550 Dr. R. D. Kleeman on the 



As a test for the formation of new molecules in a mixture 

 of two substances we have then that if it is found that the 

 heat of mixture of the substances in masses proportional to 

 their molecular weights differs considerably from that calcu- 

 lated by the above or previous formula 2, we may conclude 

 that new molecules are formed. The extent of the formation 

 of new molecules in a mixture of two liquids in any given 

 proportion will probably depend, however, on the proportion 

 between the constituents. 



The various formulae for the heat of mixture of liquids all 

 labour under the unavoidable disadvantage of appearing as 

 the difference between quantities which are usually very 

 large in comparison with this difference, which has the effect 

 of magnifying all errors, and thus usually preventing a good 

 agreement with the facts being obtained. If one of the 

 substances is in the form of a vapour the formulae suffer less 

 from this defect. This is a point to be borne in mind when 

 the formulae for the heat of mixtures are used. 



A simpler test than the above for the formation of new 

 molecules in a mixture of equal numbers of different mole- 

 cules is the following. It will be evident, from the relative 

 distribution of the molecules in such a case (which we have 

 discussed), that the volume of occupation is the same for 

 each kind of molecule. It follows, therefore, that if nc new 



BV BV 

 molecules are formed we must have -s — = -k— • This formula 



CC'i oc 2 



involves quantities which can be easily measured. In using 

 this formula in practice, however, we are hampered by the 

 difficulty — which occurs also in connexion with the previous 

 formulae — of not being sure of the molecular concen- 

 tration of the liquids used, as these may be polymerized to 

 some extent. Water is an example : it has been shown 

 to be polymerized from surface-tension and other considera- 

 tions, and consists probably of a mixture of molecu'es poly- 

 merized in different degrees. We are therefore not able to 

 use the extensive data on the solution of substances in water 

 in connexion with the above formula, till w T e possess more 

 reliable information on the size of a water molecule. On the 

 other hand, the data relating to other solvents is not sufficiently 

 extensive to be of any use. But experiments having the 

 object of testing the formula could be easily and rapidly 

 carried out. 



The above considerations suggest a slightly different way 

 of testing for the formation of new molecules. Since the 

 internal heat of evaporation of the molecules 1 and 2 when 



