Page 37 - Adsorbents - fundamentals and applications

22 SORBENT SELECTION: CRITERIA

3.1.3. Ideal Adsorbed Solution Theory for Mixture and Similarities
with Langmuir and Potential Theories

The ideal adsorbed solution (IAS) theory of Myers and Prausnitz (1965) was
the first major theory for predicting mixed gas adsorption from pure component
isotherms, and it remains the most widely accepted. There have been approxi-
mately a dozen other theories that have been discussed in Yang (1987); however,
they are not repeated here.
The adsorbed mixture is treated as a two-dimensional phase. From the Gibbs
isotherm, one can calculate a spreading pressure for each component based on
its pure component isotherm. The basic assumption of the IAS theory is that the
spreading pressures are equal for all components at equilibrium.
The spreading pressure, π, is given by:

πA P q
= dP (3.13)
RT 0 P

where q is related to P by any pure component isotherm. Assuming the activity
coefficients are unity for all components in the adsorbed mixture, the IAS model
consists of the following set of equations, for a two-component mixture:

P 0 P 0
1 q 1 2 q 2
dP = dP (3.14)
P P
0 0
The Raoult’s law, or Eq. 3.15, is written for both species:
0
PY 1 = P X 1 (3.15)
1
0
0
PY 2 = P X 2 = P (1 − X 1 ) (3.16)
2
2
0
where P is the equilibrium “vapor pressure” for pure i adsorption at the same
i
spreading pressure, π,and the same T as the adsorbed mixture. These three
equations (Eqs. 3.14, 3.15, and 3.16) define the adsorbed mixture. For example,
if P and Y 1 (and Y 2 ) are given (T is already given), the three equations are solved
0
0
for P , P ,and X 1 . Equation 3.14 can be integrated to yield an algebraic equation
1 2
if the isotherms have certain forms like Langmuir and Freundlich equations.
0 0
Otherwise, Eq. 3.14 is solved numerically. With the values of P , P ,and X 1
1 2
determined, the following equations are used to calculate q 1 , q 2 ,and q t :
1 X 1 X 2
= 0 + 0 (3.17)
q 1 (P ) q 2 (P )
q t
1 2
(3.18)
q 1 = q t X 1 and q 2 = q t X 2
For systems following the Langmuir isotherm, the IAS theory is identical to
the extended Langmuir equation for mixtures, if the saturated amounts are equal