LEWIS. — FREE ENERGY AND EQUILIBRIUM. 27 



III. Dimolecular Systems. 



Solutions. — The simplest case of a system composed of two molecular 

 species is one in which the two species are chemically neutral, only acting 

 on each other by the process of solution. 



Before taking up such systems it will be convenient to consider briefly, 

 in the light of the results of the last section, a question concerning the 

 general equation of equilibrium, namely, the nature of the function //. 

 In equation (5), which expresses the free energy of a simple constituent 

 of a system, the quantity %} x entered as an integration constant, and 

 nothing was known regarding its nature except that it must be indepen- 

 dent of the temperature. After differentiating equation (5), it was found 



/ ill 



that — r — was a function which could represent in the later equations 

 a v x l 



the volume correction corresponding to the quantity b in the equation of 



van der Waals. Since this was true in the widely differing states of gas 



aud liquid, it is probable that in any state in which the molecule itself is 



not changed - "' may be expressed as such a volume correction, rep- 

 resenting the diminution of the space available for the free motion of the 

 molecules, due to the space actually occupied by the molecules themselves. 

 If, therefore, we subtract from It}, the term representing the volume 

 correction, there will remain a quantity which will be constant under all 

 conditions when the molecule itself does not change, and whose value will 

 depend only on the nature of the substance considered. We will use ft 

 hereafter to denote this quantity. The volume correction enters in the 

 most general way in the consideration of a phase containing a number of 

 molecular species. "When we consider each species, the volume must be 

 corrected for the volume actually occupied by its own molecules and also 

 for that occupied by the other molecules present. The volume with the 

 first correction may be expressed as in the van der Waals equation bv 

 v — b, where b is the correction due to the space occupied by its own 

 molecules. The volume may be corrected for the space occupied by the 

 other kinds of molecules by multiplying the actual volume by a factor, r, 

 representing the fraction of any volume of the mixture which is left 

 available for the free motion of the molecules of the particular species 

 under consideration. The nature of this species should have no effect on 

 the quantity r. We have, therefore, for the corrected volume of a sub- 

 stance dissolved in any mixture the value r (v — b), where r depends 

 solely on the nature of the solvent, b on that of the solute. 



