APPLIED THERMODYNAMICS SYMPOSIUM
ALAN 1. MYERS
ADSORPTION OF GAS MIXTURES A Therrnodynarn ic Approach Mixture adsorption data can be predicted with accuracy from experimental adsorption isotherms of the pure gases
he monograph of Young and Crowell (20) contains T an excellent summary of the literature on the adsorption of gas mixtures up to about 1959.
The intent here is to describe several recent developments on this subject. A workable statistical mechanical model of physical adsorption is not yet available. Indeed, an improved empirical equation for the adsorption isotherm of a pure gas would make a welcome addition to the literature. It will be shown, however, that mixture adsorption data can be predicted with good accuracy if the experimental adsorption isotherms for the pure gases are available. Thaory
The thermodynamics of physical adsorption has been uiscussed in previous work (74). The basic differentia1 equation for the adsorbed phase is:
dU = TdS
- TdA + &dn,
(1)
Strictly, Equation 1 should contain a PdV work term, but it can be shown that for cases of practical interest the PdV term is negligibly small. The analogous equation for a liquid phase is:
dU = TaS
- PdV
+ &ini
(2)
The only difference between Equations 1 and 2 lies in the intensive variables (r and P ) and the extensive variables ( A and V ) of the work term. The same useful analogy applies to all of the thermodynamic equations. Therefore a formal development of the thermodynamics of adsorption is unnecessary. Although the thermodynamic equations for an adsorbed phase are analogous to those for a liquid phase, there is an important difference. The pressure, P, can be determined by means of direct macroscopic measurements, whereas the spreading pressure, I,must be determined indirectly. The reason for this distinction is that an adsorbed solution, unlike a liquid solution, is not of macrosopic dimensions. Fortunately the spreading pressure can be derived from macroscopically measured quantities. The isothermal Gibbs adsorption isotherm is:
Adr =
En&,
(3)
Equation 3 is analogous to the familiar isothermal Gibbs-Duhem equation for a liquid phase. For the case of a pure adsorbate, Equation 3 reduces to:
Adr = ndp = nRTd In f
(4) The pressure is nearly always small enough to permit the replacement of the fugacity of the gas by the pressure; with this assumption Equation 4 simplifies to:
Ad7 = nRTd vni
In P
6 0 NO. 5 M A Y 1 9 6 8
(5) 45
Integration of Equation 5 at constant temperature yields the spreading pressure : TA
RT = -
sop
and 1116s (75, 76). The spreading pressure for these adsorbates is calculated by means of Equation 6; the result of the integration is shown on Figure 2. The vapor pressures of the pure adsorbates are obtained directly from Figure 2. For n A / R T = 100 cc. STP/g. :
;dP
Equation 6 shows that the spreading pressure may be calculated from the experimental adsorption isotherm.
PIO = 1280 mm. Hg
The Ideal Adsorbed Solution
P20
The basic expressions for the ideal adsorbed solution can be written intuitively by appealing to the analogy between adsorbed solutions and liquid solutions. For the case of an ideal liquid solution, Raoult’s law for component i is: Pyi = P{OX, (71 P
