Biomedical Engineering Reference
In-Depth Information
Saturation region
1
A = K A C A
A
1
2
0
0
C A
FIGURE 9.4 Monolayer surface coverage, typical Langmuir adsorption isotherm.
this quantity at a given partial pressure (for adsorption from gas phase) or concentration to
that at saturation can be taken as a direct measure of surface coverage. Mathematically,
n AS
n max
q A ¼
(9.16)
where n AS is the number of moles of A adsorbed on the surface and n max is the maximum
number of moles that can be adsorbed on the surface.
At this point, we observe that the ideal (or Langmuir) adsorption isotherms for a single
component and a multicomponent mixture are quite similar. Indeed, in general, the ideal
adsorption isotherm or coverage for a particular species j is given by
K j C j
q j ¼
(9.17)
þ P N s
1
1 K m C m
where q j is the fraction of sites that are covered by species j . If there are dissociative species in
the mixture, modification of Eqn (9.17) needs to be made for the dissociative species in the
same fashion as that in Eqn (9.14) .
The interpretation of data on adsorption in terms of the Langmuir isotherm is most easily
accomplished using the procedure previously described for reaction rate data. As pointed
out earlier, the total number of active site is not dependent on the temperature or concentra-
tion, the Langmuir isotherm is restricted then by the total amount of adsorbate could be
adsorbed on the surface.
Examples of false obedience to the Langmuir isotherm abound. These usually arise when
adsorption data have not been obtained over a sufficiently wide range of concentrations or
partial pressures (of gas adsorbate); a good test is to see if value of the saturated adsorbate
n max evaluated from isotherm data at different temperatures are equal, since within the
framework of the Langmuir surface model the saturation capacity should not vary with
the temperature. It can be difficult to tell, however, in view of experimental error. It is, on
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