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298 4. Adsorption and Ion Exchange

volume of solution was 0.1 L, and the mass of zeolite used w as 2 g. The zeolite properties
,
were: particle size, 1–3 mm; porosity 0.325; and solid density 2.12 (g/cm , 3 ). The equilib-
rium followed the Langmuir isotherm with Q M 14.91 mg/g and K 0.0434 L/mg.
Some experimental kinetic data are gi able 4.21 (approximate v alues). T v en in
Meshko et al . (2001) used a homogeneous solid model taking into account both inter-
The fusion. nal and external dify found that the adsorption of the dye had not been signif i-
cantly affected by the agitation speed, which indicated that the process was solid
diffusion–controlled. Furthermore, for the specified conditions, they found that k 6.66
f
10 –5 m/s and D s =10 12 m 2 /s.
atterson’ Use Ps equation to model the kinetic data. Furthermore, propose a design for
the agitated batch reactor .

Solution
Kinetics and equilibrium analysis To use Ps model (eq. (4.52)), we first need the atterson’
parameter w , and thus the equilibrium liquid-phase concentration C . The maximum load- e
ing of the zeolite particles for the specific initial concentration can be calculated by means
of the equilibrium relationship (eq. (4.5)):

KC o
q max Q M 12.12 mg/g
1 KC o

Then using eq. (4.123),

fX() C o V
0.413
1 X q max m

The function f ( X ) is the dimensionless equilibrium relationship, which for the Langmuir
isotherm is (eq. (4.9))

X
fX() 0.413 1 X

La X 1
La

Table 4.21
Experimental data
t (min) q (mg/g)
t
15 1
30 1.2
60 1.6
120 2.1
180 2.5