192 PHENOMENA, ATOMS, AND MOLECULES 



In order, however, to account for the manner in which W^ had been 

 observed to vary with temperature and pressure, it was necessary that 

 E2 should increase with the temperature up to a limiting value of 0.68, 

 but at the same time should decrease in a complicated way as the pressure 

 increased. Similarly, Ei would have to increase with the pressure and de- 

 crease with increasing temperature. This theory gave no clue as to the cause 

 of the variations of 81 and 82. 



The fact that 81 and 82 were found to be such complicated functions 

 of both temperature and pressure suggested the third hypothesis, namely, 

 that the reaction does not occur at the surface, but that there is an actual 

 equilibrium in the wire which determines the velocity of the reaction. 

 This view was strengthened by the fact that 81 and 82 varied with the tem- 

 perature and pressure in the way that would be expected of the partial 

 pressures of two gases in equilibrium. 



On the basis of the third hypothesis, the coefficients Si and 82 lose their 

 fundamental significance, while the coefficients ai and ao take their place. 

 The fact that the latter coefficients prove to be constant and practically 

 equal to unity over such wide ranges of temperature and pressure is ex- 

 cellent evidence that, in the present theory, we are dealing with the factors 

 that fundamentally determine the velocity of the reaction. 



By means of our present theory we are enabled to calculate 81 and 80 at 

 any temperature and pressure. 



Let us consider the case that hydrogen molecules at pressure p2 strike 

 die wire, but that the hydrogen atoms formed do not again return to the 

 wire. Then 82m2 represents the rate of formation of atomic hydrogen. 

 This, however, is equal to the quantity we have called co (see Equation 17) : 

 thus, 



W2 = 62^2. (72) 



Substituting this, together with the value of 1112 (by Equation 5) in 

 (26), we obtain, after placing ai = '\/2a-2 = i 



K = V?^-^-^ (73) 



This equation shows clearly that at low temperatures, where K is small, 

 82 is inversely proportional toV/'2, whereas at higher temperatures it ap- 

 proaches a limiting value of 0.7 1. Thus the variation of 82 with the tem- 

 perature and pressure which it was necessary to assume when working 

 with the second hypothesis, receives a complete explanation b}^ the third 

 hypothesis. 



In a similar way, the value of Si may be calculated for the case that the 



