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4.2 Design of Adsorption and Ion-Exchange Processes 273

the objective is generally to remoe a little amount of a pollutant from a gaseous or liquid v
, stream, and thus, the o w v ery lo en if the heat per mole of adsorbed e v erall heat released is v
species is considerable, due to the low number of moles remo ed. v
In the follo two general cases are considered: wing,

• adsorption under conditions of constant or nearly constant solution concentration
(infinite solution volume), and
• adsorption in batch with finite volume (finite solution v olume).

In the adsorption in batch (second case), the concentration of the fluid varies from its
initial to the equilibrium concentration. The partition ratio is used to discriminate between
these two cases, which for the case of the solid phase initially free from the solute, is
defined as (Perry and Green, 1999; Ruthv 1984) en,

qM C C
w e s o e (4.33)
CV oo C o

where:
q e the equilibrium concentration expressed in solid phase in mass of solute
per mass of the solid
M s the mass of the solid
C o the fluid-phase initial concentration
C e the equilibrium fluid-phase concentration
V o the volume of the fluid phase.
Generally, when w
0.1, solutions for the second case are required.
xchange,
In the case of ion e this ratio is somewhat differently defined (Helf ferich,
1962):

QM
w M s (4.34)
CV oo

Then,

• for w 1, we hae the infinite solution volume condition and v
• for w 1, we hae the finite solution volume condition v

Here, Q M represents the REC per unit mass of solid. Helfferich uses the total concen-
tration of ions in equivalents for both phases. ference is due to the dif This dif ferent nature
of adsorption and ion exchange. In ion e the concentration in equialents in both xchange, v
phases is constant throughout the process (stoichiometric phenomenon). On the other
hand, in adsorption this is not the case. This is why in ion e the total amount in xchange,
equivalents in the solid phase Q M is used, whereas in adsorption the equilibrium uptak e q e
is used.