THEORY OF CONCENTRATED SOLUTIONS. 137 



ever x mols of compound ABn be formed,, then we have in the 

 equilibrium 



(v - x) mols A ^ 

 (i — y - nx) mols I> > total mols (1 — fix 

 x mols AI>„ ) 



Taking active mass as proportional to molar fraction we 

 have for the expression of the mass law 



<y — x) /i — y — nx\" Kx 



i — nx V i — nx J i — nx 



where K is the equilibrium constant for a given constant tem- 

 perature. 



i.e., [y — .v)(i — y — nx)" = Kx(i — nx)" 



This expression governs the relation between the amounts of 

 A, B, and ABn in the solution as the composition varies from 

 ioo</c A to 1 00% total B. 



1 (ix 



\\ hen y = — ; — t = ° 



J n -■■ 1 dy 



and x has a maximum value. 



Hence the composition of the solution or mixture at which 

 the amount of compound is a maximum gives n i.e. the formula 

 of the compound formed. 



Further if n = I, that is, the formula of the compound is 

 AB, then the molar fraction of A in the true compound is 



0.5 i.e. - 



n + 1 



In short the composition of the mixture which contains the 

 maximum amount of the compound is also the composition of 

 the compound formed. This is quite independent of the degree 

 of dissociation of the compound, since the expression for maxi- 

 mum amount of compound 



1 



y = 



n + i . 

 is independent of the value of the equilibrium constant K. 



This result might be foreseen from the following considera- 

 tion. Suppose we have the compound ABn, which, however, is 

 more or less dissociated. If we add to it excess of the com- 

 ponent A we are performing two distinct operations, each of 

 which affects the equilibrium. Firstly, we are decreasing the 

 degree of dissociation of the compound according to the principle 

 of mass action, but secondly we are also decreasing the active 

 mass or concentration of the constituent B, and also increasing 

 the volume of the system or the total number of mols present 

 This tends to increase the degree of dissociation of the com- 

 pound. The second process has much the greater effect, and 



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