FUNDAMENTAL EQUATIONS OF IDEAL GASES 369 



£3. Fundamental Equations from Gibhs-Dalton Law. The 

 fundamental equations in the form given in [291], [292] and 

 [293] are easily obtained. The latter equation may also, how- 

 ever, be expressed in the form: 



r = 2 ^'^^^^ '^ mit(ci + ai - Hi)] 



- 2 ci^i^ log f - 2 «i^i^ log ^> (87) [293] 



where Xi, the mol fraction, is equal to r The content of the 



paragraph following [293] should be carefully noted. 



24. Case of Gas Mixtures Whose Components are Chemically 

 Reactive. Thus far only gas mixtures with independently 

 variable components have been considered. The material 

 following [293] (Gibbs, 1, 163) therefore emphasizes the distinction 

 which must be made between gas mixtures of the former kind, and 

 those with convertible or chemically reactive components. The 

 characteristic of the latter is of course that chemical changes 

 proceed by whole numbers or fixed ratios. Two molecules of 

 hydrogen always require one molecule of oxygen, never more 

 nor less, to form one molecule of water, and three molecules 

 disappear when two water molecules are formed. As a 

 consequence we need only be concerned, in our equations of 

 thermodynamics for chemically combining gases, with these 

 whole number ratios and not with actual masses. Thus it is 

 clear that, in so far as convenience is served, our equations for 

 gas mixtures could be expressed in units of mass proportional 

 to the masses of the molecules of the separate and distinct 

 chemical species. This, of course, is the almost universal custom 

 in chemistry at present, and in all the preceding formulae it is 

 merely required that n, the number of mols, be substituted for 

 m the masses. The constants ai, 02, . . . must also be expressed 

 in terms of the mol as the unit of mass. Thus (87) [293] would 

 be written 



f = 2^^ 



r^i + tic + R- i7i)] 



Rt 



- 2 ^^1^1^ log f - 2 ^1^^ log '^' (88) ^293] 



