Light Absorption and Fluorescence. 27 



re-absorption, since these lire based on the same atomic 

 frequencies as those of the initial substance. It is obvious, 

 as stated above, that the total energy evolved by the 

 activated molecules when reacting will equal the sum of: the 

 energy absorbed and the known heat of the reaction. Wo 

 have therefore 



Known heat of the reaction 



= total energy evolved, less total energy absorbed. 



Now, the energy absorbed is equal to a whole number 

 of quanta at the infra-red fundamental, and if the energy 

 given up by the activated molecules when reacting is, 

 as suggested, a whole number of quanta at the infra-red 

 fundamental, then the known heat of the reaction must 

 also be a whole number of quanta at the infra-red funda- 

 mental. Indeed, it would seem that considerable support 

 would be obtained if the observed heat of the reaction 

 for a single molecule is equal to a whole number of quanta 

 at the infra-red fundamental of that molecule. Now, the 

 observed heat of decomposition of hydrogen peroxide is 

 23059 calories, which is 1*564 xlO -12 erg per molecule. 

 The quantum at the infra-red fundamental of hydrogen 

 peroxide (assumed equal to that of water) is 3*2184 X 10" 13 , 

 and therefore the heat of reaction per molecule is almost 

 exactly 5 quanta at the infra-red fundamental. 



There are relatively few substances for which accurate 

 values are known of both the infra-red fundamental and 

 heat of formation. But it is more than probable from the 

 evidence which exists that this relation is a true one. Thus 

 the heat of formation of the molecule of water is 2*312 X 10~ 12 

 erg, which is very nearly equal to 2*2526 X 10 -12 erg, or 

 7 quanta at the infra-red fundamental. Again, the heat of 

 formation of one molecule of sulphur dioxide from gaseous 

 sulphur and oxygen is 4*737 x 10~ 12 erg, which is very 

 nearly equal to 4*782 xlO -12 erg, or 18 quanta at the 

 infra-red fundamental of sulphur dioxide. Since the infra- 

 red fundamentals of these substances are known accurately, 

 it is justifiable to calculate the heats of formation from these 

 on the basis of the present relation. The heat of formation 

 of a gram-molecule of water calculated on the basis of 

 7 quanta at the infra-red fundamental is 33,200 calories, and 

 that of sulphur dioxide on the basis of 18 quanta is 70,360 

 calories, the observed values being 33,993 and 69,800 calories 

 respectively. 



Similar discrepancies to those in the case of photochemical 

 reactions will also be found between the number of energy 



