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Heats of Adsorption of Pure SF6 and CO2 on Silicalite Pellets With Alumina Binder D. V. Cao and S. Sircar* Air Products and Chemicals, Inc., 7201 Hamilton Boulevard, Allentown, Pennsylvania 18195-1501
Isosteric heats of adsorption of pure SF6 and CO2 were calorimetrically measured on a sample of pelletized silicalite with alumina binder. The corresponding heats of adsorption on a sample of gamma alumina were also measured. The silicalite is a homogeneous adsorbent for these gases, but the presence of the binder in the pelletized silicalite sample introduces an energetic heterogeneity for adsorption of these gases. However, the heterogeneity is largely masked for adsorption of SF6, except in the region of very high coverage because it is only weakly adsorbed on the binder. The heterogeneity for adsorption of CO2 on the pelletized silicalite is more pronounced because it is very strongly adsorbed on the binder and the binder exhibits a high degree of heterogeneity for its adsorption. A thermodynamic model is presented for calculation of the isosteric heats of a gas on a composite adsorbent using its adsorption characteristics on the constituent materials. It is found that the slopes of the adsorption isotherms of the gas on the constituent materials play an important role in establishing the overall isosteric heat of adsorption of the gas on the composite material. of adsorption (q) as3
Introduction The isosteric heat of adsorption of a gas is an important variable for design of adsorption processes.1 It determines the local changes of adsorbent temperature inside an adsorber during the adsorption (desorption) process. The adsorbent temperature, in turn, defines the local adsorption equilibria and kinetics, which ultimately determine the separation performance of the adsorber. The isosteric heat of adsorption of a pure gas is not a function of adsorbate loading when the adsorbent is energetically homogeneous. On the other hand, the isosteric heat of adsorption decreases with increasing adsorbate loading when the adsorbent is energetically heterogeneous. The isosteric heat of adsorption can increase with increasing adsorbate loading at larger surface coverages if the lateral interactions between the adsorbed molecules are pronounced.2 The energetic heterogeneity of an adsorbent can be caused by a distribution of micro-meso pores of different sizes and shapes within its mass, as well as by a distribution of adsorption sites of different chemistry (polarity) within the pores. The energetic heterogeneity in a pelletized adsorbent can also be created by the presence of a binder material, even though the primary adsorbent itself is energetically homogeneous. This work reports a calorimetric study of the isosteric heats of adsorption of pure SF6 and CO2 on a pelletized sample of silicalite with alumina binder and provides a model for correlating the pure-gas isosteric heats on such adsorbents.
[ ]
q)-
δHo δnm
(1)
T
where Ho is the total enthalpy of a closed adsorption system containing a unit amount of an adsorbent and having a specific void volume of vo. The adsorbent is in equilibrium with the gas phase at pressure P and temperature T, and the equilibrium GSE of the gas under these conditions is nm. It can be shown from the thermodynamic analysis of the GSE model for the closed adsorption system that, for an ideal gas, one obtains3
q ) RT2
ln P [δ δT ]
nm
(2)
where R is the gas constant. Equations 1 and 2 represent very general definitions of the isosteric heat of adsorption of a pure ideal gas, and they can be conveniently used to describe the heat balance in adsorption columns.3 Thus, they are very practical. It follows from eq 2 that q can be estimated as functions of nm and T by measuring pure-gas GSE isotherms [nm vs P at constant T] at different temperatures. Alternatively, a calorimeter can be used to directly measure q as functions of nm for a given T.1 The second approach, which is often more accurate, will be employed in this work. Calorimetric Measurement of Isosteric Heat
Definition of Isosteric Heat of Adsorption The equilibrium Gibbsian surface excess (GSE) model for adsorption of a pure gas defines the isosteric heat * Author for correspondence.
A Tian-Calvet type heat flux microcalorimeter can be used to directly measure the pure-gas isosteric heats of adsorption. Figure 1a is a sketch of such a calorimeter cell, which is surrounded by thermopiles for directly measuring the heat flux through its walls. Figure 1b shows the schematic drawing of the thermostated
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∆Q ∆P -v( ( [ ∆N) ∆N)] q) [1 - RTv (∆N∆P)] o
o
(3)
o
where q is the isosteric heat of adsorption of the pure gas at Po and To, or nm and T, as defined by eqs 1 and 2. The equilibrium GSE of the gas at Po and To is nm. Equation 3 assumes that (a) the temperature of the gas entering the sample side of the calorimeter is always equal to To during the entire process [T(t) ) To] and (b) the experiment is carried out under a differential condition (∆N f small, P∞ f Po). Both of these conditions were satisfied by our experiments.1 It should be noted here that the above-described calorimeter can also be used as a conventional volumetric adsorption apparatus for measuring the GSE isotherm of the pure gas if the sample and dosage sides of the assembly are allowed to reach equilibrium during the process [Pdf ) P∞]. A mass balance, in that case, yields1
∆nm ) ∆N -
vo∆P RTo
(4)
Equation 4 shows that the change in the equilibrium GSE of the gas (∆nm) during the experiment can be estimated by measuring ∆N and ∆P. A cumulative set of differential adsorption experiments can be carried out to generate the entire pure-gas GSE isotherm using eq 4 and starting with a clean adsorbent [Po ) 0, nm ) 0]. Figure 1. Schematic drawings of (a) calorimeter cell and (b) calorimeter assembly.
calorimeter assembly. It consists of the calorimeter cell (sample side) connected to a gas holder (dosage side) through a valve. A known weight of the regenerated adsorbent sample is placed within the calorimeter cell and the specific void volumes of the sample (vo, cm3/g) and dosage (vd, cm3/g) sides of the assembly are measured by helium expansion. The sample side is then equilibrated with the pure adsorbate gas at pressure Po and temperature To, which is also the temperature of the thermostated bath. The dosage side is then filled with pure adsorbate gas at pressure Pdo (>Po), and a very small amount of the gas (∆N, mol/g) is slowly admitted into the sample side from the dosage side. The pressure of the dosage side at this point is Pdf. The valve is then closed. The temperature of the gas entering the sample side [T(t)] is continuously monitored during this process as a function of time (t). Eventually, the sample side reaches a new equilibrium state at pressure P∞ and temperature To. The total quantity of heat evolved (∆Q, cal/g) during the entire process is obtained by integration of the precalibrated thermopile output curve (voltage vs time). The change in the gas pressure of the sample side is given by ∆P ) (P∞ - Po). The total amount of adsorbate (ideal gas) introduced into the sample side is given by ∆N ) (Pdo - Pdf)vd/RTo. A more detailed description of the calorimeter design, the experimental procedure, and the thermopile calibration protocol can be found elsewhere.1 It can be shown, by combining the mass and heat balances for the above-described experiment, that1
Experimental Systems and Data The above-described microcalorimeter and experimental protocol were used to measure the pure-gas GSE isotherms and the isosteric heats of adsorption as functions of adsorbate loadings (GSE) of SF6 and CO2 at 305 K on (i) a commercial pelletized (1/8-in. diameter and 1/4-in. length) sample of silicalite (type SP 115 obtained from UOP Corporation) and (ii) a commercial beaded (1.93-mm diameter) sample of gamma alumina (type AA 300 obtained from Alcan Corporation). Each data set was repeated at least three times in order to verify its reproducibility. A chemical analysis of the bound silicalite sample indicated that it contained ∼19% (by weight) alumina as the binder.1 Both adsorbents were regenerated by heating under vacuum (10-3 µm) at 200 °C, and they were transferred to the calorimeter cell under dry N2 inside a glovebox. The adsorbents were then further subjected to vacuum (10-3 µm) for 1 h at the temperature of the experiment before the tests were conducted. The adsorbate gases [SF6 (99.99% pure) and CO2 (99.995% pure)] were supplied by Air Products and Chemicals, Inc. Table 1 lists some of the key properties of these two adsorbates. Figures 2 and 3, respectively, show the pure-gas adsorption isotherms on the pelletized silicalite and the beaded alumina samples. All isotherms are type I by the Brunauer classification.4 SF6 is more strongly adsorbed than CO2 on the silicalite sample, whereas CO2 is more strongly adsorbed than SF6 on the alumina sample. Figures 4 and 5 show the corresponding lowpressure isotherms (Henry’s law region) for the silicalite and alumina, respectively. They indicate that the isotherms are linear with a slope of unity when plotted as ln nm vs ln P in that region, as required. Table 2
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Table 1. Properties of the Adsorbates
adsorbates
molecular weight
liquida molar volume (cm3/mole)
SF6 CO2
146 44
72.74 33.32
a
permanent moments
kinetic diameter (Å)
polarizability (x 10-25 cm3)
dipole (x 1018 esu cm)
quadrupole (x 10-26 esu cm2)
5.13 3.3-3.9
65.4 26.5
0.0 0.0
0.0 4.3
At normal boiling point.
Figure 2. Adsorption isotherms of pure SF6 and CO2 on a pelletized silicalite sample at 305 K.
Figure 4. Adsorption isotherms of pure SF6 and CO2 on pelletized silicalite sample in the Henry’s law region at 305 K.
Figure 3. Adsorption isotherms of pure SF6 and CO2 on a sample of gamma alumina at 305 K.
Figure 5. Adsorption isotherms of pure SF6 and CO2 on gamma alumina sample in the Henry’s law region at 305 K. Table 2. Henry’s Law Constants
provides the relevant Henry’s law constants for these systems. It can be seen that SF6 is adsorbed on the alumina sample very weakly. Figures 6 and 7, respectively, show the calorimetrically measured isosteric heats of adsorption of the pure gases at 305 K on the silicalite and the alumina samples. They are plotted as functions of the equilibrium GSE (nm) of the adsorbates. The isosteric heat of adsorption of SF6 on the silicalite is practically independent of surface coverage (∼9.4 kcal/mol) over a large range of adsorbate loading (0 e nm < 1.4 mmol/g) and then it rapidly falls when the saturation adsorption capacity (nm ≈ 1.6 mmol/g) is approached. The isosteric heat of adsorption of SF6 on the alumina remains constant (∼4.8 kcal/mol) over the entire range of the data (0 e nm < 0.6 mmol/g). The isosteric heat of adsorption of CO2 on the silicalite decreases with increasing adsorbate loading before leveling off in the high coverage region (nm > 0.8 mmol/g). The limiting values of the isosteric heat for CO2 on the silicalite at zero surface coverage and at higher coverages are,
Ki (mmol g-1 atm-1) adsorbates
pelletized silicalite
gamma alumina
SF6 CO2
17.53 6.67
0.17 8.34
respectively, 9.5 and 6.0 kcal/mol. The isosteric heat of adsorption of CO2 on the alumina decreases (in a much more pronounced way than for the silicalite) with increasing coverage over the entire range of the data (0 e nm < 0.9 mmol/g). The isosteric heat at the limit of zero surface coverage, for this case, is ∼17.0 kcal/mol, and it decreases to a value of 6.5 kcal/mol when the adsorbate loading (nm) is ∼1.0 mmol/g. These data indicate that the adsorption of SF6 on both the silicalite and the alumina samples are energetically homogeneous except for the very high coverage region on the silicalite. On the other hand, the adsorption of CO2 on the silicalite is moderately heterogeneous, whereas that on the alumina is highly heterogeneous.
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Model for Pure-Gas Isosteric Heats of Adsorption on Heterogeneous Solids Consider an energetically heterogeneous adsorbent composed of k different patches (or materials). Each individual patch or material can be energetically homogeneous or heterogeneous. The total specific amount of a pure gas adsorbed (n, mol/g) on the composite adsorbent at pressure P and temperature T is given by
∑k Rknk, ∑k Rk ) 1
n)
Figure 6. Calorimetric isosteric heats of adsorption of pure SF6 and CO2 on pelletized silicalite sample.
(5)
where Rk is the weight fraction of the kth patch (or material) in the composite adsorbent and nk is the specific amount of gas adsorbed (mol/g) on that patch at P and T. The weight fraction can be conveniently used to quantify the size of a homogeneous patch when the adsorbent is composed of more than one material. The adsorption on patch k can be described in functional notation as
nk ) nk(P,T)
(6)
It follows from eq 6 that
dnk ) nkP dP + nkT dT nkP )
( )
(7)
( )
δnk δnk ,n ) δP T kT δT
P
(8)
Equation 7 can be differentiated with respect to T at constant value of nk to give Figure 7. Calorimetric isosteric heats of adsorption of pure SF6 and CO2 on gamma alumina sample.
The crystalline silicalite is a nonpolar, microporous adsorbent with practically no cation exchange capacity. Consequently, in a defect-free form, these crystals are expected to be physicochemically homogeneous for adsorption of SF6 and CO2. In fact, previous calorimetric measurements of isosteric heats of adsorption of pure CO2 and SF6 on a sample of unbound silicalite crystals showed that the heat of adsorption of CO2 remains practically independent of surface coverage and the heat of adsorption of SF6 slightly increases with increasing coverage.5 Thus, pure silicalite crystals are energetically homogeneous for adsorption of these gases. The alumina binder is an amorphous, polar material that exhibits very high energetic heterogeneity for adsorption of CO2 because of its large permanent quadrupole moment. Previously published data also depicts this behavior.6 The adsorption of nonpolar SF6 on the alumina is, however, remarkably homogeneous. The presence of the alumina binder in the pelletized sample of silicalite used in this work introduces a moderate degree of heterogeneity for the adsorption of CO2 because CO2 is very strongly adsorbed on the binder. On the other hand, the heterogeneity introduced by the binder for SF6 adsorption on the pelletized silicalite sample is masked because the adsorption of SF6 on the binder is relatively weak (Figure 3). The following section proposes a simple thermodynamic model for describing the observed behavior of the isosteric heats on bound adsorbents.
Pqk
nkT ) -
nkP RT2
(9)
where qk is the isosteric heat of adsorption of the pure gas on the kth patch at P and T (or nk and T).
ln P (δ δT )
qk ) RT2
nk
(10)
Equation 5 can be differentiated with respect to T at a constant value of n to give
∑k
( )
Rk
δnk δT
)0
(11)
n
Equation 7 can be differentiated with respect to T at a constant value of n to give
( ) δnk δT
n
)
PnkP (q - qk) RT2
(12)
where q is the isosteric heat of adsorption of the pure gas on the composite adsorbent at P and T (or n and T).
q ) RT2‚
ln P (δ δT )
n
Equations 11 and 12 can be combined to give
(13)
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q)
∑k RknkPqk ∑k RknkP
(14)
Equation 14 shows how the isosteric heat of adsorption of the pure gas at P and T on a composite adsorbent is related to the isosteric heats of adsorption of the same gas on the constituent patches (or materials) at P and T. A very interesting feature revealed by eq 14 is that the adsorption isotherm slopes (nkP) of the gas on the constituent patches at P and T are required to estimate q. It should also be noted from eq 5 that the denominator of eq 14 is equal to the slope of the adsorption isotherm of the gas on the composite adsorbent [∑kRk‚nkP ) (δn/ δP)T]. It follows from eqs 5 and 14 that, in the Henry’s law region, where the adsorption isotherms are linear [n ) KP, nk ) KkP], one has
K)
qo )
∑k RkKk
∑k RkKkqok ∑k RkKk
(15)
(16)
where K and Kk are the Henry’s law constants for the pure gas on the composite adsorbent and the constituent kth patch, respectively. The variables qo and qok are the isosteric heats of adsorption of the pure gas in the Henry’s law region on the composite adsorbent and on the kth patch, respectively. For the special case of an adsorbent composed of only two patches (k ) 1, 2), eq 14 simplifies to
q ) q1 - (q1 - q2)β
(17)
R2n2P R1n1P + R2n2P
(18)
β)
The value of the parameter β as a function of P and T will depend on the characteristics of the adsorption isotherms (homogeneous or heterogeneous) on the two patches. Consequently, q will vary with P and T (or n and T). Assuming that patch 1 has a higher isosteric heat of adsorption than patch 2 (q1 > q2) at any P and T, and recognizing that β(g 0) is a positive quantity, eq 17 shows that q will decrease with increasing P (or n). Masking of Heterogeneity When the gas is adsorbed much more strongly on patch 1 than on patch 2 (q1 > q2, K1 . K2), it can be shown that the value of β is very small over a large range of P (or n). Consequently, eq 17 shows that q ≈ q1 over that range of n. Thus, the isosteric heat of adsorption on the composite adsorbent is approximately equal to the value for patch 1 in that range of n, even though there are patches of lower energy in the composite material. Furthermore, if patch 1 is energetically homogeneous (constant q1), then q on the composite adsorbent also appears to be independent of adsorbate
loading over a large range of n. Hence, the true adsorbent heterogeneity of the adsorbent is masked in that case. This behavior can be simply demonstrated by considering an adsorbent composed of two different homogeneous Langmuirian patches (or materials) so that
nk )
mkbkP , bk ) bok exp(qk/RT), Kk ) mkbk (19) 1 + bkP
where mk and bk are, respectively, the saturation adsorption capacity for the gas and the gas-solid interaction parameter at T on the kth patch (k ) 1, 2). The variables bok are constants. Equations 18 and 19 can be combined to give
β)
R2K2 1 + b2P R2K2 + R1K1 1 + b1P
(
)
2
(20)
Equation 20 shows that, when patch 1 adsorbs the gas much more strongly than patch 2 [b1 . b2], the value of the parameter β approaches zero and unity at the limits of P f 0 and P f ∞, respectively. Thus, q approaches q1 and q2, respectively, at these two limits. Furthermore, eq 20 shows that β is very small for a large range of P (or n) values before it approaches unity very rapidly as Pf ∞. Consequently, q is approximately equal to q1 (constant) over a large range of adsorbate loadings before it decreases to q2 as P f ∞, and the adsorbent heterogeneity is masked. It should be noted that the term adsorbate loading (n or nk) used in the above section actually refers to the GSE of the adsorbate. Isosteric Heats of Adsorption of SF6 and CO2 on Pelletized Silicalite The pelletized silicalite sample of the present work can be considered to be composed of the silicalite crystals (patch 1, R1 ) 0.81) and the alumina binder (patch 2, R2 ) 0.19). Both patches are homogeneous for adsorption of SF6, whereas CO2 adsorption is homogeneous on patch 1 and heterogeneous on patch 2. We measured the isosteric heats of adsorption and the puregas adsorption isotherms at 305K for both SF6 and CO2 on the composite adsorbent (Figures 2, 4, and 6) and on the binder material (Figures 3, 5, and 7). Equation 5 can then be used to estimate the pure-gas adsorption isotherms on the silicalite crystals (patch 1), as shown by Figure 8 (points). The isotherms of Figure 8 can be adequately described (solid lines) by the homogeneous multisite Langmuir (MSL) model of Honig7 and Nitta8 using the parameters of Table 3. The MSL model is given below
bP )
θ , b ) bo exp(q/RT), θ ) n/m (1 - θ)a
(21)
where n is the specific amount of gas adsorbed at P and T. The corresponding fractional surface coverage is given by θ. The variables m and a are, respectively, the saturation adsorption capacity of the gas and the number of adsorption sites occupied by each gas molecule on the surface. The gas-solid interaction parameter for the model is given by b, which is an exponential function of T. Thermodynamic consistency of the MSL
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pellets. The exact physicochemical nature of the alumina binder in the silicalite pellets might also be somewhat different from that of the alumina sample selected in this work to represent the binder. A key conclusion from the present study, however, is that the adsorption characteristics (isotherms and heats) of the gases on the composite material can be described by measuring them independently on the constituent materials and invoking simplified thermodynamic models. Summary
Figure 8. Estimated adsorption isotherms of pure SF6 and CO2 on silicalite crystals at 305 K. Solid line is best fit by multisite Langmuir model (MSL). Table 3. Parameters of the MSL Model adsorbates
m (mmol/g)
a
b (atm-1)
SF6 CO2
3.06 3.60
3.53 3.00
9.15 1.75
model requires that the constraint ma ) constant be obeyed for different gases,9 and the constraint was used in data fitting. The ability of the MSL model to describe SF6 and CO2 adsorption isotherms on the silicalite crystals suggests that the zeolite is indeed energetically homogeneous for adsorption of these gases. We then used the adsorption isotherms of Figure 8 (patch 1) and those given by Figure 3 (patch 2) to calculate the isosteric heats of adsorption on the composite adsorbent using eqs 17 and 18. The solid lines of Figure 9 (a and b) compare the calculated isosteric heats with the experimentally measured values (squares). It can be seen from Figure 9a that the proposed model describes the isosteric heat of adsorption of SF6 on the composite adsorbent remarkably well and illustrates the phenomenon of heterogeneity masking due to weak adsorption of SF6 on the binder. The model also describes the isosteric heat of adsorption of CO2 on the composite material fairly well (Figure 9b), demonstrating the creation of heterogeneity on the composite adsorbent because of the strong adsorption of CO2 on the binder. It should be pointed out here that there might be some uncertainty in estimating the exact weight fraction of the binder material in the silicalite
A microcalorimeter was used to directly measure the isosteric heats of adsorption of pure SF6 and CO2 as functions of adsorbate loadings on a sample of pelletized silicalite with alumina binder and on a sample of gamma alumina at 305K. The isosteric heat of adsorption of SF6 on the pelletized silicalite remained constant over a large range of adsorbate loading, and then it decreased rapidly as the adsorbate saturation capacity was approached. The heat of adsorption of SF6 on the alumina remained constant over the entire range of the data. The isosteric heat of adsorption of CO2 on both adsorbents decreased with increased adsorbate loading. This effect was much more pronounced on the alumina. These data indicate that the energetic heterogeneity introduced by the presence of alumina binder in the otherwise homogeneous silicalite crystals was masked for adsorption of SF6 on the pelletized silicalite sample except at very high surface coverage, because of its weak adsorption on the binder material. On the other hand, the strong adsorption of CO2 on alumina binder created a significant heterogeneity for its adsorption on the pelletized zeolite. A simple thermodynamic model is presented to calculate the isosteric heat of adsorption of a gas on an adsorbent composed of different patches or materials, which can be individually homogeneous or heterogeneous energetically. The model reveals that the slopes of the adsorption isotherms of the gas on constituent patches or materials form key variables in establishing the heat of adsorption of the gas on the composite material. The model described the experimental heat data for SF6 and CO2 on the bound silicalite sample fairly well. The adsorption isotherms of pure SF6 and CO2 on the alumina and pelletized silicalite samples at 305K were also measured by using the calorimeter as a volumetric adsorption apparatus.
Figure 9. Model description of pure-gas isosteric heats of adsorption of (a) SF6 and (b) CO2 on pelletized silicalite.
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Acknowledgment The authors are grateful to Ms. B. Messersmith for measuring some of the heat data presented in this work. Literature Cited (1) Sircar, S.; Mohr, R.; Ristic, C.; Rao, M. B. Isosteric Heat of Adsorption: Theory and Experiment. J. Phys. Chem. B 1999, 103, 6539. (2) Sircar, S.; Rao, M. B. Heat of Adsorption of Pure Gas and Multicomponent Gas Mixtures in Microporous Adsorbents. In Surfaces of Nanoparticles in Porous Materials; Schwarz, J. A., Contescu, C., Eds.; Marcel and Dekker: New York, 1999. (3) Sircar, S. Gibbsian Surface Excess for Gas Adsorptions Revisited. Ind. Eng. Chem. Res. 1999, 38, 3670. (4) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: Washington, D.C., 1992. (5) Dunne, J. A.; Mariwala, R.; Rao, M. B.; Sircar, S.; Gorte, R. J.; Myers, A. L. Calorimetric Heats of Adsorption and Adsorption
Isotherms I: O2, N2, Ar, CO2, CH4, C2H6, and SF6 on Silicalite. Langmuir 1996, 12, 5888. (6) Rosynek, M. P. Isotherms and Energetics of Carbon Dioxide Adsorption on Gamma-Alumina. J. Phys. Chem. 1975, 79, 1280. (7) Honig, J. M. Adsorption Theory from the Viewpoint of Order-Disorder Theory, Gas Solid Interface; Flood, E. A., Ed.; Marcel and Dekker: New York, 1966. (8) Nitta, T.; Shigetomi, T.; Kuro-oka, M.; Katayama, T. An Adsorption Isotherm of Multisite Occupancy Model for Homogeneous Surface. J. Chem. Eng. Jpn. 1984, 17, 39. (9) Rao, M. B.; Sircar, S. Thermodynamic Consistency for Binary Gas Adsorption Equilibria. Langmuir 1999, 15, 7258.
Received for review July 11, 2000 Revised manuscript received October 17, 2000 Accepted October 19, 2000 IE000650B
