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4.10 Multiphase Systems 147

mole fraction in the adsorbate. For the propylene-propane
mixture, propylene is adsorbed more strongly. For example,
for an equimolar mixture in the gas phase, the adsorbate con-
-
tains only 27 mol% propane. Figure 4.30b combines the data
- for the equilibrium mole fractions in the gas and adsorbate
with the amount of adsorbate per unit of adsorbent. The
- mole fractions are obtained by reading the abscissa at the
two ends of a tie line. For example, for equilibrium with
yp = y* = 0.50, Figure 4.30b gives xp = 3E* = 0.27 and
2.08 mmol of adsorbatelg adsorbent. Therefore, y~ = 0.50,
and XA = 0.73. The separation factor analogous to the rela-
tive volatility for distillation is

= 2 mmol = I mmol
ZF = PI (A + P) = 0.5 y*=Pl(P+A) -
This value is much higher than the a-value for distillation,
which, from Figure 2.8, at 25°C and 1,100 kPa is only 1.13.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Accordingly, the separation of propylene and propane by
Mole fraction propane in adsorbate, x
adsorption has received some attention. Equilibrium calcula-
(a) tions using data such as that shown in Figure 4.30 are made
2.4 in the usual manner by combining such data with material-
balance equations, as illustrated in the following example.

Propylene (A) and propane (P), are to be separated by preferential
adsorption on silica gel (S) at 25°C and 101 Ha.
Two millimoles of a gas containing 50 mol% P and 50 mol%
A is equilibrated with silica gel at 25OC and 101 Wa. Manometric
measurements show that 1 mmol of gas is adsorbed. If the data of
Figure 4.30 apply, what is the mole fraction of propane in the equi-
librium gas and adsorbate, and how many grams of silica gel are
used?

1.5 SOLUTZON
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Mole fraction propane in adsorbate, y, x A pictorial representation of the process is included in Figure 4.30a,
where W = millimoles of adsorbate, G = millimoles of gas leaving,
(b)
and ZF = mole fraction of propane in the feed.
Figure 4.30 Adsorption equilibrium at 25OC and 101 Wa of
The propane mole balance is
propane and propylene on silica gel.
[Adapted from W.K. Lewis, E.R. Gilliland, B. Chertow, and W. H.
Hoffman, J. Am. Chem. Soc., 72,1153 (1950).]
With F = 2, ZF = 0.5, W = 1, and G = F - W = 1, Eq. (1) be-
comes 1 = x* + y*.
The operating (material-balance) line y* = 1 - n* is the locus
of adsorption is to separate these two components, other of all solutions of the material-balance equation, and is shown
methods of representing the experimental data may be pre- in Figure 4.30a. It intersects the equilibrium curve at x* = 0.365,
ferred. One such representation is shown in Figure 4.30, y* = 0.635. From Figure 4.30b, at the point x*, there must be
from the data of Lewis et al. [15], for the adsorption of a 2.0 mmol adsorbatelg adsorbent; therefore there are 1.012 = 0.50 g
propane (P)-propylene (A) gas mixture with silica gel at 25OC of silica gel in the system.
and 101 kPa. At 25"C, a pressure of at least 1,000 kPa is
required to initiate condensation (dew point) of a mixture of
propylene and propane. However, in the presence of silica 4.10 MULTIPHASE SYSTEMS
gel, significant amounts of the gas are adsorbed at 101 kPa.
Figure 4.30a is similar to a binary vapor-liquid equilib- In previous sections of this chapter, only two phases were
rium plot of the type discussed in Section 4.2. For adsorption considered to be in equilibrium. In some applications of mul-
equilibria, the liquid-phase mole fraction is replaced by the tiphase systems, three or more phases coexist. Figure 4.31