144 



THEORY OF CONCENTRATED SOLUTIONS. 



Owing to the fact that there, are equal numbers of mols on 

 each side of the equation the volume of the system has, of course. 

 no effect on the equilibrium. 



Differentiating with respect to y we find that the number of 

 mols and the active mass of bisulphate in the system is a maxi-" 

 mum when y = I, i.e.. when the system as a whole contains 

 equal molecular amounts of the two components. 



But on our theory x is proportional to the contraction on 

 mixing, and hence this contraction should reach a maximum 

 value at the composition y — \. It is evident from the curves 

 shown in Fig. 6 (taken from Holmes's paper) that this is very 

 exactly the case. 



From the equation (y — .r ) ( i — y — x) = Kx' 1 . 



we see that when K approaches zero, i.e., total combination 

 between the components, ( y — .v) ( I — V — x) = o. 



The relation between x and y is then represented by two 

 straight lines equally inclined to the composition axis and meet- 

 ing at a point whose abscissa is given by y = T 



This is exactly the case given by Holmes for solutions of 

 HC1 and NaOH, where combination is, of course, practically 

 complete. When combination is not complete, i.e., the compound 

 formed is more or less dissociated, the straight lines become 

 curves, and instead of a point maximum where two straight 

 lines meet, we get a smooth curve with a more or less pronounced 

 maximum. Hence the flattening of the curve at the maximum 



