512 Transactions. 



Art. LIX. — The Effect on Temperature of Molecular Association 



and Dissociation. 



By S. Page. 



[Bead before the Philosophical Institute of Canterbury, 6th September, 1905.] 



In this paper it is proposed to show that in certain chemical 

 reactions much of the temperature-change may be due to a 

 source overlooked in Berthelot's fundamental proposition as 

 stated in 1879 — viz., " The heat disengaged in any reaction is 

 a measure of the chemical and physical work done in that 

 reaction." In recent criticism of Berthelot's proposition this 

 source appears to remain unnoticed. 



According to the kinetic theory the temperature of any 

 given gas is proportional to the mean square of the molecular 

 velocity, and for different gases the temperature is proportional 

 to the average kinetic energy of translation of the molecules. 



If we mix equal volumes of two different gases without any 

 temperature-change resulting it can be shown that mnv 2 — 

 m/iv/, where m and v represent the mass and average velo- 

 city of the molecules in the one, and m / and v y the corre- 

 sponding quantities in the other, gas. That is to say, at the 

 same temperature the average kinetic energy of translation of all 

 gaseous particles must be the same whatever be their masses. 



If we have two gases with molecular masses of m and f 

 respectively, then, where their average molecular velocities are 

 equal, their respective kinetic energies are as 2:1, and their 

 respective absolute temperatures therefore as 2 : 1. Let us apply 

 this, in the first instance, to those numerous cases in which 

 gaseous molecules when heated split up into two or more parts, 

 reassociating on cooling — e.g., water, carbon-dioxide, ammonium- 

 chloride, nitrogen-peroxide, &c. The dissociation absorbs heat, 

 while the reassociation, promoted by cooling, gives out heat. 



Consider the case of N 2 4 — nitrogen-peroxide : If this gas 

 be heated above 0° C. some of the molecules split into two parts, 

 as is shown by the lessened density. Disregarding any work 

 done in bringing about this disruption, and further neglecting, 

 for the present, any change in the internal energy of the mole- 

 cule, we may fairly assume that the sum of the kinetic energies 

 of translation of the two parts must be equal to the kinetic 

 energy of translation of the original molecule. But each part is 

 now an independent molecule, having half the kinetic energy 

 of translation of the molecules around it. So mv 2 has become 

 2 x f v 2 , and therefore each N0 2 molecule in impact with the 

 rest will have its velocity increased, and will not be in equi- 



