mi the Analogy between Solutions and Gases. 93 



But this relation can be further developed. Different 

 solutions may be compared with each other, and a second law 

 may be deduced, which Raoult has also discovered experimen- 

 tally. The following reversible process, consisting of two 

 operations, is carried out with a very dilute solution of P per 

 cent., at temperature T. 



1. Remove, by use of cylinder with semipermeable wall, a 

 portion of the solvent containing a kilogram-molecule (M) of 

 the dissolved substance : here the total quantity of solution is 

 supposed so great that no alteration of concentration occurs, 

 and the expenditure of work is therefore 2T. 



2. This quantity, — p — kilograms, of the solvent is returned 



as vapour ; it may be conceived as produced from the liquid 

 by evaporation at its vapour-pressure ; then expanded till its 

 pressure is equal to the vapour-pressure of the solution ; and 

 finally liquefied in contact with the solution. The kilogram- 

 molecule of the solvent (W) will thus receive an expenditure 

 of work of 2TA, where A represents the relative diminution 



of pressure ; and the — p — kilograms will receive 2TA . 



Here -p M is Raoult's molecular diminution of pressure, which 



we shall term K ; employing this abbreviation, the expression 



. 200 TK 



becomes — ^p — 



From the second law of thermodynamics, again, the alge- 

 braic sum of the work expended during this cycle at constant 

 pressure must equal zero ; hence the work done by the solu- 

 tion during the first stage must equal the work done on it 

 during the second ; and thus 



2T= 200TK. or i00K = M'. 



This expression includes all Raoult's results. It expresses the 

 fact, as stated above, that the molecular diminution of vapour- 

 pressure is independent of the nature of the dissolved body ; 

 and it also expresses, what Raoult found experimentally, that 

 this diminution is independent of temperature. It also con- 

 tains Raoult's second conclusion, that the molecular diminution 

 is proportional to the molecular weight of the solvent, amount- 

 ing to about one hundredth of the latter. This is seen from 

 the following table : — 



