PHYSICS: I. LANGMUIR 
255 
For volatile or soluble substances, however, there is another method 
by which the cross-sections and lengths of molecules in the surfaces of 
liquids may be determined. 
According to Gibbs' equation 
(1) 
^ RT dc ^ 
we may calculate q the amount of material adsorbed per square centi- 
meter in the surface of a liquid, by determining the rate at which the 
surface tension, y, changes as the concentration of a dissolved substance, 
or that of a vapor above the liquid, is altered. It has been pointed 
out by Milner^ that when substances strongly depressing the surface 
tension are added to water, the surface tension varies linearly with the 
logarithm of the concentration for all except extremely dilute solutions. 
If we write equation (1) as follows: 
= - — — (2) 
^ RT d\nc ^ ^ 
it is evident that under these conditions q is independent of the con- 
centration. Milner thus calculates from Whatmough's data for acetic 
acid solutions, that q is 3.8 X IQ-^^ grams mol. per square centimeter 
over a rather wide range of concentrations. This should correspond to 
a monomolecular film. Multiplying the above result by N, we find 
that it corresponds to 23. X 10^^ molecules per square centimeter. The 
area occupied by each molecule is the reciprocal of this, or 43 X 10"^^ 
sq. cm. per molecule. If the whole of this area were covered by a single 
molecule of acetic acid, the value of r would be only 2.2 X 10~^ cm. 
It is therefore probable that the group molecule forming the surface 
layer contains water adsorbed around the acetic acid group. The polar 
character of the — COOH group should exert its influence on the CHs 
radical, causing it to pack into the surface layer surrounded by a definite 
number of water molecules. This hypothesis is in accord with the 
fact that acetic acid mixes in all proportions with water. 
Still more conclusive evidence in support of the new theory is fur- 
nished by a paper by Szyszkowski,^ in which surface tension data for 
water solutions of propionic, butyric, valeric, and caproic acids are given. 
The results are found to be given quite accurately by the purely 
empirical relation 
1 - — = ^ logio ^-^^ (3) 
To a 
