114 PHENOMENA, ATOMS, AND MOLECULES 



to determine the degree of dissociation ^ and the heat of combination of 

 the atoms to form molecules. Since these experiments were made more 

 accurate data for determining the temperatures of tungsten filaments have 

 come into use. G. N. Lewis and M. Randall ^" and others have pointed out 

 that the third law of thermodynamics gives a relation between the heat of 

 dissociation and the degree of dissociation. 



With this relationship and the new temperature scale of Forsythe and 

 Worthing/^ the degree of dissociation of hydrogen has been recalculated 

 from the experimental data of 19 14. The results are expressed by the 

 equation 



01 200 

 logio /< = - ^^-y h 1.765 logio r (2) 



-9.85X10-^7-0.256 

 where K is the equilibrium constant defined by 



K = />iV/'2 ( 3 ) 



Pi being the partial pressure of atomic hydrogen and p2 the pressure of 

 molecular hydrogen, both expressed in atmospheres. Let x, the degree of 

 dissociation, be expressed as the fraction of the hydrogen molecules which 

 have been dissociated into atoms. Then if P is the total pressure, pi and p2 

 are given by 



Pi = 2Px/(i+x);P2= (i~x)P/(i+x) (4) 



and the equilibrium constant K in equation (2) is also given by 



■ K = 4Pxy(i-x^) (5) 



Table I gives the equilibrium constant K and the degree of dissociation 

 at various temperatures^- as calculated from equations (2) and (5). 



T Old New 



2000 deg. 0.00165 0.00122 



2400 deg. 0.0109 0.0104 



2800 deg. 0.0421 0.0488 



3200 deg. 0.1 17 0.154 



From equation (2), by applying the Clapeyron equation, we can cal- 

 culate H, the heat absorbed by the dissociation of the molecular hydrogen 

 ( at constant pressure) , as follows : 



H = 97,000 4- 3-5 ^ - 0.00045 ^" (6) 



'^ Laiigniuir and Mackay, Jour. Amcr. Chcm. Soc, 36, 1708 (1914); 37, 417 



(1915) ; 38. 1145 (1916). 



"* Lewis and Randall, "Thermodynamics," McGraw-Hill, New York, 1923, 

 page 470. 



^^ Forsythe and Worthing, Astrophys. Jour., 61, 146 (1925). 



^^ The revision in the calculation of x in 191 5 changed the values of x as follows : 



