[ 18 ] 



II. On the Kinetic Theory of the Phenomena of Dissociation 

 in Gases. By Ladislaus Natanson*. 



IT is well known that the problem of the dissociation of 

 gaseous bodies has been successfully attacked by several 

 physicists by thermodynamic methods. If one attempts to 

 apply the kinetic theory, it will be found difficult to make a 

 complete calculation without introducing certain assumptions 

 as to the mode of combination of the atoms in gaseous mole-v 

 cules. Therefore the first task of the theory consists in making 

 such assumptions as are either in agreement with experiment, 

 or else, on the other hand, the most general possible. As this 

 object does not appear to be sufficiently evident, I have allowed 

 myself to enter into a more detailed consideration of a simple 

 case. 



§ 1. In the space v there are present N x free atoms and N 2 

 diatomic molecules ; every atom has the same properties. 

 The total number of atoms is N = Ni + 2N 2 . If m is the mass 

 of an atom, the mass of the gas will be mN ; I shall assume 

 henceforth that we are always dealing with unit mass. The 

 problem which was usually considered was the determination 



N 

 of the ratio -^ (the dissociation ratio) as a function of the 



pressure and temperature ; and its object was attained some- 

 what after the following manner. 



Let p x and p 2 denote the partial pressures of the two gases 

 (molecular and atomic) ; let p be the total pressure, t the 

 common temperature, and E : and E 2 the mean values of the 

 kinetic energy of a free atom and of the centre of mass of a 

 molecule respectively. Apart from phenomena of dissociation 

 let both gases be considered perfect. Then we may write 



fpi« = NiE l5 §jy>=N»E f ; p=pi+p 2 - • • (A) 



Further, according to Maxwell's law, Ej = E 2 ; and we use 

 the magnitude of this energy as a measure of the temperature 

 by assuming 



E 1 = E 2 =X^ (B) 



where A, is some constant. From (A) and (B) it will be 

 found that 



f^ = (N 1 + N 2 )\« (1) 



Now let us introduce the condition for equilibrium. This 



* Translated from Wiedemann's Annalen, xxxviii. p. 288 (1889) by 

 James L. Howard, D.Sc. 



