SURFACES OF DISCONTINUITY 555 



already been stated that Thomson's equation has a close kinship 

 with some equations of Langmuir and others. We can enlarge a 

 little on this point. The surface film of a liquid is a region 

 where the potential energy of a molecule of the solute is greater 

 by a definite amount e than that possessed by the molecule 

 when in the bulk of the solution. It follows from the funda- 

 mental statistical law that since r/f is the volume concentration 

 in the film 



r 



~ = c exp 



V kt) 



or 



r 



€ = - kt log — • 



Langmuir has applied this result to Szyszkowski's measure- 

 ments of the surface tensions of solutions of the fatty acids and 

 to the adsorptions calculated therefrom. If e„ and €„_i are the 

 energies of adsorption per molecule for acids with n and n — 1 

 carbon atoms, respectively, then 



E„ — €„_i = — kt 



'"K«X-'°^ffL. 



assuming that the film thickness f is the same in all cases. In 

 the case of dilute solutions where c is small compared to a this 

 result becomes by (19) 



€n - €„_i = -^^{log ttn-l " log a„} , 



since g, i.e. hao/Rt, is the same for all the acids. Now, as men- 

 tioned above, an-i/ctn has an almost constant value about 3.4, 

 so that log a„_i — log a„ is the same for any pair of successive 

 acids. Thus the energy of adsorption increases by a constant 

 amount for each CH2 group added to the hydrocarbon chain of 

 fatty acids. "This must mean that each CH2 group is situated 

 in the same relation to the surface as every other such group in 

 the chain, and this can only be the case if chains lie parallel 



