98 PHENOMENA, ATOMS, AND MOLECULES 



negligibly small. Placing F = o we see that the maximum area covered per 

 molecule will be 



n.v = <7o g^ (58) 



-To 



For the case we have considered where Oo = 18, and Fo= — 13, we 

 obtain Qm = 18 + 32.3 = 50.3 A^ as the maximum area for an "expanded 

 film" of myristic acid on water. This equation shows that the maximum 

 area Cm depends principally upon Fq. By Equation 57 we see that Fq is the 

 difference between two relatively large quantities which are nearl}^ equal. 

 A very small percentage change in yn causes a relatively large change in Fo 

 and therefore in Om- As a matter of fact Adam finds that Gm varies only 

 moderately for dififerent substances. As the length of the chain increases 

 he finds a slight decrease in Qm and considers this a strong argument against 

 the view that the molecules tend to lie flat if they have sufficient room to 

 do so. We have seen, however, by our comparison of octane with tetra- 

 decane that yj? and therefore — Fq increase with the length of the chain, 

 and therefore, by Equation (58) , Qm should actually increase as the chain is 

 made shorter. The changes in anf observed by Adam may be accounted for 

 by very small percentage changes in Yi?- 



This theory of "expanded films" requires that the molecules remain in 

 contact while Adam concluded that in such films the "molecules become 

 separated and move about independently on the surface" and that "there 

 are spaces not covered by molecules." Adam considered that the molecules 

 of the film behaved as a two-dimensional gas while we conclude that it is 

 only the heads of the molecules that behave in this way. 



The fact that a palmitic acid film shows no measurable tendency to ex- 

 pand beyond a certain definite area is in accord with the following values 

 of 1 which have been calculated from the y's by the principle of independent 

 surface action. 



7.1 = 181 X io~^^ erg for a molecule oriented vertically in a water 



surface with the carboxyl group down and surrounded by 



water molecules except at its upper end which reaches the 



free surface. 

 Y2 = 64 X io~^^ for a molecule lying flat in the surface with the 



carboxyl group turned downward into the water at one end 



of the molecule. 

 Y3 = 4 X io~^^ for a horizontal molecule at the edge of a film of 



vertically placed close-packed molecules. 

 ?.4 = — 17 X io~^'* for a vertically placed molecule at the edge of a 



film of similar vertical molecules. 



