202 



tde form of infra-red radiation of very definite frequency, wiiich 

 radiation is present in tlie medinni in virtue of its tiiermal condition. 

 By the application of Planck's law of the normal partition of energy, 

 the density of radiation of tliis frequency can be calculated at every 

 temperature, and from this the fraction of the molecules that are 

 in i-eactive condition. Lewis derives that the increment of enei-gy E. 

 is equal to a quantum (of the absorbable type) per molecule. 



E ■=■ Nh 2 Vrewjents- 



Lkwis derives for tiie constant of reaction of a bi-moleciilar 

 reaction : 



7 T> ./^' ' ' —h{VA + VB)lkr 



in which P^ ::= constant, 7^= absolute temp., iia and ??,/,> = index of 

 refraction of the substance A res|). B, and k = gas constant per 

 molecule. The formida shows very clearly the rapid increase of k 

 on rise of temperature. 



The nearer the value of the critical energy is to that of the 

 mean energy per molecule, the greater will be the number of 

 molecules becoming active per second, hence also the velocity of 

 reaction, the sairie conclusion, therefore, to which Tkautz came. By 

 taking the logarithm of the above formula, and differentiating this 

 with i-espect to time, the following form results: 



dlnk_Nh{vA-\- vb) + 'I^RT _E-[-'l,RT 

 dt ~ RT^ ~ RT^ 



Of reactions which take place as much as possible under the same 



circumstances, only more slowly or more quickly (to be realized 



with little catalyst), the quicker reaction must have a smaller E 



(lln k 

 according to the above, from which it then follows that — — has 



dt 



become smaller, hence also the temperature coefficient of the reaction 



constant, for the temp.coëf. 



kTA-\ü '^'^^^^i dk dink 

 jL±}^—. li_ 1 I 10 =:1 + 10 . 



k'f kT kj'dt dt 



Lewis (like Trautz) dra\'\s the conclusion that a strongly catalyzed 

 reaction will indicate a decrease of the temperature coefficient 

 compared with the same reaction weakly or not catalyzed. 



On half thermodynamic, half kinetic grounds Kohnstamm and 

 Schepper have derived a relation between the velocities of reaction 

 and the thermodynamic potentials of the substances participating in 



