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4.2 Design of Adsorption and Ion-Exchange Processes 285

Ash (solid) diffusion contr ol

t
6 bD
2/3
s
1 3 (1 ) X (1 2 ) 2 ∫ C d t
X
B B A
Bo r 0
(4.91)
where D s is the efve diffusion coefficient of fluid phase reactant in the solid (ash). fecti
Reaction kinetics contr ol
t
bk
1/3
1
1( X ) B d C A ∫ t
Bo r 0 (4.92)
where k is the first-order rate constant for the surface reaction.
All these equations could be viewed as linear:

t
fX ( B ) S C t d A ∫
0 (4.93)

where the slope S and the function f ( X B ) are different for each controlling mechanism.

Example 1
Inglezakis et al . (2003) studied the removal of Pb 2 (500 ppm) in a batch system using the
TP-207, atit w chelating resin Le under rigorous agitation (650 rpm) and ambient tempera-
ture (30 °C). The ion-exchange process is followed by an irreersible reaction in the resin v
phase, represented by the follo wing scheme:

2
R Pb R Pb 2
N
a
2Na
where R is the organic resin. The volume of the liquid is 350 cm 3 and the mass of dry
resin used is 0.6 g. The capacity of the resin is experimentally found to be 388 mg Pb/g
of dry resin. The density of the resin particles is 1.18 g/cm 3 and the mean particle radius
is 0.55 mm. By using the kinetic data of T find the controlling mechanism and
able 4.17,
Table 4.17

Experimental data (approximate v alues)
t (min) C (ppm)
t
5 383
10 325
15 275
25 213
45 138
60 91