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LX. The Heat of Mixture of Substances and the Relative 

 Distribution of the Molecules in the Mixture. By R. D. 

 Klebman, D.Sc, B.A., Mackinnon Student of the Royal 

 Society, and Clerk Maxwell Student of tlie University of 

 Cambridge *. 



WHEN two quantities of different substances are mixed 

 and no new molecules are formed, we will assume in 

 this paper that the heat of mixture is the change in. the total 

 potential energy of the matter due to the "chemical" 

 attraction between the molecules. We made a similar 

 assumption in a previous paper in the case of the internal 

 heat of evaporation of a pure liquid, which led to results 

 agreeing well with the facts. But even if a change in the 

 intra-molecular potential energy of a number of molecules 

 with a change in their state of aggregation takes place, it 

 could only be small in comparison with the change in the 

 potential energy due to the attraction between the molecules, 

 since the change in the internal latent heat of evaporation 

 of a liquid with temperature is large in comparison with the 

 corresponding changes in the intra-molecular energies of the 

 vapour and liquid, that is, the specific heat at constant volume 

 of the vapour and liquid. 



We shall deduce formulae on the above assumption in this 

 paper applying to various cases of mixture of two or more 

 substances, using the law of attraction between molecules 

 which was deduced f from the internal latent heat and 

 surface-tension of liquids. The law of attraction between 



two molecules of the same kind is d>J~ ,rp- ) • K ? where 



T ~\x c YJ z h 



T is the temperature of the molecules and z their distance of 

 separation, x c denotes the distance of separation of the mole- 

 cules in the liquid state at the critical temperature T c , 2a/wii 

 denotes the sum of the square roots of the atomic weights of 



/z T \ 



molecule, and </> 2 ( — ,^ ) is an arbitrary 



function of the ratios — ,=■ . As the exact form of the 

 os Q lc 



function <£ 2 cannot be deduced from latent heat or surface- 

 tension data there is little other data relating to physical or 

 chemical properties of substances from which any informa- 

 tion on the exact form of <j> 2 can be obtained. ' We have 



* Communicated by the Author, 

 t Phil. Mag. May 1010, p. 783. 



the atoms of 



