276 PHENOMENA, ATOMS, AND MOLECULES 



the old faces are thus destroyed and three new ones are produced so that 

 the lateral area of the edge of the film (whether in contact with vapor or 

 water) is not altered by the presence of a new molecule. The change in 

 surface energy due to the new molecule is thus : 



1. The energy of the upper end in contact with vapor. This area may 

 be estimated as 30 X A^ so that the energy is 30 X 50 = 15 X 10"^^. 



2. The energy of the head in contact with the water. We may assume 

 that the area 30 . A- is in contact with the water while the remaining 

 15. A^ of the head is in contact with the adjacent heads. This energy 

 is thus 30 X — 30 = — 9. X io~^^. 



3. The energy due to the water surface destroyed which is — 20 X 

 117= — 23.4 X 10'^^ 



The total energy of a palmitic acid molecule at the edge of a film is 

 thus 15 — 9 — 23.4 = — 17.4 X 10"^* erg. 



In Case 13 the new molecule at the edge of the film is assumed to lie 

 horizontally being in contact with the other molecules of the film only over 

 one of its six faces. 



Case 15 deals with the change in energy when a molecule is removed 

 from a surface film of horizontally packed molecules (not at its edge) so as 

 to leave a vacancy. 



An examination of the surface energies 1 of the molecules in various 

 environments as given in Table III shows that they explain many of the 

 properties of these substances. The small difference between X in Cases i 

 and 2, being less than the value of kT (4X 10'^* erg at ordinary tem- 

 perature), indicates that both palmitic and butyric acids should be miscible 

 with hydrocarbons in all proportions. 



It is of interest to note that the difference between l for a molecule in a 

 hydrocarbon and in its own liquid increases as the chain becomes shorter. 

 An example of an effect of this kind, sufficient to lead to relative in- 

 solubility, is observed in the case of n\ethyl alcohol which is miscible with 

 hexane in all proportions only at temperatures above 43° C. 



The solubility of palmitic acid in water is immeasurably small while 

 butyric acid mixes with water in all proportions at temperatures above 

 — 2.5° C. These facts are in general accord with the values of ?i given under 

 Case 5. Comparing these with the values for the corresponding hydro- 

 carbons (Table I) we see that the introduction of the carboxyl group 

 lowers the value of X by 40 units. This accounts for the great increase in 

 solubility. 



Comparing Cases 5 and 6 we conclude that the tail of the palmitic acid 

 molecule in water must assume a nearly spherical form while with the 

 butyric acid molecule, thermal agitation will be able to cause the tail to 

 spread out as a chain. 



