HYDROGEN INTO ATOMS 173 



Here Ci is to be expressed in mols per cc, and is equal to 



c^ = Pi/RT. (28) 



Tlie diffusion coefficient varies with the temperature according to 

 Sutherland's formula, but at the high temperatures we are dealing with, 

 this becomes equivalent to stating that the diffusion coefficient varies with 

 the 3/2 power of the temperature. We will assume that the diffusion 

 coefficient of hydrogen atoms through molecular hydrogen varies in this 

 way with the temperature, although we shall avoid assumptions as to its 

 actual magnitude. Since the diffusion coefficient is inversely proportional 

 to the pressure, we may thus place : 



D = Do(T,/273)"'.(76o/P) (29) 



where Do is the diffusion coefficient at 0° and 760 mm. pressure, and Tq 

 is the temperature of the gas around the wire {i.e., at the distance X 

 from it). 



Combining (29), (28), and (3) we obtain, after substituting the 

 numerical value for R 



Wd = 1 1-3 X io-« SgiDoVTa ^i/P- (30) 



This equation gives us the desired relation between pi, the partial pressure 

 of hydrogen atoms around the wire, and W©. It enables us to calculate the 

 degree of dissociation if we know S, qi and Dq. 



EQUATIONS INVOLVED IN CALCULATING THE DISSOCIATION 



CONSTANT, ETC. 



Equation 27 has given us a means of calculating the dissociation con- 

 stant from the partial pressures of hydrogen atoms and molecules around 

 the wire. These partial pressures may be expressed in terms of the diffusion 

 constant by means of Equation 30. By combining these two equations it is 

 possible to obtain a general solution of the problem in the following form : 



where 



K=VT./T "^'oiBP^Zy (31) 



B = 885oo/(SDogiVTa) cm. per watt (32) 



C = iSiVTa/Ca^gi) mm. of Hg per watt/cm. (33) 



E = i85VT„/(aig'i) mm. of Hg per watt/cm. (34) 



The dissociation constant K increases rapidly with the temperature, 

 while B, C and E depend only to a small degree on the temperature, and 

 therefore we see by (31) that at low temperatures Wd will increase ap- 



