﻿Constitution of Aqueous Solutions. 17 



it is shown that while for normal mixtures the surface tension 

 « and the density p are connected with « 3 , « 4 , p 3 , p 4 for the 

 pure ingredients by the formula 



^p'=(ps4ip 3 +pA/p4Y, .... (20) 



this does not apply to aqueous solutions, because it contains 

 no provision for taking account of the change produced in the 

 water by the solute. It is also shown that a for aqueous 

 solutions is given by the empirical formula 



a/p 2 ^plocjpl +p\b 4 2p^c 



= «M+Pl(«*/Pl + I>-2c) + 2pt(c-« 3 /pl), . (21) 



in which b and c are parameters characteristic of the solute. 

 The parameter b in this has not the value ajp 2 v as in the 

 formula (20) for normal mixtures. This then is the chief 

 abnormality in the surface tension of solutions. In the paper 

 just mentioned values of b and c were found for a large 

 number of solutes. We shall be able to use these by estab- 

 lishing the connexion between (21) and a theoretical equation, 

 taking account of the change in the amount of (H 2 0) ;i caused 

 by the solute. Let all symbols in this section refer to the 

 surface-film : for instance, if there are p x of (H 2 0) 2 and p 2 of 

 (H 2 0) 3 in a gramme of surface water, the values of pi and p 2 

 are very different from those in the bulk ; but no special 

 symbol will be provided to distinguish surface from bulk. So 

 also, when a solution is made of p s water and p 4 solute in a 

 gramme, p± in the surface is different from p 4 in the bulk. 

 For the surface tension of water we have 



«*IpI=(Pi«1/Pi+P24Ip*Y (2 2 ) 



This equation and (20) summarize the theory of the surface 

 tension of solutions. As most of the experiments have been 

 made below 40°, we shall avail ourselves of the simplification 

 that in the surface of pure water at these temperatures p 2 =l. 

 Hence by (5) in a solution 



P2 = 1 -Pi = 1 ~ terpje, 

 and 



a T f 5It (a\ ti\ a \ ) all 2 



p L I e r \ Pi p 2 t p 2 \ r * p J 



With p s +p i z=l and expanding in powers of p A as far as 

 Plnl Mag S. 6. Vol. 12. No. 67. July 1906. C 



