356 KEYES ART. J 



not far from that calculated by the ideal gas law for mixtures. 

 At higher or lower temperatures, nevertheless, the differences 

 may be greater or less than that given by the latter law. As a 

 general and approximate statement present knowledge warrants 

 the conclusion that as far as low pressures are concerned, the 

 order of accord of the actual behavior of pure gases and mixtures 

 with the prediction of the perfect gas laws does not often 

 exceed two percent from zero degrees to higher temperatures. 

 Below zero the actual behavior of gases may show larger depar- 

 ture from the idealized state in special cases. 



16. Gihhs' Generalized Dalton's Law. The rule of pressures 

 stated in italics (Gibbs, 1, 155, 7th line) is one of very great inclu- 

 siveness.* It leads, for example, to a proposition relative to the 

 entropy of a gas in a mixture which is of very far reaching 

 theoretical significance and practical importance. It contains 

 and is also far more inclusive than Dalton's rule of partial 

 pressures as commonly stated, since its consequences involve 

 the proposition that the energy and all the thermodynamic 

 functions of gases in a mixture are of the same value as though 

 each gas alone occupied the same volume as the mixture, the 

 temperature remaining unchanged. In the formulation there is 

 incorporated also the idea of equilibrium, which does not appear 

 to be associated with the usual statement of Dalton's Law. The 

 significance of the equilibrium idea, both thermal and mechani- 

 cal, must be emphasized because of its extensive importance in 

 every application to which thermodynamics lends itself. 



The Gibbs rule may be written, where the constants 



— ^- -^ and -—^ — ^ are represented by hi and Ci. 



Ml - ^1' 



aieH% "' , (42) [273] 



* Gillespie (P/iys. Rev., 36, 121, (1930)) has recently discussed in con- 

 siderable detail the implications contained in Gibbs' italicized state- 

 ment. It is shown that Gibbs' statement is, as would be expected, 

 an approximation. It is, however, a useful rule, and is analogous to 

 the Lewis and Randall rule of fugacities (Lewis and Randall, Thermo- 

 dynamics, p. 226, 1923). The Gibbs rule and the fugacity rule often 

 show deviations of opposite sign from the true pressures of binary 

 mixtures. 



