176 PHENOMENA, ATOMS, AND MOLECULES 



each of these pressures is given in the following table, along with the 

 ratio P/Wc, which, according to (40), is equal to C: 



The constancy of C at the lower pressures and its increase at the higher 

 pressure, is in full accord with Equation 33, which states that C is pro- 

 portional to VTq- At very low pressures T^ must be equal to the tempera- 

 ture of the bulb (300° K.), just as it was at lower filament temperatures 

 (see Table V). At higher pressures, however, where the hydrogen atoms 

 recombine long before reaching the surface of the bulb, the heat evolved 

 raises the temperature of the gas considerably. At the lower pressures, 

 however, we may safely place T^ = 300, and we then find, by comparing 

 Table VII with Equation 33 : 



C = 0.0048 VTo (46) 



a2?i = 27300 (47) 



This indicates, since by definition ao cannot exceed unity, that qi must 

 be greater than 27300, or the heat of formation of 2 g. of hydrogen mole- 

 cules, must be greater than 54600 calories. 



If we compare (46) with the value C = 0.112 obtained for P = 0.207, 

 we find To = 545. This is, as we shall see later, an entirely reasonable value. 



2. Cnltulation of an Approximate Value of qi. — -If we can determine 

 qi then by (47) we can calculate ao. This will, in a certain measure, give 

 us a check on our theory, for we know that a2 cannot exceed unity. 



To calculate gi we may make use of van't Hoff's equation 



d In K/dT = g/RT2. (48) 



Here q is the heat of reaction at constant pressure since K is expressed 

 in terms of partial pressures. The relation between q and gi is 



g = 2gx + RT. (49) 



If we use ordinary logarithms in place of naperian and substitute 

 R = 1 .98 calories, we may write Equation 48 as follows : 



dlogK/d(i/T)^-q/4.57 (50) 



Since q varies so little with the temperature, we should, according to 

 (50), obtain practically a straight line if we plot log K against i/T. The 



