25 
1917 - 18 .] Thermodynamics of Adsorption. 
If we denote by T the excess concentration on unit area of the surface 
over and above what it would be if occupied by the gas alone without 
alteration of the volume of the adsorbent, 
1 0o- 
V dp 
(9) 
= -#^7- when ^ v=RT • • • m 
Jhl op 
which is the well-known equation due to Gibbs.* 
It is interesting to notice that since the amount adsorbed per grin, 
adsorbent is usually calculated without correcting for the volume of the 
adsorbed gas, etc., what is measured is not a, but FA. Thus, let 
v 1 — volume of reservoir containing gas, 
v 2 — „ adsorption chamber less volume of adsorbent. 
Then with the above notation we have 
_ v l ( v 2 - ga V a + gv Q - gv a 
n ~ y + y 
+ (J a. 
Hut if a denote the calculated value of a, neglecting the volume of the 
adsorbed gas, etc., 
v, v 9 
— y + y + { 1 a , 
or 
ga = go. 
gaV a - g(v 0 - v a ) 
Y 
+ 
v 0 - v a 
V 
= r a. 
On the analogy between the specific volumes of a liquid and its 
saturated vapour the difference between a and a will, in ordinary cases 
of adsorption, be less than 1 in 1000. 
From equations (5) and (7) we have by differentiation as before 
or 
1 / 0 2 E „d*v\ 
T\dsdT +I> dsdT/ 
1 / 0 2 E 0o- \ 
T\3s0T +P dsd T _ 0T/ 
1 /0E 
r 2 V0^ 
du X \ 
+p ds - V 
(10) 
* Papers, vol. i, p. 235. For other methods of deriving the equation, see, among others, 
Milner, Phil. Mag. (1907) (vi), 13, p. 96 ; Ostwald, General Chemistry (1912), p. 499 ; 
and, more recently, Porter, Trans. Far. Soc. (1915), vol. xi, p. 51, and Harlow and Willows, 
ibid., p. 53. 
