ADSORPTION PHENOMENA 203 



Put— $=U-T<f> + PV 



Then, d$ = -<f>dT + *dS+VdP (2) 



or, since the temperature is constant and dT = o : 



d$ = adS + VdP. 



But d$ is a perfect differential, and therefore : 



(©.-(£). (3) 



If the solution contains n grams of solute, and if p is the 

 excess of solute in the surface, in grams per cm. 2 , over and above 

 that of the bulk concentration, the concentration in the rest 

 of the solution, instead of being n/V, will be : 



n-PS T , n-PS 

 c = — ~ — or V = 



Hence, 



(dV\ (dV\ P 



\is)-Kds)r~~c (4) 



Also, for dilute solutions : 



P=RTc, or dP = RTdc (5) 



Substituting equations (4) and (5) in equation (3) we have at 

 once the required formula : 



1 RT dc 



Experimental Investigations of Gibbs' Expression 



The great majority of the cases of surface-condensation 

 with which we are familiar refer to effects produced at the 

 surfaces of solids. Apart from the question of whether such 

 effects are true adsorption effects or not, it is evident that 

 the results obtained cannot be used to verify Gibbs' expression 

 simply owing to the fact that it is impossible to measure the 

 interfacial tension between a solid and another phase. To 

 investigate the expression it is essential that the adsorption 

 process take place at the interface between two liquids, or 

 between a liquid and a gas, as it is only at such interfaces 

 that the tension o- is directly measurable. 



The earliest measurements of this nature are those of 

 Milner {I.e.), who succeeded in showing that aqueous solutions 

 of acetic acid and sodium oleate exhibit positive adsorption 



