SURFACES OF DISCONTINUITY 569 



of a given amount of gaseous film and the surface area over 

 which it extends resemble in form the laws for gases, such as 

 Amagat's and van der Waals'. Actually there appear to be 

 processes in the surface analogous to fusion and vaporization 

 and a whole new "two-dimensional" world seems to be open- 

 ing up. 



So far these remarks have been concerned with films of 

 insoluble or nearly insoluble materials, and have had no direct 

 connection with adsorption from solutions, but in the paper 

 already cited Langmuir used Gibbs' equation to indicate that 

 similar conditions exist in adsorbed films. By using Szysz- 

 kowski's data on the relation between surface tension and 

 concentration he calculated from the adsorption equation the 

 amount adsorbed and thus obtained the area per molecule in 

 the film for various bulk concentrations of the solutions of the 

 very short-chain fatty acids, from 3 to 6 carbons in length. 

 He found that with increasing bulk concentrations this tended 

 to decrease to a constant value roughly consistent with what 

 might be regarded as the sectional area of the molecule, thus 

 suggesting that at the limit of adsorption there exists a close- 

 packed unimolecular film in the surface. For the most dilute 

 concentrations the film is, of course, much more sparsely occupied 

 by the adsorbed solute molecules, and these appear to have the 

 properties of a gaseous film. This^is easily shown from the 

 Szyszkowski formula 



Langmuir, interpreting o-q — <r as the "surface pressure" (actu- 

 ally Traube suggested this interpretation for the lowering of 

 surface tension in these adsorption films long ago), writes it 



F = aoh log (l + H 



c 1 c^ 1 c^ 

 a 2 a^ 3 o^ 



= <^o&^7-o7; + o3- etc. 



