Kinetic 1 heory of the Ideal Dilute Solution. 527 



E l>f^ = Sr CvTX") '" + ^ "*>' {"^equation [10]}* 



and not Dr. Shorter's similar but incomplete expression (A) 

 in which the heat of dilution (Q) is left out of account. But 

 it is evident that in cases where Raoult's law is obeyed, and 

 where the heat of dilution is very small, as at very great 

 dilutions, the theory leads to the result that the factor 



-|= — %r — in the above equation must be practically equal to 



unity. When this is true, the expansion (e) in the combined 

 volumes of the solvent and the solute, due to mixing one 

 molecule of the solute with a large volume of the solvent, 

 would be given by the expression 



6=(V 1 -6 1 )-(V 2 -6 2 ). 



But this latter expression only holds good for infinitely dilute 

 solutions, or in the case of stronger solutions which both obey 

 Raoult's law and have no heat of dilution. 



As minor points I may mention further that in discussing 

 the volume changes undergone during the mixing of two 

 liquids, Dr. Shorter seems to have misunderstood my defi- 

 nition of the quantity e, which is the excess of the volume of 

 the solution over the sum of the volumes of the two pure 

 components. Moreover, I stated at the outset of the paper 

 that I only dealt with solutions in which it is commonly 

 accepted that there is no molecular association, and not with 

 such solutions as alcohol in water, with which Dr. Shorter 

 illustrates his discussion. 



1 am, 



Yours faithfully, 



Frank Tinker. 



* This expression can be brought into a form which contains quantities 

 which are all directly measurable by combining- it with the relationship 

 established between the free space and the coefficient of compressibility 

 on p. 447 of my paper. The equation then becomes 



Pl ' N\/3xllT ) e ^ K 



where /3i and /3 2 are the coefficients of compressibility of the pure solvent 

 and solute respectively. 



Similarly the expression giving the expansion on mixing one molecule 

 of the solute with a large volume of the solvent becomes 



e=RT(0 1 -j3 2 ). 



