572 RICE 



ART. L 



precise surface tension measurements of Szyszkowski. A two- 

 dimensional analogue of van der Waals' equation has also been 

 suggested, but data do not appear to be available over a wide 

 enough range of temperature to justify a definite opinion. 



26. Unimolecular Layers and the Dividing Surface 



This use of Gibbs' equation and the consistency of the 

 information which it gives concerning the surface structure, is 

 strong evidence for its validity in the case of substances such 

 as the shorter-chain fatty acids. Indeed, this conception of the 

 unimolecular Gibbs layer may throw some light on the dis- 

 crepancies which have raised doubt concerning its validity. 

 There does not appear to have been any such idea in Gibbs' 

 own mind. Possibly he held the view which, with the weight of 

 Laplace's name behind it, seems to have been prevalent in his 

 day, viz., that the discontinuous layer, although physically 

 very thin, is nevertheless many molecules thick and shows a 

 gradation of properties as it is passed through. Yet if the layer 

 is really only a molecule or two thick, the placing of the dividing 

 surface becomes a somewhat perplexing matter. Indeed, the 

 whole physical theory of placing the "surface of tension" so as 

 to exclude the Ci 8ci + C2 dc2 terms in the original differential 

 equation becomes very doubtful. Earlier in this commentary 

 we have somewhat expanded Gibbs' presentation of this in 

 order to assist the reader to an understanding of his concise 

 formulation, and on referring to this again the reader will see 

 that the basis of it is hardly tenable for a unimolecular layer. 

 A very significant illustration of the point involved here will be 

 found in two well-known calculations made by Schofield and 

 Rideal (Proc. Roy. Soc., 109 A, 57, (1925)) ; they refer to alcohol 

 and pyridine. The data for the surface tension of mixtures of 

 water and ethyl alcohol from pure water to pure alcohol were 

 known from some work of Bircumshaw, and data for the partial 

 vapor pressure of ethyl alcohol could also be obtained so as to 

 give the activity and therefore the potential. With the aid of 

 these the surface excess of alcohol was calculated by the strict 

 Gibbs' equation for over a dozen mixtures between the extreme 

 limits. It was found that this excess rose very rapidly until it 



