936 Mr. S. A. Shorter: Application of tlte Theory of 



Consider two homogeneous systems at the same temperature 

 and under the same pressure, the first containing masses M 

 and Mi + SMi respectively of the components S and S l5 and 

 the second masses M and M l — SMj. If these two systems 

 are put into communication w T e shall have finally a homo- 

 geneous system containing masses 2M and 2M V of the 

 components. This irreversible process of uniform mixing 

 must result in a diminution of the total thermodynamical 

 potential, so that we must have 



<D(2M , 2M l9 p, 0) <<S>(M , U^SK^p, 0) + <S>(M o , M~m l:P , 0). 



From this we may readily prove the inequalities 



If v(j, p, 6) denotes the specific volume of the solution we 

 have 



op 



By differentiating this equation with respect to M and 

 introducing the variable s, we obtain the equation 



|_/ ( 5 , p, 0) = v (s, p, 6) - s(l + s) | s . r(*, p, 6) . 



Tbe value of ^ may be obtained in a similar manner. 

 dp J 



The functions f (s, p, 6) and fi{s, p, 6) are called the 

 chemical potentials of the components of the system. The 

 importance of the chemical potential lies in the fact that if a 

 system consists of two or more homogeneous parts in equili- 

 brium, the chemical potential of any component must be the 

 same in all parts of the system, so long as the motion of a 

 quantity of that component from one part to the other is a 

 possible virtual modification of the system. This follows 

 from the general condition of equilibrium. 



Tlte Effect of a Finite Change of Pressure on the Chemical 

 Potential of the Solvent in the Solution. 



In the previous section we have shown that the value of 

 --— fo( s - Vi 0) can be calculated from simple experimental data. 



By 



