274 



PHENOMENA, ATOMS, AND MOLECULES 



The surface energies of these molecules in various environments have 

 been calculated from the data in Table II by means of the assumed values 

 of the y's and the results are given in Table III. The assumed locations 

 and orientations are illustrated diagrammatically in Fig. i, in which the 

 numbers correspond to those in the first column in Table III. The relative 

 lengths and diameters shown in Fig. i agree with those given for palmitic 

 acid in Table II except that the molecule marked 6b illustrates the butyric 

 acid molecule in a cylindrical form. 



As an example of the method of calculating the surface energy let us 

 consider Case lo in which a molecule of palmitic acid is adsorbed on a 

 water surface. The hemispherical upper end of the molecule which extends 

 above the water has a surface of 40. A^ and since the surface energy ^r is 

 50 this part of the molecule contributes 20. X 10"^^ erg. The surface of the 

 chain in contact with the water is 375 — 40 = 335, and the surface of the 

 head is 45. The surface of water destroyed by the presence of the mole- 

 cule is 20, so that the total energy, obtained by multiplying these surf- 

 aces by the corresponding y and adding is (40 X 50) + (335 X 59) + 

 (45 X - 30) - (20 X 117) = i8i- X lo-i^ erg. 



Fig. I. — Diagram illustrating the various locations and environments of molecules 



considered in Table III. 



In Case 2 where we consider a palmitic acid molecule in liquid palmitic 

 acid we assume a random distribution of the molecules of the liquid. Each 

 molecule has a tail having a surface of 375. while the surface of the head 

 is 45, the head thus occupying 10.7 per cent of the whole surface. Consider- 

 ing the tail of a given molecule, we thus conclude that 0.107 of 375 or 40.2 

 is the area of the tail in contact with the heads of neighboring molecules 



