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288 4. Adsorption and Ion Exchange

It is obvious that the best fit is gien by the reaction kinetic control equation. The slope v
of the line is 2 10 5 L/mg min. Then,
bk 5

210
Bo r
In this equation, b 2 and

q max p 457.84 10 mg/L 3
B

and
21 5 r
0
k Bo 2.52 mm/min
2
Other simplified models for adsorption and ion e hang xc e

The following models hae been mainly used in liquid-phase adsorption and biosorption v
and, in some cases, for ion-exchange systems with inorganic ion exchangers (Rengaraj
et al ., 2004; Bektas and Kara, 2004).

First-order adsorption kinetics model A simple first-order reaction model is based on
v
a reersible reaction with equilibrium state being established between two phases (A—
fluid, B—solid):
A
B

The kinetic rate in differential form and its analytical solution can be expressed as
d C d C
B A kC k C
d t d t 1 A 2 B (4.94)

ln 1 Ut () (4.95)
t
k
where U ( t ) is the fractional attainment of equilibrium, k the reaction constant in s 1 , and t
the time in s.

en’
Pseudo-first-order kinetic model (Lagers rate equation) In this model, the
gr
kinetic rate in differential form and its analytical solution can be expressed as
d q
t ( kq q ) (4.96)
d t e t

k
e (
log q ) t log ( ) e t (4.97)
q
q
2.303