68 SECTIONAL ADDRESSES. 
by the analysis of foams and froths. In 1908 S. R. Milner used 
the same method in the case of aqueous solutions of sodium oleate, 
and arrived at a mean value of 1.2x107'° gram mols. excess concentra- 
tion per sq. cm. of surface. Now, in the case of dilute solution, we 
can calculate q, the amount concentrated or ‘ adsorbed ’ in the surface 
per sq. cm. (excess surface concentration) by making use of the equa- 
tion of Gibbs, 
Oey 
q on 
where y =surface tension and »=chemical potential of the adsorbed 
substance in the bulk of the solution. Writing » = RT log a + k, 
where a=‘ activity ’ of the solute, and k is a quantity dependent only 
on the temperature and nature of the solute and solvent, du=R T d 
log a, and so Gibbs’ equation can be written in the form 
wp dleg hed borg 
RT d log a 
i 
If for very dilute solutions (or for so-called ‘ ideal ’ solutions) we 
put a=c, we can write 
ee sedh Grate ade Hay. 
RT d log ¢ RT de 
q= 
In this way Milner has calculated from Whatmough’s data for aqueous 
solutions of acetic acid that the ‘saturation’ value of gq is 3.8x10-"° 
mols. per sq. cm., from which it follows that the area per molecule in 
the surface is 50x107** sq. cm. In a similar manner, Langmuir has 
calculated from B. de Szyszkowski’s data for aqueous solutions of 
propionic, butyric, valeric, and caproic acids that the surface area per 
molecule adsorbed in the saturated layer is equal to 31x10-** sq. cm., 
whilst Harkins has arrived from his own measurements for butyric 
acid at the value 36x10-** sq. cm. 
In 1911 Dr. J. T. Barker and myself made a direct determination 
of q for a solution of nonylic acid in water. For a practically saturated 
surface layer it was found that q was about 1.0x10-’ grm. per sq. cm., 
or 3.1x10™ molecules per sq. cm. From this result it follows that 
the surface area per molecule is 26x10-"* sq. cm. 
If we consider these various values, it will be at once evident that 
they are not very different from the values found by Langmuir and 
by Adam for the oriented unimolecular layers of practically insoluble 
fatty acids resting on the surface of water. That in the present case 
some of the values are larger might easily be explained on the ground 
that these adsorption layers are partially, or completely, in the state of 
‘surface vapours.’ For Adam and Marcelin have recently made the 
important discovery that the unimolecular surface films investigated 
by them may pass rapidly on increase of temperature from the state 
of ‘ solid’ or ‘ liquid’ surface films to the state of ‘ vaporised ’ surface 
films, in which the juxtaposed molecules become detached from each 
other and move about with a Brownian or quasi-molecular motion, 
