388 KEYES ART. J 



of p, it should be noted, can be positive, negative or zero de- 

 pending on the temperature, and of course the coefficient of xip 

 has the same property although the temperature at which each 

 coefficient vanishes will not in general be the same. 



Certain considerations may be shown to make plausible the 

 assumption that 2/3i = ^2, ^Ai = A2; where /3i, Ai, ^2, A2, are the 

 constants in mols of the equations of state. Under such an 

 assumption the last equation reduces to 



log K,/Ko = [I - ^J (x. - X,) V 



'^2 A2 



[ 



Rt (my 



1 - 3« 



1 + a 



V, (133) 



where a is the fraction of N2O4 dissociated. 



A recent paper by Verhoek and Daniels " contains material 

 which affords a test of the formulation above. The measure- 

 ments show that the values of log Kp/K^ do actually vary 

 linearly with pressure over a range of pressure which however 

 does not exceed one atm. The data have been used to pre- 

 pare Fig. 2 illustrating the course of the experiments at three 

 temperatures. The slopes of the lines do not appear to be in 

 regular order as would be expected from the equation above. 

 However, if the equation above were capable of representing 

 the data, a line would start from the origin for every isothermal 

 series of experiments forming a "fan" composed of lines in both 

 the positive or upper part of the diagram and the lower or nega- 

 tive part. Eventually Kp will equal Kq independent of the 

 pressure but, as P increases, the sign of the right hand member 

 would come to depend upon {x2 — Xi). A continuation of the 

 exact investigation of this reaction evidently holds much of 

 interest. The reformulations of the data '^2, 63 q^ ^^ig reac- 

 tion, using the ideal gas laws, which have appeared since the 

 publication of Gibbs' papers, can add nothing to the thermo- 

 dynamic theory as applied to cases of convertible components. 



29. General Conclusions and the Equation of State of an Ideal 

 Gas Mixture Having Convertible Components. The heat capacity 

 at constant volume for a real gas possessing a coefficient {dp/dt)v 



