Page 60 - Adsorption Technology & Design, Elsevier (1998)

Fundamentals of adsorption equilibria 57

mixtures compared with predictions made employing 'single-component
adsorption data and applying the method of Grant and Manes.

3.4.4 Ideal adsorbed solution (IAS) model

Equilibrium between the adsorbed phase and the gas or vapour phase
requires the chemical potentials in each phase to be equal. If p0 (a function
of spreading pressure), denoted p0/ (tr), is the saturated vapour pressure
exerted by component i in its pure state at the same temperature and
spreading pressure of the adsorbed state and xi is the mole fraction of i in the
adsorbed phase, then the pressure p~ exerted by component i in the mixture
is
pi'-p 0 (l[)Xi (3.38)

which is equivalent to Raoult's law for ideal liquid-vapour systems. If the
mole fraction of i in the vapour phase is yi and the total pressure is P, then the
equilibrium conditions between component i in the adsorbed phase and the
same component i in the vapour phase requires
yiP=p ~ (if) X/ (3.39)

For equal spreading pressures in a mixture the condition/t'i = ff] = ffmix must
be obeyed. Thus from equation (3.28) (which gives the spreading pressure tr
in terms of the moles adsorbed), for a mixture composed of components i
and j we can write

p~
7rA/R T = ~ n o (p)d lnp = f n o (p)d In p
(3.40)
0 0
where n o (p) is the isotherm for the pure component i and n~ (p) is the
isotherm for pure j. The above two equations are subject to the conditions
~,x~ = Zyi = 1 and define the adsorbed mixture. Assuming the total
pressure P and mole fraction y~ of component i in the vapour phase are
known, then the calculation procedure for a binary mixture would be to find
p~l, p~2 and xl from the three equations (3.38), (3.39) and (3.40). The
integrals in (3.40) may be evaluated numerically provided the form of the
pure component isotherms n~ or equivalently q0(p), are known. Once
values of p~ p~ and xt have been found, nt and n2 may be calculated. A
similar procedure would be followed for a multicomponent mixture. Figure
3.11 is a comparison of experimental data, determined by Szepesy and Illes
(1963), with mixture isotherms computed from single-component isotherm
data.