Heat of Mixture of Substances. 515 



The change in volume of the liquid phase during the evapora- 

 tion is therefore 



1 , 1 



(/i : + n 2 + x) ( x + ?i 2 ) —7 = v say. 



PS P$ 



From Olapeyron's equation we then have 

 where L", as before, is given by 



If the heat of mixture of a saturated solution of molecules 1 

 in 2 per gram of mixture be denoted by H t , and that of a 

 saturated solution of molecules 2 in 1 per gram of mixture 

 by H/, we have 



/ \ 4/3 



B t (> h + n 2 + x) = L w / - ~-| A i (^ ) (2 x/mif + H t\n 2 -f a), 



where x and L Ul ' are given by the above equations. This 

 equation expresses the relation between the quantities H* 

 and H/. If the molecules 2 instead of 1 be allowed to 

 evaporate the above equations apply if the suffixes 1 and 2 

 and the symbols H^and H/are interchanged, and p 5 is written 

 for p v The last equation thus becomes 



4/3 



H/(« 1 + « 2 + .r) = L % '- £a 2 (£) (zym 2 y + n t (n l + .v). 



The elimination of H/ from the above two equations gives an 

 expression for the value of H^. The value of either H^ or BY 

 may also be obtained by means of one of the formulae given 

 previously. 



It will be observed that some of the formula? for the heat 

 of mixture obtained apply whatever the changes are that 

 take place when the substances are mixed, such as the 

 formation of new molecules, &c. Both types of formulae 

 obtained are perfectly general, and therefore apply when 

 one or both of the substances are in the gaseous state. 



It is unnecessary to develop formulae for the mixture of 

 three or more liquids, as these can now be developed wiihout 

 difficulty along the lines indicated. 



