54 Mr. W. Sutherland on Weak Electrolytes and 



rules for surface tension in normal mixtures. But it is well 

 known that the surface tension of mixtures of water with the 

 alcohols and fatty acids is exceptional. The abnormality in- 

 creases with increasing molecular weight of alcohol and acid, 

 for instance, while water has a surface tension 71 dynes/cm. 

 and isoamyl alcohol 24, a mixture containing 2 per cent, of 

 isoamyl alcohol has a surface tension 30, almost that of the 

 pure alcohol^ while 2\ per cent, of isovaleric acid reduces 

 the surface tension of water to 36, that of the pure acid 

 being 26. Probably then isoamyl alcohol and isovaleric 

 acid are far more concentrated in the surface film than in 

 the bulk of the mixtures. Similar causes to those which 

 convert the water of the bulk into trihydrol produce a higher 

 concentration of the alcohols and fatty acids in the surface of 

 mixtures than in the bulk. So we shall now investigate the 

 ratio pis/pi of concentration in the surface film to that in 

 the bulk. The fundamental equation for the surface tension 

 « of a mixture is (Phil. Mag. (6) xx. p. 262, 1910) 



u/p^ip^+p^y (45) 



With p Y -\-p 2 =l this becomes an equation for finding p^ 

 as p ls the value in the surface film when the us and p's are 

 known. The surface tensions of mixtures of water with 

 alcohols and fatty acids from 15° C. to 20° have been 

 measured by Traube (Joarn. f. prakt. Chem. xxxiv. p. 292, 

 1886 ; Ann. der Chem. cclxv. 1891). At each temperature 

 u 2 for water is u 2 for trihydrol 12 dynes/cm. at 15° and 71*7 

 sit 20° according to Traube's data, while /? at 0° is about 

 0'88, say 0*877 from 15° to 20°. For ethyl alcohol at 17°'5 



«! = 22'0 and / o 1 = 0'7906. 



From his data for u and p the following values of Pisjpi have 

 been calculated : — 



100 p l 



10 



20 

 291 



SO 

 2-36 



40 

 1-95 



50 

 1-66 



60 

 1-435 



80 



3-90 



115 



A mixture of ethyl alcohol and water containing 10 per 

 cent, of alcohol in the bulk has a strength of 39 per cent, in 

 the surface film. These ratios can be expressed by the 

 formula 



Pl /p ls = 0165 + 0-88 Pl .... (46) 



with a maximum error of 1*2 per cent, when p 1 = 0'3. This 

 simple formula shows how alcohol is distributed between 

 water in the bulk and trihydrol in the surface, when p 1 has 

 values between 0*1 and 0*8.. 



