1218 VAPOR AND GASEOUS POLLUTANT FUNDAMENTALS

Amount adsorbed

Amount adsorbed

p p

p p p

II III

IV V

I

FIGURE 4 Types of adsorption isotherms.

the equilibrium adsorption concentration, C, is obtained in

terms of the gas phase concentration C 1 and the total adsorp-

tion site concentration, C 0

C

C

K C

0 K C

1 1

(^1) 1 1


.
(8)
Here, K 1 is the adsorption equilibrium constant which varies
only if temperature varies.
Diatomic molecules such as chlorine might be expected
to simultaneously adsorb and dissociate on adjacent sites.
Such an adsorption might be described symbolically by
A X X
k
k
1 2 2 0 1
1
1
 �
−
in which case the equilibrium isotherm expression can readily
be shown to be
C
C
K C
0 K C
1 1
1 2
1 1
 1  1 2
( )
( )
.
/
/
(9)
If more than one pollutant is being adsorbed, each compo-
nent, Aj, undergoes
A X Xj+^0 � j.
The equilibrium for single site adsorption of component Aj
becomes
C
C
K C
K Cj j
j
n
0
1 1
1
1



∑
.
(10)
The latter may be referred to as competitive adsorption.
Figure 5 depicts the different dependence on gas phase con-
centration for the adsorption types described thus far.
Another isotherm finding wide use, particularly in multi-
layer adsorption, is that of Brunauer, Emmett and Teller (1938),
the BET equation
C
C
Q X
X Q X
s
max ( )[ ( ) ]

  
2
1 1 2 1
(11)
in which:
Cs, Cmax—amount of gas absorbed per gm. of solid,
and maximum amount, respectively
Q 2 —term exponentially dependent on heat of
adsorption
X—ratio of equilibrium gas phase concentration of
saturation Value.
If neither the Langmuir or BET equations are satisfactory,
a plynomial fit to adsorption data may be required.
C022_001_r03.indd 1218 11/18/2005 2:32:43 PM