Environmental Engineering Reference
In-Depth Information
through Lagergren's first order rate equation [84], with an understanding
that initially there is no adsorbate present on the surface of the adsorbent.
Thus, by assuming the dye molecule is a non-dissociating substance the
sorption phenomenon is treated as the diffusion controlled process [85].
Therefore for the adsorption of small amount of the adsorbate (dq) over
a small period of time (dt), the rate of reaction can be calculated using
expressions:
dq
dt
)
(11.12)
(
qq
e
t
dq
dt
)
(11.13)
or
kq q
ad
(
e
t
where q
e
and q
t
(mol.g
-1
) denote the amount adsorbed at equilibrium
and at any time t respectively and k
ad
(s
-1
) is the first order rate constant of
adsorption. By integrating the Equation 11.13 with the boundary condi-
tions q
t
= 0 at t = 0 to q
t
= q
t
at t = t, we get the following linear form of the
Lagergren's pseudo-first-order kinetics [86]:
k
(11.14)
ad
2 303
log (
qq
)
log
q
t
e
t
e
.
Thus, by plotting a graph between log (q
e
-q
t
) versus time (t) a straight
line is obtained with the intercept on y-axes providing the value of log q
e
and slop giving value of the rate constant (k
ad
).
11.6.1.3
Elucidation of Reaction Mechanism
A survey of literature reveals that for the proper interpretation of the exper-
imental data, it is essential to identify the steps in the adsorption process
which govern the overall removal rate in each case. To identify whether
the ongoing process is particle diffusion or film diffusion, the kinetic data
obtained by finite batch method has been treated by an ingenious math-
ematical treatment suggested by Boyd
et al.
[87] and Reichenberg [88].
It is considered that the adsorption of an organic/inorganic compound
over a porous adsorbent normally involves the following three steps:
i. Film diffusion mechanism, in which transport of the ingo-
ing ions (adsorbate) to the external surface of the adsorbent
takes place.
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