10 PROCEEDINGS OF THE AMERICAN ACADEMY. 



rium, we have four equations of the type of (Ho); one referring to 

 the equilibrium iu the gaseous state of the reaction, 2 CH3COOH =: 

 (CH3COOH)2 ; another, referring to the same reaction in the liquid 

 phase ; a third, referring to the liquefaction or vaporization of the double 

 molecules ; the fourth, to the liquefaction or vaporization of the single 

 molecules. Of these four equations three are independent. 



Returning to the discussion of the general equation of equilibrium, 

 equation (Ha), it is interesting first to determine what form it will take 

 when we limit the system considered to the conditions under which 

 equation (10) was deduced, namely, that the reacting system shall in- 

 clude, besides gases and dilute solutions, only " condensed " phases of 

 definite composition. Combining equations (10) and (11), 



Now V, the change of volume, is due in this case to the change in vol- 

 ume of the gaseous constituents, and will therefore, at constant temper- 

 ature, be inversely proportional to P. Therefore P Fis a constant, and 

 at constant temperature, 



In '' \ •' • = C\ and " ", ' " ^ /v (a constant). (12) 



This equation is the familiar mass law of Guldberg and "Waage, but 

 it is also, since it is not restricted to homogeneous systems, the law of 

 the constancy of the ratio of distribution among different phases. This 

 includes the law of Henry. 



That equation (12) does not represent a universally accurate law of 

 nature is shown by comparison with equation (Ho) ; for it is only when 



IT, H. C„ —Q. , and F Fare constant that —, — ,"„, is constant. 



' - Vi ly'i 1 . . . 



If this fraction for convenience is denoted by /i, which may be called, 

 instead of the equilibrium constant, the equilibrium ratio, then K is a 

 function, not only of the temperature, but also of U, H, 0^^ , C^„, P V. 

 The nature of this function may be shown from equation (11 a), 



BTlnK=FV- U+ T C^ ^^'^ ~ ^'^ dT-JIT; (13) 



