ADSORPTION ISOTHERM AND THE STATES OF ADSORPTION

Adsorption Isotherm and the States of Adsorption
deduced 22 ) just over the range, where F(E) is directly based on the observed
v, by applying the SOMMERFELD'S method of evaluating Ii of Fermi gas from
known F(E), inversely to the present problem as follows. According to
SOMMERFELD 25 ) ,
Cp 00 (n- RT)2'" { d 2 "'-l F(E) }
v=J_oo F (E)dE+22';:j- (2m-)!-(2 2m -1)B", -dpm--l - E=p' (3. a)
where Bm is the Bernoulli's number, i. e., 1/6, 1/30, 1/42,······ for m = 1,2,
3 ....... respectively. KEII has shown 26 ) that the ROGINSKY'S approximation 5 )
for evaluating F(E) from observed v corresponds to the first term of (3. a)
only being retained and he worked out 26 ) F(E) and hence the heat of adsorption
reserving first two terms.
It has now been shown 22 ) retaining the whole terms that (3. a) leads with
special reference to (2. F), exactly to the equation
v sm n-c
F (E)E=p = RT----n-- .
(3. b)
Eq. (3. b) defines the function F(E) just over the range of E equal to Ii,
which is determined directly by observations by (2. Ii), thus basing F(E) solidly
upon observations.
The explicit function F(E) is obtained from (3. b) by substituting Ii from
(2. F), expressing P, thus introduced, by (2. Ii) and identifying Ii with E for
F(E)E=p, as
V l sin 2n-c Clil 2cE
logjo F(E) = loglo -- n-RT- - 2.301