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296 4. Adsorption and Ion Exchange

(b) Its accessibility to the incoming species : Accessibility is used to express the ease of
movement of the species within the solid phase to reach the available site. It is closely
fusion coef connected to the kinetic behavior (dificients) of the system. f

Here, it has to be noted that the a and accessibility depend not only on the char- v ailability
acteristics of the site but also on the nature of the incoming species. wn in rele As sho ant v
experiments, a site can be aailable for the incoming species but may not be easily acces- v
sible to them and vice v ersa.
Design of a batch reactor system for adsorption and ion e xc hang e

Suppose that the system obeys the following equilibrium equation:

Y ()
f X
(4.118)
This is a general type of adsorption isotherm. In the case of ion e it is easy to xchange,
correlate data in a way to hae the same type of relationship for the ion that is remo v ed v
from the liquid phase. When equilibrium is reached,

q
Y e q e Yq max (4.119)
q max

and

C
X e C e XC o (4.120)
C o

where C o is in mg/L and q max is in mg/g. Here, q max is the solid-phase concentration in equi-
librium with C o for adsorption or the MEL in ion exchange. Using the equilibrium rela-
tionship (eq. (4.118)):

q e Yq max f X q () max (4.121)

v erall Applying an o material balance in the batch reactor and using eq. (4.120),

(
)
qm e C ( C V C ) e XC V o X C V) o (1 o (4.122)
o
where V is the vand olume of the fluid in L m the mass of the solid phase in g. equat- Then,
ing (4.121) and (4.122), we ha e v

V q max fX()
(4.123)
m C o 1 X