Heat of Mixture of Substances. hAl 



pressure of the mixture of saturated vapours and 3/ the 

 volume of occupation of a molecule 1 in the vapour. 

 Similarly we have for the heat of evaporation of a mole- 

 cule 2, L 2 '-L 2 " = Pi,2$ 2 -- P'i, 2 V, where L 2 "=P' lf2 &,\ 



If the temperature of a mixture is gradually increased, a 

 temperature will ultimately be reached when L/— L/'^O, 

 in which case Pi j2 •^i = P'i ) 2^i'. Similarly, L 2 ' — L 2 " will 

 pass through zero for some temperature, when we have 

 P 12 d 2 = P / 1)2 d 2 / . If both the expressions pass through zero 



at the same temperature we have —=^7. Now this 



<\7 2 <\J 2 



equation would also apply when the relative concentrations 

 of the different molecules in the liquid mixture and the 

 saturated vapour are the same, since, as we have already 

 remarked, the relative distribution of the molecules should 

 then be the same. It appears, therefore, that when the 

 internal heats of evaporation, of the molecules of a mixture 

 pass through zero at the same temperature the relative con- 

 centration of the different molecules in the vapour and the 

 liquid must be the same. Further, since we then have 

 Jj 1 i = L 1 ,/ and L 2 ' = L 2 " the density of the vapour and liquid 

 must be the same. 



A saturated solution of molecules 1 in a liquid of mole- 

 cules 2 has the same partial vapour pressures as a saturated 

 solution of molecules 2 in a liquid of molecules 1, since they 

 remain in equilibrium in contact with one another. It follows, 

 therefore, from Olapeyron's equation that at low tempera- 

 tures, when the volume of the vapour of a grm. of molecules 

 of the same kind is large in comparison with the corre- 

 sponding volume of the mixture, the heat of evaporation of 

 a molecule of the same kind is the same for each mixture. 

 Therefore, if P' is the intrinsic pressure of one of the 

 mixtures and V/ and V 2 ' the volumes of occupation of the 

 molecules 1 and 2, and the corresponding quantities for 

 the other mixture are P", V/', V 3 ", we have ?%' = ?'%", 



V ' V " 

 and P'V 2 ' = P"V 2 ". From these equations we have m = —77 , 



or the ratio of the volumes of occupation of the two kinds of 

 molecules is the same in each mixture; further, we have 



P' V/' 



pT/= y—» or the intrinsic pressure of each of the mixtures is 



inversely proportional to the volumes of occupation of one of 

 the molecules. 



