LEWIS. — A NEW SYSTEM OF THERMODYNAMIC CHEMISTRY. 273 



The surface C does not change its position during these operations 

 (according to the definition of the ideal solvent). The total work 

 done by the system is therefore equal to the sum of ^i, A^, A3, and 

 Ai, and since the cycle is isothermal and reversible this sum is equal 

 to zero, by the second law of thermodynamics. Equating the terms to 

 zero and simplifying gives, 



i-dP - v'dn = 0. 



v' , the molecular volume in the ideal solution, is equal to -pj- . Sub- 

 stituting this value in the last equation gives, 



BT 



The activity of Xi , $, is the same in the mixture A and the solution B 

 and its value in terms of 11 is given by equation III. Substituting for 

 n and expressing in the equation the constancy of temperature and com- 

 position,^ we have, 



9 In A v 



dP )t,n RT (IX) 



This is the general equation for the influence of pressure upon the 

 activity of one constituent of a binary mixture. The quantity v is of 

 very great importance in the thermodynamics of mixtures. It is the 

 increase in volume of an infinite quantity of a mixture when one mol 

 of the constituent in question is added to it. We will call v the ^wr- 

 tial molecular volume of that constituent. 



Similarly we may define the partial molecular energy, entropy, etc., 

 and these quantities play the same r6le~ in the thermodynamics of 

 mixtures that the molecular volume, energy, entropy, etc., do in the 

 treatment of pure substances. 



An important difference between the partial molecular volume in a 

 mixture and the molecular volume of a pure substance is that while 

 the latter is always positive the former need not be. Therefore the 

 activity of one of the constituents of a mixture may either be increased 

 or diminished by increase of pressure on the mixture. 



9 We will use the subscript N with tlie p.artial diiierential coefficient to denote 

 constancy of composition in the mixture. 



VOL. XLIII. — 18 



