SURFACES OF MOLECULES 239 



where px is the partial pressure of the suhstance A, the total pressure of the 

 pure component A is Pa ; the mole fraction of the component A is repre- 

 sented in this equation by A. The quantity S^ is the surface area per 

 molecule of area ; q) is a constant characteristic of the binary mixture but 

 independent of the concentration of the components, which can be cal- 

 culated in terms of such quantities as a, c, yac, etc. The quantity /5 may be 

 called the surface fraction of the component B in the binary mixture of A 

 and B. It corresponds to the ordinary conception of mole fractions but is 

 expressed in terms of the relative surfaces of the molecules instead of the 

 numbers of the molecules. Thus 



fi = BSB/(ASA + BSn) 



This equation with only one adjustable constant, q), apparently agrees 

 in general better with experimental data than a somewhat similar equation 

 with two adjustable constants derived by van Laar on the basis of thermo- 

 dynamical considerations. 



C. P. Smyth has recently used this equation in connection with his own 

 measures of the vapor pressures of binary mixtures. The agreement, in 

 most cases, is fairly good, but, as is to be expected in the case of more 

 polar molecules, mixtures of alcohols with water show considerable devia- 

 tions. It is probable that these can in large part be taken into account by 

 developing the theory further to allow for orientation and segregation of 

 the molecules within the liquid. 



Views of the type which I have been discussing may thus be applied 

 quantitatively, often w^ith considerable accuracy, in studying the inter- 

 actions between molecules of organic substances. The energy relations 

 based on the conception of surface forces between molecules, together with 

 the Boltzmann equation, frequently permit decisions to be made as to the 

 mechanism of various surface phenomena. For example, in expanded films 

 of oils on water it has often been assumed that the molecules could remain 

 erect on the surface without touching one another. Simple energy con- 

 siderations of the kind which we have been using indicate immediately that 

 this is impossible. The tails of the molecules must remain in contact w^ith 

 each other in the case of long chains, but with shorter chains, the molecules 

 may separate but must then lie flat upon the surface of the water. The 

 principle of independent surface action affords one of the greatest safe- 

 guards against the setting up of impossible hypotheses. 



REFERENCES 



(i) Hardy, H. B., Proc. Roy Soc. (London), 86A, 634 (1912) ; 88A, 330 (1913). 



(2) Langmuir, I., Chcm. Met. Eng., 75, 468 (1916). 



(3) Langmuir, L, Jour. Ammer. Chan. Soc, 39, 1848 (1917). 



