5±8 Dr. R. D. Kleeman on the 



'Lest for the Formation of New Compounds in a Mixlur 



If two quantities of different liquids containing an equal 

 number of molecules be mixed and no new molecules are 

 formed, the relative distribution of the molecules in the 

 mixture can be deduced as we have seen. The functions 

 B l5 B 2 , Ci, and C 2 , in the formula for the heat of mixture 

 £iven, can then at once be formed if the form of the function 

 <f> 2 in the law of attraction is known. It will then be most 

 convenient to express the relative distribution of the mole- 

 cules in terms of that of the molecules of one kind in the 

 mixture. 



We have pointed out that there is some evidence that the 

 function </> 3 does not depend very much on the magnitude of 

 the variables it contains. If we assume it approximately a 

 constant an approximate formula for the heat of mixture 

 can be obtained. Let us first find the value of L Wl ^ 2 on this 

 supposition. When a molecule 1 is removed from the mixture 

 the work done against the attraction of the remaining mole- 

 cules 1 is 



Ul (i) ( V».) 2 , where «, = f,g , 1-), 



p 7 denotes the dens-ity of the molecules 1 in the mixture, 

 and x e denotes their distance of separation. This is at once 

 obtained by supposing the molecules 2 absent, when we are 

 dealing with a liquid in which the molecules are evenly 

 distributed as in a pure liquid, and a corresponding formula 

 applies. The work done against the attraction of the mole- 

 cules 2 in removing the molecule 1 is obtained as follows. 

 Suppose the molecules 2 replaced by molecules 1. The work 

 done against the attraction of all the molecules is then 



and xr x denotes the mean distance of separation of the mole- 

 cules. The term which is raised to the 4/3 power is equal 



to — ; we have expressed this quantity in terms of quantities 



relating to the mixture. The work done against the molecules 

 1 which replaced the molecules 2 is therefore 



».(mS3,)"*' s «•-(€)" «V55\ 



as is at once evident from the nature of the distribution of the 

 molecules. The work clone against the molecules 2 if thev 



