Chemical Potential to the Theory of Solutions. 937 



As this quantity plays a very important part in the subsequent 

 theory, it will be denoted by the special symbol P (s, p, 0). 

 If the volume W of the solution is regarded as a function of 

 M , M l5 p, and #, it can be shown that 



This quantity is evidently positive and of the same order oE 

 magnitude as the specific volume of the pure solvent. In 

 cases where the change of volume on solution is small the 

 two quantities are approximately equal. 



In the case of a liquid mixture, the changes of pressure 

 involved in the phenomena under consideration cause only a 

 very small change in the density, so that we have approxi- 

 mately 



M*>p* 0)—M s >pi> 0)=(p2—pi)Yo{s>pk 0). 



If we write 



P<z-PK 



i c 



Pu(*» Pr*P» B) = ~ j Po(*» *, 0)dx, 



Pz—PiJ Pi 



we have the exact equation 



/<>(*, Pi, 0) —/„(*, pi, 6) = {p 2 ~p l )'P (s, pi-+p a9 6) . . (1) 



The quantity P («s pr*pa, 0) may be called the mean value 

 of P between the pressures p>i and p 2 . 



An expression for this mean value may be obtained if we 

 assume that 



v(s,p,e)=v( s ,v, ff)\i-fi{p-w)\ 



where ft is the compressibility of the solution and ot any 

 convenient pressure, which in this case we will assume to 

 be atmospheric pressure, since the density measurements 

 necessary for the calculation of P will have been made 

 under atmospheric pressure. 



Assuming that -^-- is independent of the pressure it can 



readily be shown that 



Po(*, pr*Pu 0) = Po(*, », 9) { l-x(£!^- w )} (2) 

 where 



X=/3- 5 (l + 5 ) 



v(s 9 g, 0) -b(3 



