Biomedical Engineering Reference
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Assuming that there is an infinite number of layers of adsorbate possible (
N
),
/ N
Eqn (9.75)
is reduced
n
s1
c
p
A
p
A
1
1
n
As;
N
¼
(9.77)
p
A
p
A
p
A
p
A
ð
1
cÞ
which is the well-known BET isotherm. The mole ratio of the total multilayer absorbate mole-
cules to monolayer adsorbate molecules is given by
þ c
p
A
p
A
1
n
As
;
N
n
As;1
¼
1
1
(9.78)
p
A
p
A
p
A
p
A
ð
1
cÞ
Of the two parameters in
Eqn (9.78)
, the most informative is probably
n
As,1
, the capacity at
monolayer coverage. We stated earlier that the physical adsorption of nitrogen on many
surfaces resembled Type II in the classification of Brunauer (as it turns out, Type III is also
seen in a number of instances). Nonetheless, the idea is that if
Eqn (9.78)
is obeyed we can
obtain a value for
n
As,1
and, following some judicious assumptions, a value of the internal
surface area. However, one should note that this assumption is flawed since the site on the
adsorbent surface could also behave similar to a site on upper layers.
Type IV and Type V adsorptions are recovered when the number of layers is finite, for
example, when
N
¼
2,
Eqn (9.72)
gives.
2
1
ð
3
ap
A
Þðap
A
Þ
n
As;2
¼ n
s1
cap
A
3
ð
1
ap
A
Þ½
1
ð
1
cÞap
A
cðap
A
Þ
2
¼ n
s1
cap
A
ð
1
ap
A
Þ½
1
þ ap
A
2
ðap
A
Þ
2
2
ð
1
ap
A
Þ
½
1
þ cap
A
þ cðap
A
Þ
which is reduced to
cap
A
ð
1
þ
2ap
A
Þ
n
As;2
¼ n
s1
(9.48)
1
þ cap
A
ð
1
þ ap
A
Þ
Thus,
Eqn (9.72)
describes type V isotherms when
N
¼
2.
Example 9-3
Adsorption of Water Vapor on Silica Gel.
Experimental adsorption data given by Knaebel (Knaebel, K.S. “14 Adsorption”, in Lyle F.
Albright ed.
Albright's Chemical Engineering Handbook
, CRC Press, Taylor & Francis Group,
Boca Raton, FL, 2009) for water vapor on silica gel at 25
C is shown in
Table E9-3.1
. Perform
data fit to Langmuir isotherm, bilayer isotherm, and the multilayer isotherm. Comment on
your solutions.
Solution
. We first examine the quality of fit for the Langmuir model as it is the simplest of
all the isotherms with a theoretical basis. Eqn
(9.9)
can be rearranged to give
ap
A
=p
A
C
As
¼ C
As
N
(E9-3.1)
þ ap
A
=p
A
1
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