FUNDAMENTAL EQUATIONS OF IDEAL GASES 371 



receive much independent assistance and support from the 

 theorems and results deducible from statistical mechanics. 

 It is also evident of course that, outside of the field of equilib- 

 rium states, thermodynamics is of no service and progress in 

 the theory of non-equilibrium states depends on the perfection 

 of statistical theory. Modern atomic and molecular theories 

 likewise have an important part to play in leading to an improved 

 knowledge of molecular constants and molecular encounters, 

 which is indispensable to the future progress of physical chem- 

 istry. 



So. Henry's Law. The law that the concentration of the dis- 

 solved constituent is proportional to the pressure of the gaseous 

 constituent is to be regarded as applying strictly only in the limit 

 where the amount of dissolved gas is vanishingly small. The 

 deviation in the case of carbon dioxide and water, for example, 

 where it amounts over the interval 30 atm. to 37 percent at 

 zero degrees and 29 percent at 12.43 degrees^* is typical. The 

 pressure of the gas phase, in this case, increases more rapidly than 

 the amount of gas dissolved. 



By way of accounting for the deviations from Henry's law 

 it may be noted that the gaseous mixture over a liquid is now 

 known to be far from a perfect gas. This particular aspect of 

 the problem has received recent attention, and the changes in 

 volume on formation of the mixture, together with the signifi- 

 cant thermodynamic formulae, have been developed '^^-^^'^ using 

 the fugacity function introduced by G.N. Lewis^^-^^-^^'^''^ This 

 convenient function in the case of a pure gas is related to the n 

 function of Gibbs as follows : 



'• [h ^' - ^'-^l 



/= pexp.\ — (n - Mi) I' (89) 



where ^ is the potential at pressure p and temperature t, and /x« 

 is the potential at the same pressure and temperature assuming 

 the ideal gas laws to hold. From the equation it is evident 

 that f —> p in the limit when the pressure approaches zero. 

 The equilibrium fugacity, /«, of one of the gases, 1, in a mixture 

 of gases, is given by the equation ^^' ^2 



/.= 



"''' '^^- [h r('' ~ f ) *]' ^'^°^ 



