336 Aggregation and Dissociation [CH. xvm 



409. Let us consider a gas in which the complete molecules are each 

 composed of two atoms, of types a, ft respectively. 



As in equations (768) the laws of distribution of dissociated atoms and 

 complete molecules are 



where >P is the potential energy of the two atoms forming the molecule. 

 The analysis will be simplified, and the theory sufficiently illustrated, by 

 regarding the atoms as point centres of force, and supposing the masses of 

 the two atoms to be equal, say m. Making these simplifications, we find as 

 the laws of distribution of dissociated atoms 



Ae- hmc *dudvdw\ 

 Be- hmc *dudvdw) 



and as the law of distribution of complete molecules 



ABe-^^dudvdwe-W^-^doidfidvlTrrtdr ......... (777), 



the law being arrived at in the same way as the law (771). 



410. Although the mathematical analysis is similar to that of aggregation 

 there is an important difference in the physical conditions. The law of 

 distribution (777) is limited to values of the variable such that ^mV 2 + 2^ 

 is negative ; as soon as ^mV 2 + %'ty becomes positive the molecule splits up 

 into its component atoms. Now in the case of molecular aggregation, the 

 attraction between complete molecules is not great, so that ^ is a small 

 negative quantity, and the range of values for V is correspondingly small. 

 In the case of chemical dissociation ^ is a large negative quantity, and the 

 range for V is practically unlimited. 



An estimate of the value of "SP can be formed by considering the amount 

 of heat evolved when chemical combination takes place. For instance when 

 16 grammes of hydrogen combine with 2 grammes of oxygen to form 18 

 grammes of water the amount of heat developed according to Thomson's 

 determination, is 68,376 units, sufficient to raise the temperature of the 

 whole mass of water by 3,600 C. The value of V necessary for dissociation 

 to occur is therefore comparable with the mean value of V at 3,600 C., and 

 these high values of V will be very rare in a gas at ordinary temperatures. 

 The exclusion from the law of distribution (777) of high values of V will 

 therefore have but little effect either on the law of distribution or on the 

 energy represented by the internal degrees of freedom, and we may, without 

 serious error, regard the law of distribution as holding for all values of V. 



