546 Dr. R. D. Kleeman on the 



Volume of Occupation of a Molecule in a Mixture. 



The decrease in volume of a large mass o£ a mixture of 

 substances on removing from it a single molecule, may be 

 called the volume of occupation of the molecule in the 

 mixture. This quantity it appears has not yet been defi- 

 nitely defined and discussed ; it seems of importance, and a 

 consistent study of it should lead to interesting results. It 

 is intimately connected with the relative distribution of the 

 molecules in a mixture. Using the same notation as before, 

 and denoting the volume of occupation of a molecule 1 by 



§i we have S i =p z -s — . We have further in the case of a 



OC[ 



mixture of molecules 1 and 2 in the proportion of rii to n 2 

 that 



*m + * 2 W 2 = ~tt ' or Si + m 2 = -pi > 



where a denotes the ratio of the concentration of the mole- 

 cules 2 to that of 1. 



We have seen that the decrease in volume of a mixture 

 when a molecule 1 is removed is $ b therefore if P lt2 

 denote the intrinsic pressure of a liquid, i. e. the pres- 

 sure due to the attraction between the molecules, P Jj2 $i is 

 approximately the work done on the molecule by the 

 mixture during its removal. If the temperature of the 

 mixture is kept constant during the process, an equivalent 

 amount of energy in the form of heat has to be supplied to 

 the mixture. This amount of work is equal to the internal 

 heat of evaporation L/ of a molecule 1 into a vacuum, or 

 equal to the ordinary heat of evaporation if the density of 

 the saturated vapour is very small in comparison with that 

 of the liquid. In the case of a mixture we have therefore 

 at low temperatures L/ = Fi )2 ^i and IV = Pi, 2^2- From 

 these two equations we have 



SV/SV 



or the internal heats of evaporation of two molecules 1 and 2 

 are to one another as their volumes of occupation in the 

 mixture. 



When the density of the saturated vapour is not small in 

 comparison with that of the liquid the value of L/', the heat 

 of evaporation of a molecule 1 of the vapour into a vacuum, 

 is not negligible in comparison with that of L/, and we have 

 for the ordinary heat of evaporation L/ — L/' = P 1( 2 $^ 

 — P'i 2"V 5 where L J // = P / 1)2 '$r, P'i.2 denoting the intrinsic" 



