202 SCIENCE PROGRESS 



form by applying the gas law, P — RTc. Gibbs' equation then 

 becomes : 



n== <L<k 



1 RTdc 



This is the fundamental expression for adsorption. Three 

 important assumptions are involved in it : (i) the process 

 must be thermodynamically reversible, (2) the temperature 

 must be maintained constant, and (3) the homogeneous phase 

 consisting of gas or solution must be sufficiently dilute for the 

 gas law to be applied. The expression is directly amenable 

 to experimental investigation provided the system is one 

 whose interfacial tension c- is measurable, as a function of the 

 concentration c of the solution or gas, and if further the actual 

 mass P of adsorbed material is sufficiently large to be mea- 

 sured. Before taking up the experimental investigation of 

 Gibbs' equation, it is of interest to point out that the equation 

 can be obtained by at least two other thermodynamical 

 methods necessarily equivalent to his, but much less general 

 in form. The first method is by means of a thermodynamical 

 cycle, and is due to Freundlich (Kapillarchemie) , who based it 

 upon a method given by Milner {Phil. Mag. [6] 13, 96 (1907)). 

 The second involves the use of the perfect differential and 

 has recently been published by Harlow and Willows {Trans. 

 Faraday Soc, 11, 53, 191 5). A. W. Porter {Trans. Faraday 

 Soc, 11, 51, 191 5), has worked out a modified equation to 

 apply when the solution is concentrated. Of these methods 

 we shall only consider that of Harlow and Willows. 



Let U be the internal energy of a given mass of solution, 

 whose osmotic pressure is P and volume V ; let also o- be the 

 surface tension, S the area of the surface at which adsorption 

 occurs, T the absolute temperature, and <£ the entropy. Let 

 S and V be changed by small amounts dS and dV at constant 

 temperature, where dV is an increase in the volume of the 

 solution due to an influx of solvent through a semipermeable 

 membrane. It may be necessary to supply a quantity of 

 heat dH to fulfil this condition, where dH = Td<j>. Then the 

 change in U is given by : 



dU=Td<l> + *dS-PdV (1) 



since work has to be done on the surface to increase its area 

 and by the solution when the volume is increased. 



