regarded as a ternary gas-mixture, having 

 the three components mentioned. This is certainly true when the 

 quantities of the compound gas and of its components are all inde- 

 pendently variable in the gas-mixture, without change of temperature 



