iiikoky OF CONCENTRATED SOLUTIONS. 1 43 



In these equations everything' is known except /> and K. By 

 eliminating the one we obtain, of course, the value of the other. 



If n is greater than one, as is usually the case, the solving ot 

 these equations is very laborious. I have heen unable to find 

 accurate numbers for a binary mixture with chemical combina- 

 tion where n = I. By extending the principle of this paper we 

 can, however, test the results by some accurate data in regard 

 to electrolytes. 



The volume changes which occur on mixing liquids have 

 heen studied hy Holmes and Sageman.* 



These authors attribute such changes to purely physical 

 molecular processes on mixing. They come to the conclusion 

 that chemical combination in solution is unnecessary to explain 

 the deviations of binary mixtures from the simple mixture law. 

 and they point out that their interpretation of the facts is totally 

 incompatible with any " hydrate " theory of solution. Further- 

 more, their theory leads them to the remarkable conclusion that 

 there is no chemical combination, i.e., no formation of bisulphate 

 when sulphuric acid and normal sulphates are mixed in aqueous 

 solution. This conclusion is difficult to reconcile with the fact 

 that bisulphates can be obtained from the solution, since a sub- 

 stance cannot crystallise from a solution which does not contain 

 it. The actual amount in solution it is true may be small, but it 

 must be finite. However, the electrolysis of bisulphate solutions 

 would appear to show that the amount of bisulphate present as 

 such is considerable. I propose to show that the accurate 

 experimental figures of the above authors afford excellent quan- 

 titative evidence of the formation of bisulphate if viewed from 

 the standpoint of mass action. Incidentally they serve as a test 

 of the theory put forward by the present author. 



Let us assume then that the formation of bisulphate takes 

 place <m mixing solutions of H t S0 4 and K S0 4 according to the 

 equation 



H 2 S0 4 + K 2 S0 4 == 2KHS0 4 



Neglecting ionisation ( which makes but little difference in the 

 present case), and considering only unionised molecules, let Us 

 further suppose that in a mixture of y mols K. 2 S0 4 - and ( i-y) 

 mols H.SO4 there are formed 2,r mols KHSOj. 



The system then consists of 



(y — x) mols free K a S0 4 1 

 (1 — y - x) „ „ H.^SC^ total 1 



2X „ „ KHS0 4 I 



Hence according to the law of mass action we have 



0' - ■')(* - y ~ ■'-) = K '"-' 



*J. C. S.. Trans., 1906, vol. 89, p. 1174. 

 J. C. S.. Trans., 1907. vol. 91. p. 1606. 



