LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 55 



behavior of the vapor deviates perceptibly from that of the perfect gas 

 the exact value of the fugacity may be found as follows : — 



From the four laws stated io the introduction it is easy to derive the 

 following, which is a rigorous statement of Henry's law, namely : Tlie 

 coefficient of distribution between a gas and its solution at constant tem- 

 perature approaches a constant with increasing dilution. This constant 

 will be designated by p. At infinite dilution, 



P _ 



where p is the gas pressure and 11 the osmotic pressure in solution. 



Now p, at infinite dilution, is equal to the fugacity of the substance in 



the gaseous phase, and also in the solution, since the two phases are in 



equilibrium. Therefore, 



^i; = pU. (8) 



That is, the fugacity of the solute in an ideal solution is equal to its 

 osmotic pressure multiplied by p. If now it is desired to find the 

 fugacity of any molecular species X in any given phase, that phase may 

 be brought in contact with a chosen solvent and the osmotic pressure 

 III of the saturated solution determined. Then by diluting this solution 

 in contact with vapor of X the limit pi of the distribution ratio may be 

 found and so the product pi IIi. So for another solvent we may find the 

 product p2 112 ; for a third, p^ lis, etc. These will all be equal except in 

 as far as the saturated solutions deviate from the ideal solution. Prac- 

 tically, the product will be the same for all solvents in which X is only 

 slightly soluble and will be the fugacity of X. Theoretically, the exact 

 value of the fugacity is the limit approached by the product, p 11, as sol- 

 vents are successively chosen in which X is less and less soluble. 



We see, therefore, that fugacity is a real physical quantity capable in 

 all cases of experimental determination. A complete appreciation of the 

 meaning of this quantity is essential for the understanding of the follow- 

 ing pages. In order, however, not to distract attention further from our 

 main object, a further discussion of fugacity will be postponed to the last 

 section of this paper, in which another independent method for the 

 determination of i/^ will be offered, using only such quantities as have 

 already been determined in many cases. 



The great utility of this new quantity will be shown to lie in the fact 

 that the approximate equations containing the vapor pressure and 

 developed rigorously except for the assumption that the vapor pressure 

 obeys the gas law, may be replaced by exact equations of the same form 



