280 PHENOMENA, ATOMS, AND MOLECULES 



sunied to take place in the manner that was suggested (on page 1865) for 

 the expanded fihn of oleic acid, viz., in the expanded film "the molecules 

 are partly reclining on the surface, while in the second case (compressed 

 film) they are packed tightly side by side and are more or less erect upon 

 the surface." 



The area covered by a vertically placed palmitic acid molecule is about 

 20. A^ while the same molecule lying flat on the surface should cover an 

 area of about 108. A^ (see Table II). Clearly then the expanded film 

 occupying an area of at most 40 A^ must consist of molecules which are 

 only slightly inclined from the vertical. As a matter of fact there is no 

 reason at all why the flexible hydrocarbon chains should orient themselves 

 at any particular angle. They will be quite free to respond to thermal agita- 

 tion and arrange themselves nearly in the same random manner as in a 

 liquid hydrocarbon, the only restriction upon their motion being imposed 

 by the condition that the lower end of each molecule must remain in contact 

 with the underlying water. We can thus readily see why the expanded films 

 are always liquid while the contracted or fully compressed films of vertically 

 oriented molecules are frequently solid. Taking the volume of the hydro- 

 carbon chain in the palmitic acid molecule as 45oA^ (Table II) we see that 

 the thickness of the hydrocarbon layer (in A units) will be 450 -^- a where 

 a is the area of the film per molecule (in A^ units). Thus when a = 20 A^ 

 the thickness is 22. 5A while for an expanded film for which a = 33A^ the 

 thickness is 13.6A. Such an expanded film is represented diagrammatically 

 by 16 in Fig. i, the area per molecule corresponding to the inclination shown 

 being about a = 60. A^. 



Consider an expanded film as covering a definite area of a water surface. 

 If additional palmitic acid molecules are introduced into the film there is no 

 change in the area of the free hydrocarbon surface. The energy of transfer 

 of a molecule from any given location to an expanded film is thus the same 

 as the energy of transfer of the molecule to an interface between hydro- 

 carbon and water as illustrated by Case 7 in Table III and Fig. i. Accord- 

 ing to the data of Table III the value of l for a molecule of palmitic acid 

 at the edge of a condensed film is — 17 (Case 14) while for a molecule in 

 an expanded film (Case 7) A is —37. This would indicate that the expanded 

 film should form in preference to the condensed film. However, the differ- 

 ence of 20 in the values of X is not greater than the probable error so that 

 the sign of the difference is somewhat uncertain. In considering the stability 

 of expanded films we must take into account the applied compressive force 

 and the effect of the forces acting between the heads of the molecules which 

 are located in the interface between the hydrocarbon film and the water. To 

 understand these relationships better let us analyze the problem as follows. 



Let n molecules of a substance (which spreads on water) be present 



