J. Phys. Chem. B 1999, 103, 6539-6546
6539
Isosteric Heat of Adsorption: Theory and Experiment S. Sircar,* R. Mohr, C. Ristic,† and M. B. Rao Air Products and Chemicals, Inc., 7201 Hamilton BouleVard, Allentown, PennsylVania 18195-1501 ReceiVed: February 2, 1999; In Final Form: May 24, 1999
The isosteric heats of adsorption of the components of a gas mixture are critical variables for design of adsorbers for gas separation. They can be unambiguously defined by the Gibbsian Surface Excess (GSE) model of multicomponent adsorption. These variables can be experimentally measured by multicomponent differential calorimetry (MDC) and directly used to describe nonisothermal behavior of practical adsorbers. There is no need to make simplified assumptions about the nature and size of the adsorbed phase, as required by conventional adsorption thermodynamic models, to define the isosteric heats. Pure gas isosteric heats of adsorption of N2 and CO2 on a pelletized silicalite sample were measured using a MDC and a data analysis algorithm based on the GSE model. The silicalite sample behaved like a homogeneous adsorbent for weakly polar N2 adsorption. The presence of polar alumina binder in the silicalite sample introduced significant heterogeneity for more polar CO2 adsorption.
Introduction The isosteric heats of adsorption of the components of a gas mixture are key thermodynamic variables for design of practical gas separation processes such as pressure swing and thermal swing adsorption.1,2 They determine the extents of adsorbent temperature changes within the adsorber during the adsorption (exothermic) and desorption (endothermic) steps of the processes. The adsorbent temperature is a key variable in determining the local adsorption equilibria and kinetics on the adsorbent, which ultimately govern the separation performance of the processes. Although many different types of differential and integral heats of adsorption have been defined in the adsorption literature,3-6,8,9 the differential isosteric heats of adsorption are found to be most useful for practical design of adsorbers.8,9 They can be (a) unambiguously defined using the Gibbsian Surface Excess (GSE) model of multicomponent adsorption system, (b) directly measured calorimetrically or indirectly estimated from multicomponent adsorption equilibrium data, and (c) conveniently used to describe heat balance using the transient GSE model of batch or flow adsorbers.8-10 The purpose of this work is to (a) review the thermodynamic definitions of multicomponent isosteric heats of adsorption and their use in process design under the framework of the GSE model,7-9 (b) discuss limitations of the conventional definition of isosteric heats of adsorption using actual amounts adsorbed as variables, and (c) demonstrate the use of the GSE model in estimating isosteric heats of adsorption from the data obtained by a differential adsorption calorimeter. Isosteric Heats of Adsorption by GSE Model Figure 1a schematically shows the GSE model for an equilibrium multicomponent gas adsorption system containing * Corresponding author. † Present Address: Chemical Engineering Department, Pennsylvania State University, College Park, PA.
a unit amount of the adsorbent.7-9 The bulk gas phase is defined by its pressure (P), temperature (T), and the mole fraction (yi) of component i. The Gibbsian adsorbed phase is defined by an arbitrarily chosen Gibbs’ interface where the local adsorbate density and compositions are the same as those of the homogeneous bulk gas phase. The extent of adsorption of the ith component of the gas mixture is given by its Gibbsian surface excess (nm i , mol/g) which can be experimentally measured. They are independent of the location of the Gibbs’ interface as long as it is within the bulk gas phase. Thus, the GSE model does not require that the exact size, structure, location, composition, and the density of the actual adsorbed phase be known. The pressure and temperature of the Gibbsian adsorbed phase are the same as those of the bulk gas phase. All conventional experimental methods for gas adsorption studies (volumetric, gravimetric, chromatographic, etc.) measure nm i as functions of P, T, and yi under equilibrium conditions (multicomponent equilibria) and nm i as functions of time under transient conditions (multicomponent kinetics). They represent the true experimental variables.8 Figure 1b schematically shows the conventional model used for multicomponent gas adsorption equilibrium. In this case, the interface between the bulk gas phase and the adsorbed phase is located exactly where the local density and composition of the adsorbed phase approach those of the bulk gas phase. The adsorbed phase is defined by its actual volume (Va, cm3/g) and the extent of adsorption of component i is given by its actual amount adsorbed (nai , mol/g). The total void volumes (bulk gas phase + pores in the adsorbent) for both systems of parts a and b of Figure 1 are the same (V0, cm3/g). They can be experimentally measured by helium expansion. The actual adsorbed phase volume of Figure 1b, on the other hand, cannot be unambiguously estimated without making extraordinary assumptions about its structure, particularly for the meso-micro porous adsorbents of practical interest. Another key point to note is that Va is an unknown function of nai and T (or P, T, and yi).
10.1021/jp9903817 CCC: $18.00 © 1999 American Chemical Society Published on Web 07/20/1999
6540 J. Phys. Chem. B, Vol. 103, No. 31, 1999
Sirca et al.
Figure 1. Schematic drawings of various adsorption models: (a) Gibbsian surface excess model; (b) conventional model; (c) model for constant P, T experiment using a pure gas.
A comparative mass balance for the components of the gas mixture using the models of parts a and b of Figure 1 yields8 a a a a a a nm i ) (ni - V Fyi) ) V (F xi - Fyi )
(1)
where F and Fa are, respectively, the molar densities of the bulk gas phase and the actual adsorbed phase (Figure 1b), and xai ()nai /∑nai ) is the mole fraction of component i in the actual adsorbed phase (Figure 1b). a a a Equation 1 clearly shows that nm i ≈ ni only when (F xi . Fyi) for a multicomponent gas and when Fa . F for a pure gas. Otherwise, there can be a large difference between experimena m tally measured nm i and calculated ni values. Furthermore, ni a and ni may be approximately equal to each other for the more selectively adsorbed component of a gas mixture (xai . yi), but a the difference between nm i and ni can be large for the less selectively adsorbed components of the same gas mixture even though (Fa . F).8 The conventional approach to develop adsorption thermodya namics is to assume nm i ≈ ni and then follow the model of 3,4 Figure 1b. This can lead to ambiguous and erratic thermodynamic and kinetic interpretation of experimental adsorption data. The problem can be resolved by developing adsorption thermodynamics and kinetics based on the GSE model of Figure 1a.8,9 The equilibrium GSE model defines the isosteric heat of adsorption of component i (qi, cal/mol) as the negative of the differential change in total enthalpy (H°, cal/g) of the closed system of Figure 1a for a differential change in the surface excess of component i (nm i ) at constant system temperature (T) and constant values of surface excesses of other components m (nj*i ) of the system8,9
[ ]
-
δH° δnm i
m T,nj*i
) +qi
(2)
It can be shown from the thermodynamic analysis of the GSE model8,9 that, for an ideal gas mixture, one has
[ ]
-
δU° δnm i
m T,nj*i
[ ]
)+
δQ δnm i
[
qi ) RT2
m T,nj*i
) qdi ) +(qi - RT)
]
δln(Pyi) δT
nm i
(3)
(4)
where U° (cal/g) is the total internal energy of the adsorption system of Figure 1a. The quantity dQ (cal/g) represents the differential amount of heat to be removed (or added) to the system for a differential change (dnm i ) in the surface excess of m component i at constant T and (nj*i ). The quantity qdi (cal/mol) in eq 2 is called the differential heat of adsorption. Equation 3 gives the relationship between qi and qdi for an ideal gas mixture. Equation 4 shows that qi can be estimated by knowing the differential change in the partial pressure (pi ) Pyi) of component i of a gas mixture due to a differential change in system temperature at constant values of nm i . This can be easily achieved for a pure gas by measuring adsorption isotherms (nm i as functions of P) at different constant temperatures8,9 but the use of eq 4 for gas mixtures containing two or more components can be formidable if not an impossible task.8 It will be shown later that direct calorimetric estimation of qi for multicomponent systems is much easier. Equation 3 shows that qdi and qi can be easily interchanged as the design variable of choice. We prefer to use qi because of its traditional thermodynamic connotation with reference to eq 4 and its conventional counterpart (eq 21). The second reason to choose qi is its temperature independence over a large range of temperature.9 The GSE model of transient mass and heat balances for ad(de)sorption of an N-component ideal gas mixture in a packed
Isosteric Heat of Adsorption: Theory and Experiment
J. Phys. Chem. B, Vol. 103, No. 31, 1999 6541 adsorbed and equilibrium gas phases are µa and µ, respectively. For an ideal gas,11
adsorbent column yields:9,10
mass balance of component i
( ) [ ] δnji δ(Gyi) )δt z δz ni )
(5)
+ Fyi
}
δT δ [GCg(T - T0)] )δt z δz
t
( ) ( )
∑qi
+ Fb
δnm i + δt z
δP δt
z
(7)
where the transient variables of eqs 5 and 7 represent the gasphase pressure (P, atm), the temperature of gas and adsorbent (T, K), the gas-phase mole fraction of component i (yi), the gasphase molar density (F, mol/cm3), the gas-phase molar heat capacity (Cg, cal/mol/K), the molar gas flow rate through the column based on empty cross section of adsorber (G, mol/cm2/ s), the surface excess of component i (nm i , mol/g), and the total amount of component i in the adsorber (nji, mol/cm3), as functions of a distance z (cm) in the adsorber column at time t (s). CA (cal/g K) is the heat capacity of the total adsorption system at t and z.9 and Fb are, respectively, the helium void fraction of the adsorber (cm3/cm3) and the bulk density (g/cm3) of the adsorbent. The heat balance equation assumes instantaneous thermal equilibrium between the gas and the Gibbsian adsorbed phases. All of the above-described variables can be experimentally measured unambiguously. Equations 5-7 can be simultaneously solved with the appropriate multicomponent adsorption equilibria and kinetic models (GSE framework) in conjunction with the appropriate initial and boundary conditions for the steps of the adsorption process in order to estimate the separation performance of the process.2 Thus, they show the practical usefulness of the isosteric heats of adsorption defined by eqs 2-4 using the GSE model. Isosteric Heat of Adsorption by Conventional Model We now focus on the adsorption thermodynamics for the conventional model of Figure 1b. Only the adsorption from a pure ideal gas will be considered for simplicity. However, a fairly detailed development is given because the published literature on this subject is often not very rigorous.3,4 The key thermodynamic relationships for the adsorbed phase described by Figure 1b (pure gas only) may be written as3,8
dUa ) T dSa - P dVa + µa dna
(8)
dHa ) T dSa + Va dP + µa dna
(9)
dG ) -S dT + V dP + µ dn a
a
a
(11)
dµ* ) h* dT
µ* - T
(12)
(6)
heat balance
() {
CAFb
i ) 1, 2, ....N
t
Fbnm i
µa ) µ ) µ*(T) + RT ln P
a
a
(10)
where Ua, Va, Sa, Ha ()Ua + PVa), Ga ()Ha - TSa) are, respectively, the internal energy, the volume, the entropy, the enthalpy, and the Gibbs free energy of the total adsorbed phase containing na moles of a pure adsorbate per unit amount of the adsorbent. The chemical potentials of the adsorbate in the
where µ* and h* are, respectively, the chemical potential (molar Gibbs free energy) and the molar enthalpy of the pure gas at temperature T and a pressure of 1 atm. They are functions of T only. The molar gas volume for an ideal gas is ν ) (RT/P) and that for the adsorbed phase is νa ()Va/na). It follows from eqs 11 and 12 that
( )
µa - T
δµa δT
na
( )
) h* - RT2
δ ln P δT
(13)
na
Equation 10 can be differentiated with respect to na at constant P and T and with respect to T at constant na to obtain
( ) δGa δT
( ) δGa δna
na
) µa
P,T
(14)
( )
) -Sa + Va
δP δT
(15)
na
Equation 14 can be differentiated with respect to T at constant na, and eq 15 can be differentiated with respect to na at constant P and T and the two results equated to obtain
-
( ) ( ) δSa δna
)
P,T
δµa δT
[( ) ] ( ) ( )
δ δP - Va a na δn δT na
-
P,T
δVa δna
P,T
δP δT
na
(16)
We now consider a process where a differential amount (dn) of pure adsorbate is transferred from the gas phase to the adsorbed phase while keeping the system closed (dn + dna ) 0) and maintaining P and T as constants. This can be achieved by fitting the gas phase of Figure 1b with a frictionless piston (as shown by Figure 1c) and then (a) by differentially moving the piston so as to decrease the total void volume of the system by dV0 (cm3/g) in order to keep P constant and simultaneously (b) by removing a differential quantity of heat (dQ, cal/g) from the thermostated system at T. By applying the energy balance for a closed system with heat transfer and mechanical work at constant P and T,12 one has
dU° ) -dQ - P dV0
constant P, T
(17)
Where U° ()U + Ua) is the total internal energy of the closed system of part b or c of Figure 1, U ()nu*) is the total internal energy of the gas phase, n is the total moles of adsorbate in that phase (n + na ) constant), and u* (h* ) u* + RT) is the molar internal energy of the gas at T. The total volume of the gas phase (V ) V0 - Va) of parts a and b of Figure 1 is given by
V)
nRT RT ; dV ) - dna P P
P dV0 ) P dVa - RT dna
constant P, T constant P, T
Equations 8-19 can be combined to get
(18) (19)
6542 J. Phys. Chem. B, Vol. 103, No. 31, 1999
[ ] δQ δna
P,T
( ) [ ( ){ ( ) ( ) }]
) h* -
δHa δna
) qj 1 -
P,T
Va na δqj + V qj δna P,T na δVa +1 Va δna P,T
(δ δTln P)
qj ) RT2
na
Sirca et al.
(20) (21)
Equation 20, which was previously unpublished, provides the rigorous relationship between the variable qj and the differential heat to be removed from (added to) the system of Figure 1c when a differential amount (dna) of pure adsorbate is ad(de)sorbed at constant P and T. However, if the molar density of the actual adsorbed phase is much greater than that of the gas phase (Fa . F; Va , V), then eq 20 simplifies to
( ) δQ δna
≈ qj
(22)
P,T
provided that the terms inside the second bracket on the righthand side of eq 20 are relatively small. Most published literature on adsorption thermodynamics derives eqs 21 and 22 by assuming that Va , V, and defines the variable qj as the isoteric heat of adsorption for a pure ideal gas3,4 because eq 21 shows that qj can be calculated from the adsorption isosteres (plots of P against T at constant na). Equation 20 shows that eq 22 is strictly valid only when Va , V and the terms [(δ ln qj/δ ln na)P,T] and [(δ ln Va/δ ln na)P,T] are small. The first criterion may be valid for adsorption of a vapor well below its critical temperature, where the adsorbed phase may be liquid like3. Otherwise, eq 22 may not be correct. The term (δqj/δna)P,T is (a) equal to zero for an energetically homogeneous adsorbent and (b) relatively small for a weakly heterogeneous adsorbent.9 The term (δυa/δna)P,T is also expected to be small when the absorbed phase is liquid-like. Thus, the second criterion for validity of eq 22 may also be satisfied when υa , υ and the adsorbent is homogeneous. In contrast, the definition of q by the GSE model [eqs 2-4] does not require any assumptions about the nature of the adsorbed phase, and it can be easily used for practical process design purposes. The parallel between the forms of eq 4 for a pure gas (yi ) 1) and eq 21 suggests that qi be called the isosteric heat of adsorption of component i of a gas mixture. A more precise terminology for qi is “isoexcess heat of adsorption of component i” for a multicomponent gas mixture. For pure gas adsorption qj and q are identical, if nm ) na, which is satisfied only if υa , υ. Calorimetric Measurement of Multicomponent Isosteric Heat of Adsorption A Tian-Calvet type heat flux microcalorimeter can be used to directly estimate the multicomponent gas isosteric heats of adsorption defined by the GSE model.9 Figure 2a is a sketch of the calorimeter cell which is surrounded by thermopiles for directly measuring the heat flux through its walls. Figure 2b shows the schematic drawing of the calorimeter assembly. It consists of the calorimeter cell, called the “sample side”, connected to a gas holder, called the “dosage side”, through a valve. The gas-phase pressure and composition of the sample side and the gas-phase pressure of the dosage side can be continuously monitored. The entire system is thermostated at a constant temperature T0. A unit amount of regenerated adsorbent is placed in the sample side, and the helium voids of the sample
Figure 2. Sketch of the calorimeter sample cell (a) and the calorimeter assembly (b).
(V0, cc/g) and dosage (Vd, cc/g) sides are measured. The sample side is then saturated with a multicomponent gas mixture at P0, T0, and yi0 and the dosage side is filled with a pure gas i (a component of the gas mixture of interest) at pressure Pd0 (>P0). A very small amount (∆Ni) of the pure gas i is then slowly introduced into the sample side from the dosage side and the valve is closed. The sample side is then allowed to reach a new equilibrium state. The temperature [T(t)] of the gas entering the sample side is continuously monitored. The total quantity of heat evolved (consumed) in the calorimeter cell (∆Qi) during the entire process is obtained by integration of the calibrated thermopile output (voltage vs time). The change in the partial pressure of component j of the gas mixture in the sample side (∆pji) is measured at the end of the process. The amount of pure gas introduced into the sample side during the above-described process is
∆Ni )
∫0t*N˙ i dt;
[ ]
N˙ i ) Vd
dFd dt
(23)
where N˙ i is the rate of introduction of the pure gas i into the sample side. It can be calculated by measuring the rate of change of density (Fd) in the dosage side. The total time taken to complete the process is t*. The enthalpy of pure gas i introduced (∆Hin) into the sample side during the process is given by
∆Hin ) (∆Ni)hhi;
∫0t*Cgi/ [T(t) - T0]N˙ i dt hhi ) ∫0t*(N˙ i) dt
(24)
where hhi is the time averaged molar enthalpy of pure gas i introduced into the sample side during the above-described process. hhi is equal to zero (assuming ideal gas) if the gas entering the sample side is at the base temperature of the experiment [T(t) ) T0]. The mass balances for the components of the gas mixture
Isosteric Heat of Adsorption: Theory and Experiment
J. Phys. Chem. B, Vol. 103, No. 31, 1999 6543
(assuming ideal gas) for the differential process yield9
∆Ni ) ∆nm i +
V0 ∆pii RT0
m ∆Nj*i ) 0 ) ∆nj*i +
V0 ∆pji RT0
(25) (26)
An energy balance for the sample side of the calorimeter (open system, ∆Hout ) 0, no shaft work) yields9,12
∆Uoi ) ∆Hin - ∆Qi
(27)
where ∆Uoi is the total change in internal energy of the sample side during the experiment. It can be shown by combining eqs 2-4 and 24-27 that for an ideal gas9
∆Qi ∆Ni
) qi -
υ0∆pji
∑j ∆N
i
{ } qj
RT0
- 1 + hhi i ) 1, 2, ... N (28)
where qi is the isosteric heat of adsorption of component i [defined by eqs 2-4] of an N component gas mixture (i ) 1,2, m 0 ... N) at P0, T0, and y0i (or nm i and T ). ni is the equilibrium surface excess of component i of the gas mixture at P0, T0, and y0i . A total of N experiments must be carried out around the base saturation conditions of P0, T0, y0i (or T0 and nm i ) by separately introducing differential quantities of each pure gas (∆Ni, i ) 1, 2, ... N). This will generate N independent equations analogous to eq 28 that relate N different unknowns (qi). Consequently, qi can be estimated for a given set of values of T0, P0, y0i (or T0 and nm i ). For adsorption of a pure ideal gas (component i), eq 28 simplifies to (base conditions of T0, P0, y0i ) 1)
q0i )
[( ) ( )] [ ( )] ∆Qi ∆Pi - hhi - V0 ∆Ni ∆Ni V0 ∆Pi 1RT ∆Ni
(29)
where ∆Pi is the change in the gas-phase pressure in the sample side during the process, and qi0 is the isosteric heat of m0 adsorption of pure gas i at P0 and T0 (or T0 and nm0 i ). ni is the equilibrium surface excess of pure gas i at P0 and T0. We now consider the special case of the above-described experiment using a pure ideal gas where (a) the gas is nonadsorbing or (b) the adsorbent is absent, and where hhi is equal to zero. The heat evolved in the sample side of the calorimeter (∆Q*) for introduction of (∆N*) moles of pure gas, in this case (qi ) 0), is given by
∆Q* ) V0∆P*
(30)
where ∆P* is the change in the gas pressure of the sample side during the process. V0 is the helium void volume of the sample side [(a) with adsorbent and (b) without adsorbent]. Experimental Measurement of Isosteric Heat by Calorimetry We constructed a multicomponent differential calorimeter (MDC) which utilizes the experimental protocol and the
Figure 3. Test results of blank experiment: (a) plot of thermopile output signal (voltage vs time); (b) plot of gas temperature entering calorimeter cell against experimental time.
algorithm for data analysis outlined in the previous section. The general design concepts of our calorimeter system were similar to those used by Myers, Gorte, and their co-workers.13,14 It consisted of two identical calorimeter cells (sample and reference) made from cylindrical stainless steel vessels. The sides and the bottom of the calorimeter cells were covered with custom-made thermopiles manufactured by the International Thermal Instrument Company of California. The tops of the calorimeter vessels were fitted with Zytel lids and thermal shunts that minimize heat loss through the tops and redirect any heat flow in that direction to the thermopiles. The sample and reference cells were installed inside snugly fit holes cut into a large aluminum block to maintain constant base temperature around the thermopiles. The sample cell was connected to a gas supply chamber (dosage cell) through a metering valve. Several multiport valves and interconnecting lines were used to (a) evacuate the sample cell and flow the initial saturating gas over the clean adsorbent at given values of P0, T0, and y0i , and (b) evacuate the dosage cell and filling it with the dosing gas at Pd0 and T0. The sample side was instrumented with differential pressure cells and thermocouples for continuous monitoring and recording of pressure and temperature in these cells. A residual gas analyzer (mass spectrometer) was connected to the sample cell through a leak valve for continuously monitoring the gas composition in the cell. A thermocouple monitored the temperature of the gas entering the sample cell from the dosage cell during the experiment. The entire calorimetric assembly was kept inside a constant-temperature air bath. Figure 2 shows a schematic diagram of the sample cell. The total amount of adsorbent in the cell was typically 8-12 g. There were two output signals (voltage against time) from the calorimeter assembly during the experiments. They were produced by (a) the sample cell and (b) the reference cell. The difference between these two outputs was used to estimate the actual heat liberated (consumed) during the ad(de)sorption experiment. The signal from the reference cell was used to correct for any spurious heat generated inside the calorimetric cell due to temperature fluctuations in the aluminum block. Figure 3a shows a typical output signal from the calorimeter. The voltage-time output signal was transformed into the rate of heat production vs time data by electrically generating a known quantity of heat inside the calorimeter and measuring the output signal. A PC-based data acquisition/control system was set up to control switch valves and to record all experimental data such as pressures, temperatures, compositions, and heat fluxes as functions of time during the experiments. Examples of Calorimetric Data Blank Experiments. We carried out several blank experi-
6544 J. Phys. Chem. B, Vol. 103, No. 31, 1999
Sirca et al.
Figure 4. Plot of the quantity of heat liberated (∆Q*) during the blank experiments (without adsorbents) against pressure change in the calorimeter cell (∆P*).
ments using pure N2 and CO2 as adsorbates. These pure gases were expanded from the dosage side to the calorimeter cell containing no adsorbent (helium void, V0 ) 24.75 cm3). Several different initial dosage side pressures (Pd0) were used with (a) an initially evacuated calorimeter cell or (b) a calorimeter cell containing pure gas at some initial pressure. The total heat liberated during each of these tests (∆Q*) was measured as a function of the corresponding change in gas pressure in the calorimeter cell (∆P*). Figure 3a shows a typical thermopile output signal from these runs. The base temperature was 303.7 K. The connecting valve between the dosage and calorimeter cells was opened at t ) 2.5 min, when the voltage output signal rose very sharply to its maximum value and then it slowly decayed down to the original baseline value in about 14 min ()t*) after the valve was opened. Figure 3b shows that the temperature of the gas entering the calorimeter cell during this period remains practically constant [T(t) ) T0]. Thus, the term hhi in eq 28 is zero. Consequently, according to eq 29, a plot of ∆Q* against ∆P* should be a straight line through the origin with a slope equal to V0, irrespective of the nature of the gas used. Figure 4 shows such a plot for both CO2 and N2. The slope of the line is 23.54 cm3, which is within 5% of the independently measured helium void of the calorimeter cell. This result validates eqs 28 and 30 for the special case of blank experiments. Experiments with Adsorbents. We measured the isosteric heats of adsorption of pure N2 and CO2 on a pelletized sample of silicalite (obtained from UOP Corporation) using the abovedescribed calorimeter and using eq 28 for data analysis. q0i was measured as functions of P0 at 303.5 K. The silicalite pellets (1/8" diameter, 1/4" long) were regenerated by heating under vacuum (1 µm) at 300 °C and then transferred to the calorimeter cell under dry N2 in a glovebox. They were then subjected to a vacuum (1 µm) for 1 h at the temperature of the experiment before the calorimetric tests were started. The thermopile output signals for all of these runs were very similar in shape to that shown by Figure 3a. The temperatures of the gas entering the calorimeter cell during these runs were also very close to the base temperature, like that shown by Figure 3b. Thus, the term hhi in eq 29 was equal to zero for all of these runs. The differential quantities ∆Qi, ∆Ni, and ∆Pi of eq 29 were measured for all runs and q0i was calculated as a function of P0 at constant T0. It should be noted here that the above-described experiments with pure gas can also be used to calculate pure gas surface
Figure 5. Pure gas adsorption isotherms of (a) N2 and (b) CO2 on the pelletized silicalite sample at 303.5 K measured using the calorimeter assembly as a volumetric adsorption apparatus. 0 0 excess isotherms (nm0 i as functions of P at constant T ) on the adsorbent using eq 25 if the sample and dosage sides are allowed to reach equilibrium during the process:
∆Ni ) ∆nm0 i +
V0∆Pi RT
(31)
A cumulative set of differential expansion experiments can be carried out to generate the pure gas surface excess isotherm using eq 31 by starting with a clean adsorbent. The procedure was identical to that for a conventional volumetric adsorption apparatus.15 Figure 5 shows the pure N2 and CO2 isotherms at 303.5 K on the silicalite sample obtained by using eq 30. These isotherm data can be combined with the isosteric heat data for the pure gases measured at different values of P0 for obtaining qi0 as 0 functions of nm0 i at a constant value of T . Figure 6 shows such results (open circles) for pure N2 and CO2 adsorption on the pelletized silicalite sample. The figure also shows the pure gas isosteric heats of adsorption of CO2 and N2 on the same silicalite sample (closed circles) calculated independently from surface excess isotherms at two different temperatures (not shown) measured by a conventional volumetric adsorption apparatus.15 The pure gas form (yi ) 1) of eq 4 was used to calculate the isosteric heats from surface excess isotherms at two temperatures. It may be seen from Figure 6 that the pure gas isosteric heats and their variation with surface excess obtained by these two methods matched very well in the range of the data. This demonstrates the validity of eq 29. The calorimetric data of
Isosteric Heat of Adsorption: Theory and Experiment
J. Phys. Chem. B, Vol. 103, No. 31, 1999 6545 occupied by CO2 on the pelletized sample at higher pressures are predominantly the silicalite sites because the isosteric heat of adsorption of CO2 on the pellet in that region matches that of pure crystals very well. A key question then is “what is the source of high-energy sites for adsorption of CO2 at low pressures in the pelletized silicalite sample?” A chemical analysis of the pelletized silicalite sample showed that it contained ∼19.0% alumina as a binder. The previously reported isosteric heat of adsorption of pure CO2 on γ-alumina at the limit of zero coverage is about 14 kcal/mol.16 The isosteric heat then drops drastically as the CO2 coverage increases. We suspect that the presence of alumina binder in the silicalite pellet is the source of its energetic heterogeneity for CO2 adsorption. The strong interaction between the large quadrupole moment of CO2 and the highly polar alumina binder appears to be the reason for high isosteric heat of adsorption of CO2 on the pelletized silicalite sample at low pressures. The interaction between the weak quadrupole moment of N2 and the alumina binder does not introduce significant heterogeneity for N2 adsorption on the silicalite pellet. Summary
Figure 6. Isosteric heats of adsorption of (a) pure N2 and (b) pure CO2 on the pelletized silicalite sample found by calorimetry (open circles) and by volumetric adsorption apparatus (closed circles).
Figure 6 for both gases were measured on the silicalite sample several times by cleaning the adsorbent by evacuation. The data were extremely reproducible. The silicalite is a nonpolar homogeneous adsorbent with practically no cation exchange capacity. Consequently, the isosteric heats of adsorption of N2 (with weak quadrupole moment of 1.5 × 10-26 esu cm2) and CO2 (with large quadrupole moment of 4.3 × 10-26 esu cm2) on the silicalite are expected to be independent of their loadings. Previous calorimetric measurements of isosteric heats of adsorption of N2 and CO2 on pure unbound silicalite crystals exhibited that behavior.13 The isosteric heats of adsorption of N2 and CO2 on the silicalite crystals were, respectively, 4.20 kcal/mol at 296.0 K and 6.59 kcal/mol at 303.7 K and they were constants (independent of nm0 i ). The data of Figure 6 shows that the isosteric heat of adsorption of N2 on the silicalite pellet is indeed constant (∼4.13 e 0.6 mol/kg). kcal/mol) over the range of the data (0 e nm0 i This agrees extremely well with the previously published isosteric heat values for N2 on silicalite.13 On the other hand, the data of Figure 6 shows that the isosteric heat of adsorption of CO2 on the silicalite pellet is very high (∼9.5 kcal/mol) at the limit of zero coverage and then it gradually decreases and levels off at a value of ∼6.3 kcal/mol. Thus, the pelletized silicalite sample exhibits significant energetic heterogeneity for CO2 adsorption. In other words, the pelletized silicalite sample possesses some high-energy sites for CO2 sorption which are preferentially occupied by CO2 at low pressures. At higher pressures, the lower energy sites (∼6.3 kcal/mol) of the sample are predominantly occupied by CO2. It appears that the sites
The isosteric heats of adsorption of the components of a gas mixture are critical variables for the design of practical gas separation processes. They can be defined unambiguously using the Gibbsian Surface Excess (GSE) model of multicomponent gas adsorption without making any extraordinary assumptions about the nature and size of the adsorbed phase as required by the conventional thermodynamic models of adsorption using actual amounts adsorbed as the primary variables. The isosteric or isoexcess heats of adsorption defined by the GSE framework can be experimentally measured by using multicomponent differential calorimeters (MDC) and they can be directly used to describe heat balance in batch or flow adsorbers. A Tian-Calvet type MDC is described for direct measurement of multicomponent isosteric heats of adsorption in conjunction with the algorithm for calorimeter data analysis. Isosteric heats of adsorption of pure N2 and CO2 were measured as functions of adsorbate loading on a pelletized sample of silicalite using the MDC. The isosteric heat of adsorption of N2 on the silicalite sample was found to be independent of its adsorbate loading, indicating that the adsorbent was energetically homogeneous toward N2 adsorption. The isosteric heat of adsorption of CO2 on the same silicalite sample, on the other hand, decreased with increasing adsorbate loading, indicating energetically heterogeneous behavior. The presence of polar alumina binder in the silicalite sample, which has a very large isosteric heat of adsorption for CO2 at low coverages, was suspected to be the cause of heterogeneity for CO2 adsorption. References and Notes (1) Sircar, S. Pressure Swing AdsorptionsResearch Needs in Industry. In Fundamentals of Adsorption, Proceedings of Engineering Foundation Conference held at Sonthofen, Germany; Mersmann, A. B., et al., Eds.; Engineering Foundation: New York, 1991; p 815. (2) Hartzog, D. G.; Sircar, S. Adsorption 1995, 1, 133. (3) Young, D. M.; Crowell, A. D. Physical Adsorption of Gases; Butterworths: Washington, DC, 1962. (4) Hill, T. L. J. Chem. Phys. 1949, 17, 520. (5) Everett, D. H. Colloq. Int. CNRS 1971, 201, 45. (6) Cardona-Martinez, N.; Dumesic, J. A. AdV. Catal. 1992, 38, 149. (7) Gibbs, J. W. The Collected Works of J. W. Gibbs; Longmans and Green: New York, 1928. (8) Sircar, S. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1527. (9) Sircar, S.; Rao, M. B. Heat of Adsorption of Pure Gas and
6546 J. Phys. Chem. B, Vol. 103, No. 31, 1999 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; Chapter 19, pp 501-528. (10) Sircar, S. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1541. (11) Prausnitz, J. M. Molecular Thermodynamics of Fluid Phase Equilibria; Prentice Hall: Englewood Cliffs, NJ, 1969. (12) Balzhiser, R. E.; Samuels, M. R.; Eliassen, J. D. Chemical
Sirca et al. Engineering Thermodynamics; Prentice Hall: Englewood Cliffs, NJ, 1972; pp 98-101. (13) Dunne, J. A.; Mariwala, R.; Rao, M. B.; Sircar, S.; Gorte, R. J.; Myers, A. L. Langmuir 1996, 12, 5888. (14) Parrillo, D. J.; Gorte, R. J. Catal. Lett. 1992, 16, 17. (15) Golden, T. C.; Sircar, S. J. Colloid Interface Sci. 1991, 147, 274. (16) Rosynek, M. P. J. Phys. Chem. 1975, 79, 1280.
