Environmental Engineering Reference
In-Depth Information
Box 6.3.2
Predictions of mixture isotherms
We can extend our single component Langmuir isotherm to mixtures. We use a
surface with
σ
max
sites. As in the case of pure components, we assume that there
are no interactions between the sites. The components A and B compete for these
sites. We have equilibrium between the surface and the gas if the number of mol-
ecules per unit time leaving the surface and going into the gas phase equals the
number of molecules per unit time going in the reverse direction for each of the two
components A and B. If we assume no interactions between the adsorption sites,
the rate of molecules leaving the surface is simply proportional to the number of
adsorbed molecules:
(
)
A
k
surface
→=
gas
c
θ σ
,
A
d
A
max
where
θ
A
is the fraction of sites occupied by A molecules. For component B we
have:
(
)
B
k
surface
→=
gas
c
θ σ
B
d
B
max
For the reverse direction, we have the molecules competing for the empty sites and
for each of the components the rate of adsorption is proportional to the partial
pressure:
(
)
(
)
A
k
gas
→
surface
=
c
1
−θ
−θ
σ
P
A
a
A
B
max
A
(
)
(
)
B
k
gas
→
surface
=
c
1
−θ
−θ
σ
P
B
a
A
B
max
B
i
i
Imposing equilibrium and using
(
i
=
A,B
) gives:
bcc
=
/
i
a
d
(
)
θ =
1
−θ −θ
bp
A
A
B
A
A
(
)
θ =
1
−θ −θ
bp
,
B
A
B
B
B
which gives the adsorption isotherms:
bp
bp
AA
θ=
+
A
1
+
bp
AA
BB
bp
bp
BB
θ=
B
1
+
+
bp
AA
BB
The importance of this result is that one can use the experimental data of the pure
component isotherms
i
b
σ
to predict the mixture isotherms. The assumption
that molecules compete for the same sites is often too simple and one needs to
use alternative approaches to predict the actual mixture isotherm. A particularly
popular one is IAST (Ideal Adsorbed Solution Theory) [6.3].
(,
)
max
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