38 Mr. S. A. Shorter : Application of the Theory 



Extension of the Theory to Solutions containing any 

 number of Involatile Solutes *. 



Most of the formulse established in the previous parts of 

 the present work may readily be generalized so as to apply 

 to solutions containing any number of involatile solutes. 

 Consider a solution containing a mass M of a solvent S , 

 and masses M 1? M 2 , ... , M n of the involatile solutes 

 Si, S 2 , ... , S„ respectively. The total thermodynamical 

 potential of the solution may be written in the form 



i=n 



®=f (Sl, *» .-. j Sn, p, #)M + % fi( Sl , S 2 , ... , S n , p, 0) M^ 



i=l 



where ^=^. 



The quantities f , /i, ..., f n are, of course, the chemical 

 potentials of the components of the solution. 

 Now 



p=(M + M 1 ... +M n )i<*i,*„ ...,s n ,p,0), 



where v(s h s 2 ,...,s n , p, 0) is the specific volume of the 

 solution. From this equation we can readily deduce the 

 relation 



Po (fb *2> • • • , Sn, p, 6) = V(s ly S 2 , . . , Sn, p, 0) 



1=11 -fo v 

 — (l + 5i+ ... +s n ) 2 «»"^-» • • • (15) 



i=l 0$i 



where 



"o( 5 l> S 2> • • > s n, P, 0) ==■ Sr~ • 



If we use a notation for the mean value of P between two 

 values of the pressure similar to that adopted previously, we 

 have, in the case of a slightly compressible liquid, 



P (*i, s 2 , . . . , s n , 2 h->P2, 0) =Po(si, $2, • • .**, «r, 0) <|l— x fr 1 *? 2 - J\\ 

 where X is related to the compressibility ft by the equation 

 h—p — (i- + s 1 + ... 4-^n;-^- 7 — z si^—. (lb) 



1 o(*l> $2> • . • $n> «", #) i=l OSi 



* The formulae relating- simply to osmotic equilibrium and to equili- 

 brium between the solution and the solid solvent also apply, of course, 

 to solutions of volatile solutes. 



