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4333
Calorimetric Heats of Adsorption and Adsorption Isotherms. 3. Mixtures of CH4 and C2H6 in Silicalite and Mixtures of CO2 and C2H6 in NaX J. A. Dunne,† M. Rao,‡ S. Sircar,‡ R. J. Gorte, and A. L. Myers* Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104 Received October 11, 1996. In Final Form: May 5, 1997X Individual heats of adsorption and selectivity of mixtures have been measured simultaneously in a calorimeter. After the weakly adsorbed component was preloaded the dosing of both components to the sample cell was adjusted to hold the loading of the weakly adsorbed component constant. Agreement with ideal adsorbed solution theory is quantitative for mixtures of CH4 and C2H6 at low coverage in an adsorbent with a weak electric field (silicalite). Mixtures of quadrupolar (CO2) and nonpolar (C2H6) gases in an adsorbent with a strong electric field (NaX) exhibit strong negative deviations from ideality. The experimental heats of adsorption are larger than those for an ideal solution, in agreement with the results of molecular simulation.
1. Introduction The selectivity of an adsorbent for a particular separation is determined by differences in the free energy of the molecules forming the mixture. Differences in free energy of adsorption arise from energy or entropic effects, or a combination of both. Given a particular set of standard states in the adsorbed and gas phases, a difference of about 6 kJ/mol in the free energy of adsorption generates a separation factor of 10 at room temperature. The magnitude of the free energy of adsorption depends upon the atomic composition and molecular structure of the adsorbate molecule and the atomic composition and topology of the adsorbent. Molecular-structure factors such as the polarity of the adsorbate molecules and the inclusion of nonframework ions in zeolitic adsorbents have a major impact on the free energy of adsorption and hence upon the separation factor. Pressure swing adsorption (PSA) processes require reversible adsorption so that the preferentially adsorbed species can be removed easily during the regenerative portion of the cycle. Therefore chemical bonding of the adsorbate molecule with the adsorbent is normally undesirable. Gas-solid interaction energies for adsorptive separations are primarily dispersion and electrostatic (ion-dipole, ion-quadrupole) interactions. The size and shape of the adsorbate molecules affect their rates of diffusion within the adsorbent. Zeolites, because of their uniform pore structure, can sometimes be used effectively as “molecular sieves” for molecules of different size and shape. However, most separations are based upon the ability of adsorbents, especially zeolites, to generate large selectivities by magnifying subtle differences in molecular structure. For example, two molecules which are identical except for a difference in their dipole moments of 0.5 D, when placed in an electric field of 6 V/nm (a typical value in zeolite cavities1 ), have a difference of 6 kJ/mol in their heats of adsorption. As * To whom correspondence should be addressed. E-mail address:
[email protected]. † Allied Signal, Santa Clara, CA ‡ Air Products & Chemicals, Inc., Allentown, PA. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Lamberti, C.; Bordiga, S.; Geobaldo, F.; Zecchina, A.; Arean, C. Stretching frequencies of cation CO adducts in alkali-metal exchanged zeolitessan elementary electrostatic approach. J. Chem. Phys. 1995, 103, 3158.
S0743-7463(96)00984-5 CCC: $14.00
mentioned previously, a difference of 6 kJ/mol in free energies of adsorption corresponds to a selectivity of 10 at room temperature. Although PSA processes are usually operated at ambient temperature, the adsorption and desorption steps in the cycle operate under approximately adiabatic conditions. The magnitude of the temperature change induced by adsorption or desorption is determined by the individual heats of adsorption of the components of the mixture through an energy balance. Since loading is highly sensitive to temperature, the selectivity is closely coupled to the magnitudes of the individual heats of adsorption. Therefore accurate design calculations require values for heats of adsorption as well as selectivities. Surprisingly, although heats of adsorption have been measured extensively for pure gases, almost nothing is known about heats of adsorption from mixtures. How do heats of adsorption vary with temperature, loading, and adsorbed-phase composition? A few theories have been proposed2,3 but comparisons with experiment await experimental data. Isosteric heats of adsorption (qi) are directly related to the temperature coefficient of the selectivity at fixed loading
[
R
]
∂ ln s ∂(1/T)
n1,n2
) q1 - q2
(1)
where s ) (x1/y1)/(x2/y2) is the selectivity of component 1 relative to component 2 in a binary mixture. Since the preferentially adsorbed species normally has the higher heat of adsorption, the selectivity normally decreases with temperature. Although selectivity is the key variable for adsorptive separations, eq 1 has never been used or derived previously because individual heats of adsorption qi for mixtures are difficult to measure by Clapeyron-type equations.4 Compared to vapor-liquid equilibrium (VLE), adsorption equilibrium is undeveloped. The concept of an ideal (2) Sircar, S. Estimation of isosteric heats of adsorption of single gas and multicomponent gas mixtures. Ind. Eng. Chem. Res. 1992, 31, 1813. (3) Karavias, F.; Myers, A. L. Isosteric heats of multicomponent adsorption: thermodynamics and computer simulations. Langmuir 1992, 7, 3118. (4) Sircar, S. Excess properties and column dynamics of multicomponent gas adsorption. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1541-1545.
© 1997 American Chemical Society
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adsorbed solution (IAS)5 provides a baseline for comparison with experiment, but nonideal behavior and its variation with pressure, temperature, and composition are difficult to correlate, much less predict. IAS theory is covered in ref 6. Nonideal VLE is described by thermodynamic excess functions. The excess Gibbs free energy function gives the activity coefficients at a particular temperature; the excess enthalpy (heat of mixing) gives the variation of the Gibbs free energy function with temperature through the Gibbs-Helmholtz equation. This concise and elegant thermodynamic description of nonidealities in the liquid phase has no counterpart for handling nonidealities in adsorbed phases. An analytic equation has been proposed7 to describe the isothermal excess Gibbs free energy of the adsorbed phase as a function of loading and composition, but the adsorbed-phase equivalent of heats of mixing of liquids has not been studied. Consequently there exists no systematic way of handling the temperature dependence of adsorbed-phase nonidealities, which is critical for the design of PSA processes. 2. Thermodynamics of Heats of Adsorption from Mixtures This section discusses two types of thermodynamic consistency tests for isosteric heats of adsorption and explains how isosteric heats of adsorption were predicted by IAS theory for comparison with the experiments. Pure Gas. The isosteric heat of a pure gas is defined by
qst ) hg - h ha
(2)
The quantity h h a is the differential enthalpy in the adsorbed phase
h ha )
[ ] ∂Ha ∂na
(3)
∫0n qst dna
(4)
Summarizing for adsorption of a pure gas, qst in eq 2 is the isosteric heat (differential enthalpy of vaporization) and ∆h in eq 4 is the integral enthalpy of vaporization. Amount adsorbed (na) refers to the usual surface excess experimental variable obtained from adsorption isotherms, and the enthalpy (Ha) refers to the experimental excess enthalpy of the adsorbed phase.4 Experimentally measured excess variables for amount adsorbed and heat (5) Valenzuela, D.; Myers, A. L. Adsorption Equilibrium Data Handbook; Prentice-Hall: Englewood Cliffs, NJ, 1989. (6) Smith, J. M.; Van Ness, H. C.; Abbott, M. M. Introduction to Chemical Engineering Thermodynamics, 5th ed., McGraw-Hill: New York, 1996; p 536. (7) Talu, O.; Li, J.; Myers, A. L. Activity Coefficients of Adsorbed Mixtures. Adsorption 1995, 1, 103.
(5)
where h h ig is the partial molar enthalpy in the bulk gas phase
h h ig )
[ ] ∂Hg ∂nig
(6)
T,P,njg
and h h ia is the differential enthalpy in the adsorbed phase
h h ia )
[ ] ∂Ha ∂nia
(7)
T,nja
The differential enthalpy of vaporization of a binary mixture is
d(∆H) ) q1 dn1 + q2 dn2
(8)
where the notation for isosteric heat (qst) has been simplified to q, and the notation for the excess amount adsorbed (na) has been simplified to n. Since H is a state function
[ ] [ ] ∂q1 ∂n2
)
T,n1
∂q2 ∂n1
(9)
T,n2
eq 9 is a differential test for the consistency of individual heats of adsorption from a binary gas mixture. The isothermal enthalpy of vaporization of the adsorbed phase is an integral. For a binary mixture
∆H )
a
na
(qst)i ) h h ig - h h ia
T
In general, heat depends upon the path. Since the isosteric heat is defined in terms of state functions, its value is independent of the path. The same loose terminology is used in vapor-liquid equilibrium: “heat” of vaporization means enthalpy change upon vaporization. The isosteric heat is a differential quantity (but not a partial molar quantity as defined in thermodynamics for bulk solutions). The molar enthalpy of vaporization (∆h) of the adsorbed phase is an integral of the isosteric heat with respect to the amount adsorbed (na)
∆h )
of adsorption may differ substantially from corresponding absolute variables obtained by molecular simulation.8 Gas Mixture. The isosteric heat of the ith component of a mixture is the differential enthalpy of vaporization of that component
∫0n ∫0n (q1 dn1 + q2 dn2) 1
2
(10)
and the molar isothermal enthalpy of vaporization (∆h) is
∆h )
∆H n1 + n2
(11)
The fact that the integral for the enthalpy of vaporization ∆H is independent of the path provides a basis for an integral test of thermodynamic consistency. Figure 1 shows two paths from zero loading to point P: path A is to preload component 1 and then add component 2 while holding n1 constant; path B is to preload component 2 and then add component 1 while holding n2 constant. If the two values of ∆H calculated from eq 10 agree, the isosteric heats q1 and q2 are thermodynamically consistent. The excess enthalpy (heat of mixing) in the adsorbed phase is the enthalpy of vaporization minus the enthalpy of vaporization of an ideal adsorbed solution
∆he ) ∆h -
∑i xi∆hi°
(12)
The enthalpies of vaporization of the pure components (∆hi°) are measured at the same spreading pressure as that for the mixture. For an ideal adsorbed solution, ∆he ) 0. The deviation of ∆he from zero is a measure of (8) Myers, A. L.; Calles, J. A.; Calleja, G. Comparison of Molecular Simulation of Adsorption with Experiment. Adsorption 1997, 3, 107.
Heats of Adsorption and Selectivity of Mixtures
Langmuir, Vol. 13, No. 16, 1997 4335
free energy (∆ge) is normally negative in the case of adsorption. Excess free energy in adsorption, as in bulk liquids, is dominated by enthalpy so ∆he is also negative. From eq 5, (qst)i ) hig - hia. Thus a negative heat of mixing in the adsorbed phase corresponds to experimental isosteric heats larger than those for an ideal solution. Molecular simulations3 show that mixture isosteric heats in nonideal systems are consistently larger that for an ideal solution. 3. Experimental Section
Figure 1. Integral consistency test for isosteric heats of adsorption. The isothermal enthalpy of vaporization ∆H calculated from eq 10 is the same for paths A and B.
adsorbed phase nonidealities. The excess enthalpy is related to the variation of adsorbed-phase activity coefficients with temperature
[
∆he ) -RT2
]
∂(∆ge/RT) ∂T
x
(13)
where the excess Gibbs free energy is
(∆ge/RT) )
∑i xi ln γi
(14)
For ideal adsorbed solutions (IAS), ∆ge ) ∆he ) 0 and individual isosteric heats of adsorption qi in mixtures can be predicted3 from the single-gas adsorption isotherms and single-gas isosteric heats by
ni°(qi - ∆hi°) )
ΣixiSi°ni°(qi° - ∆hi°) ΣixiSi°
(15)
where the degree sign refers to standard-state properties for the single gases, all measured at the same value of spreading pressure as the mixture. xi is the mole fraction of the ith component in the adsorbed phase, ni° is the loading of the pure gas in the standard state, and ∆hi° is the molar enthalpy of vaporization of pure adsorbate from eq 4. The weighting function Si° is
Si ° )
[
]
∂ ln ni° (n °)-2 ∂ ln Pi° T i
(16)
Si° is evaluated from the slope of the adsorption isotherm on a log-log plot. Equation 15 for IAS obeys the differential and integral tests for thermodynamic consistency. Equations 12-16 apply when the bulk phase is a perfect gas and its residual enthalpy is zero. At high pressure, corrections for the variation of the enthalpy of the bulk gas with pressure are necessary. IAS theory for isosteric heats is based upon the assumption that the heat of mixing in the adsorbed phase is zero. The theory accounts for cooperative interactions and for competition of different components for available sites. Nonideal mixing stems primarily from local segregation into regions of different composition within the micropores. This segregation effect, which stems from differences in the polarity, size, and shape of the adsorbate molecules, generates negative deviations from Raoult’s law (activity coefficients less than unity). The excess Gibbs
The multicomponent calorimeter shown in Figure 2 is similar in design to the single-component calorimeter described previously.9 The Pyrex cell within which adsorption occurs is surrounded by thermopiles and embedded in an aluminum heat sink. Pressure in the adsorption cell is measured by a pressure transducer with small dead space (≈0.5 cm3). Adsorbate is introduced into the cell by means of a 10 cm3 dosing loop which is connected to a six-port Valco sampling valve. The valve and loop are connected to the cell with a small bore tube (0.01 in i.d.). This tube contributes only 5 × 10-3 cm3 to a total cell volume of 20 cm3. The valve is electrically actuated and the dosing loop may be switched between the high-pressure dosing section (during loading of the sample loop) and the adsorption cell (during dosing of adsorbate into the cell). Gas phase composition in the cell is determined by a 0-100 amu residual gas analyzer (Leybold Inficon Model TSP C100F) connected to the cell by means of a manually operated leak valve (Granville-Phillips Model 203). The leak valve has a custom-built 8-in. extension which allows the valve to be controlled from outside the isothermal enclosure. The leak-valve orifice is located directly above the Pyrex cell (see blowup in Figure 2). High vacuum (< 10-8 Torr) is maintained on the analyzer side of the leak valve by means of a turbo molecular pumping station (Balzers Model TSU 062). Dimensions of the Pyrex cell were minimized to reduce mixing time in the gas phase; the longest distance inside the cell is 11 cm from its base to the leak-valve orifice. Figure 3 shows the time required to approach equilibrium for a mixture of CO2 and C2H6 in a cell containing no adsorbent. In 5 min the mole fraction is within 0.01 of the equilibrium value; in 10-15 min the mole fraction is within 0.001 of the equilibrium value. Helium Test. Adsorption isotherms and heats of adsorption of ethane on silicalite were measured with varying amounts of helium present in the sample cell. Helium was chosen as a second component because its adsorption is negligible at room temperature; therefore the heat of adsorption of ethane should be independent of the amount of helium present. Also, helium has a high diffusivity, and therefore tests the assumption of no backdiffusion of gas into the dosing loop. Figures 4 and 5 show that the equilibrium loading and heat of adsorption of ethane in the mixture are unaffected by the presence of helium. The adsorption isotherm for pure ethane was measured at 23.03 °C. The solid line on Figure 4 is the adsorption isotherm for pure ethane corrected to 19.92 °C using the heat of adsorption of ethane; the corrected adsorption isotherm agrees with the experimental data for adsorption of ethane at 19.92 °C in the presence of helium. The heats of adsorption of ethane in the presence of helium in Figure 5 agree with the heats of adsorption from pure ethane within the estimated experimental error (5%). Experimental Procedure. First the adsorbent is preloaded with component 2 to pressure Pc. Then the dosing loop is evacuated and filled to pressure Pd > Pc with component 1. The valve between the dosing loop and the sample cell is opened for two minutes and then closed to avoid back diffusion of the gas mixture into the dosing loop. The pressure in the dosing loop at this instant is recorded (Pdf) to determine the amount of component 1 dosed into the adsorption cell. The total heat released (Q) is measured by integrating the voltage signal from the thermopile until the signal returns to baseline, and the pressure Pc and composition of the gas phase (yc) in the sample cell have equilibrated with the adsorbed phase at the temperature (9) Dunne, J. A.; Mariwala, R.; Rao, M.; Sircar, S.; Gorte, R. J.; Myers, A. L. Calorimetric heats of adsorption and adsorption isotherms: 1. O2, N2, Ar, CO2, CH4, C2H6, and SF6 on silicalite. Langmuir 1996, 12, 5888.
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Dunne et al.
Figure 2. Schematic diagram of multicomponent calorimeter.
Figure 3. Equilibration time for gas-phase mixing of CO2 and C2H6 in a cell containing no adsorbent at 760 Torr. Mole fraction of CO2 after mixing {0.045, 0.504, 0.930}. of the calorimeter. Then dosing is alternated between the pure components to traverse a locus from infinite dilution to high concentration of component 1 in the adsorbed phase. The composition of the gas phase at equilibrium is measured by opening the leak valve to release a differential amount of the gas phase (≈0.05 µmol) to the analyzer. The amount of gas removed from the cell is negligibly small compared to an average dose (50-150 µmol) and does not disturb the equilibrium conditions in the sample cell. The incremental amount of each component adsorbed (∆ni) is calculated from a gas-phase material balance
∆ni )
1 d d d [V yi (P - Pdf) + Vc(Pc,i-1yic,i-1 - Pc,iyic,i)] RT
(17)
where V is volume, P is pressure, and yi is the mole fraction of component i in the gas phase. The superscripts d and c refer to the dosing loop and adsorption cell, respectively; the superscripts i - 1 and i refer to the state of the system prior to dosing the adsorbate and at equilibrium, respectively. The heat (Q) released by the incremental adsorption and desorption of both components (∆n1, ∆n2) is related to their individual heats of adsorption by
Figure 4. Adsorption isotherms of pure C2H6 and C2H6/He mixture in silicalite. (O) pure C2H6 at 23.03 °C; (solid line) pure C2H6 at 19.92 °C calculated from the Clapeyron equation; (b) C2H6/He mixture at 19.92 °C. For the mixture points, the partial pressure of He is as follows: 0 Torr for points 1-6; 2.6 Torr for points 7-9; 117.45 Torr for points 10-13; 244.90 Torr for mixture points 14-15.
QA ) q1∆n1A + q2∆n2A
(18)
QB ) q1∆n1B + q2∆n2B
(19)
where qi is the differential heat of adsorption of component i in the mixture. The individual heats of adsorption of each component (qi) are obtained from two experiments (A and B) as the solution of two simultaneous linear equations (18) and (19), one for the dosing of each pure component. Dosing the preferentially adsorbed species (1) displaces the other component (2) so that ∆n1 is positive and ∆n2 is negative. Doses are alternated between the two pure components; the solution of eqs 18 and 19 is undetermined for successive doses of mixtures of the same composition. The incremental loading ∆ni has an optimum: the value must be small enough to yield a differential heat but large enough to register an accurate value of Q. A sample calculation is given in the Appendix. Adsorbents and Pretreatment Procedure. Adsorption equilibria and heats of adsorption have been measured in silicalite
Heats of Adsorption and Selectivity of Mixtures
Langmuir, Vol. 13, No. 16, 1997 4337 Table 1. Isosteric Heat and Amount Adsorbed x1 P y1 adsorbed qst1 nt qst2 pressure gas phase amount phase heat heat (Torr) composition (mmol/g) composition (kJ/mol) (kJ/mol) C2H6 (1)-CH4 (2) in Silicalite at 25.29 °C (W ) 1.598 g) 53.75 0.000 0.064 0.000 21.30 111.21 0.000 0.126 0.000 20.59 177.98 0.000 0.195 0.000 20.44 253.81 0.000 0.267 0.000 20.19 270.48 0.0194 0.388 0.330 30.86 20.19 347.03 0.0157 0.450 0.284 30.91 21.06 365.31 0.0308 0.553 0.431 31.16 21.04 442.57 0.0264 0.608 0.391 31.14 20.85 463.75 0.0382 0.702 0.486 31.91 20.86 547.49 0.0341 0.754 0.451 31.93 21.04 573.28 0.0455 0.844 0.523 30.99 21.03
Figure 5. Isosteric heats of adsorption of pure C2H6 and C2H6/ He mixtures in silicalite: (O) pure C2H6 at 23.03 °C; (b) C2H6/ He mixture at 19.92 °C. For the mixture points, the partial pressure of He is as follows: 0 Torr for points 1-5; 2.6 Torr for points 6-8; 117.45 Torr for points 9-12; 244.90 Torr for points 13-14. and NaX. These samples are identical to those described previously.9,10 The bakeout procedure for NaX was modified slightly: 12 h at ambient temperature, temperature ramped from ambient to 400 °C over a period of 24 h, and finally 12 h at 400 °C.
4. Results for Mixtures of Ethane and Methane in Silicalite Multicomponent equilibria and heats of adsorption are reported in Table 1 for the system C2H6 (component 1) and CH4 (component 2) in silicalite. Since this mixture should be ideal, comparison of IAS theory with experiment is a check of the validity of the experimental procedure. To ensure adherence to IAS theory, the mixture was studied at low loadings in Henry’s law region. The loading of each component was less than 0.5 mmol/g. Figure 6 shows the locus traversed by the mixture calorimeter. First the adsorbent was preloaded with pure CH4 to a coverage of 0.267 mmol/g. Then successive doses of pure C2H6 (1) and pure CH4 (2) were added to the system until the total loading was 0.844 mmol/g, corresponding to a mole fraction in the adsorbed phase x1 ) 0.523. IAS calculations for this system are summarized in Table 2. Independent variables for the IAS calculation are T, P, and y1. Comparison of the experimental points with the predictions of IAS theory shows that the mixture is ideal as expected. The selectivity s1,2 ) (x1/y1)/(x2/y2) is plotted in Figure 7; experimental values are in the range s12) 23-25, which agree within the estimated experimental error of 5% with the IAS prediction s12 ) 23. The heat of adsorption of pure C2H6 increases slightly with coverage.9 The isosteric heats of pure C2H6 at coverages of 0 and 0.5 mmol/g are 31.1 and 31.4 kJ/mol, respectively. The isosteric heat of adsorption of pure CH4 at coverages between 0 and 0.5 mmol/g is 21.0 ( 0.1 kJ/ mol.9 If the heats of adsorption of the pure components are constant, IAS theory predicts that the heats of adsorption from the mixture are constant and equal to the value for the pure components. Thus the IAS prediction of isosteric heats for C2H6 and CH4 is 31.25 ( 0.2 and 21.0 ( 0.1 kJ/mol, respectively. Figure 8 shows (10) Dunne, J. A.; Rao, M.; Sircar, S.; Gorte, R. J.; Myers, A. L. Calorimetric heats of adsorption and adsorption isotherms: 2. O2, N2, Ar, CO2, CH4, C2H6, and SF6 on NaX, H-ZSM-5, and Na-ZSM-5 Zeolites. Langmuir 1996, 12, 5896.
14.22 27.67 40.73 54.99 69.16 71.66 87.06 92.04 110.69 119.89 134.06 147.33 178.92 204.04 227.19 291.71 334.53 383.61 438.69 495.75 569.94 636.18 724.73 781.01
CO2 (1)-C2H6 (2) in NaX at 29.4 °C (w ) 0.852 g) 0.000 0.205 0.000 0.000 0.398 0.000 0.000 0.586 0.000 0.000 0.786 0.000 0.000 0.980 0.000 0.002 1.141 0.143 49.45 0.002 1.332 0.122 49.46 0.005 1.510 0.229 47.73 0.004 1.695 0.204 47.74 0.008 1.902 0.296 46.82 0.007 2.016 0.279 46.84 0.011 2.215 0.350 45.60 0.024 2.590 0.458 0.023 2.701 0.439 44.34 0.033 2.877 0.481 42.93 0.053 3.256 0.562 0.049 3.344 0.547 42.16 0.070 3.529 0.583 41.42 0.085 3.704 0.617 0.073 3.766 0.607 40.49 0.101 3.935 0.639 40.65 0.109 4.064 0.664 0.098 4.117 0.655 40.49 0.121 4.205 0.671 41.33
26.73 26.61 26.73 27.02 27.88 27.88 28.08 28.08 28.18 28.18 28.69 28.69 28.75 28.75 30.70 30.70 30.08 30.08 32.75 32.78
CO2 (1)-C2H6 (2) in NaX at 28.94 °C (w ) 0.755 g) 13.82 0.000 0.224 0.000 29.86 0.000 0.482 0.000 27.35 45.60 0.000 0.735 0.000 27.80 61.80 0.000 0.990 0.000 28.16 79.13 0.000 1.249 0.000 28.43 98.66 0.000 1.517 0.000 29.29 119.41 0.000 1.768 0.000 29.50 144.60 0.000 2.026 0.000 30.09 174.38 0.000 2.275 0.000 30.73 209.74 0.000 2.506 0.000 31.12 226.61 0.002 2.677 0.072 51.75 31.12 250.56 0.001 2.787 0.070 51.77 31.27 275.49 0.003 2.956 0.134 49.99 31.27 297.60 0.003 3.028 0.130 50.21 32.63 332.50 0.006 3.198 0.191 49.00 32.64 370.71 0.008 3.354 0.243 415.99 0.007 3.439 0.237 48.06 32.61 463.57 0.011 3.581 0.284 47.52 32.61 504.96 0.010 3.637 0.280 47.52 32.59 554.16 0.016 3.754 0.318 46.51 32.60 614.34 0.013 3.813 0.314 46.70 33.16 674.74 0.021 3.929 0.352 46.15 33.17 737.10 0.016 3.974 0.349 46.30 33.57 801.70 0.024 4.082 0.385 46.76 33.54
that the experimental heats of adsorption agree quantitatively with IAS theory. The ideal behavior that we observed for mixtures of CH4 and C2H6 in silicalite disagrees with the results obtained by Hampson and Rees11 for mixtures of C2H6 (11) Hampson, J. A.; Rees, L. V. C. Adsorption of Ethane and Propane in Silicalite-1 and Zeolite NaY: Determination of Single Components, Mixture and Partial Adsorption Data using an Isosteric System. J. Chem. Soc., Faraday Trans. 1993, 89, 3169.
4338 Langmuir, Vol. 13, No. 16, 1997
Dunne et al. Table 2. IAS Calculations
n1, mmol/g P, Torr 253.81 270.48 347.03 365.31 442.57 463.75 547.49 573.28
exptl
y1 0.0 0.0194 0.0157 0.0308 0.0264 0.0382 0.0341 0.0455
0.0 0.128 0.128 0.238 0.238 0.341 0.340 0.442
n2, mmol/g
IAS
exptl
C2H6 (1)-CH4 (2) in Silicalite at 25.29 °C 0.0 0.267 0.267 0.119 0.260 0.265 0.120 0.323 0.330 0.235 0.315 0.323 0.237 0.370 0.380 0.341 0.361 0.373 0.348 0.414 0.426 0.459 0.402 0.416 P, Torr
nt, mmol/g
x1
exptl
qst1, kJ/mol
IAS
y1 IAS
exptl
0.980 1.141 1.332 1.510 1.695 1.902 2.016 2.215 2.590 2.701 2.877 3.256 3.344 3.529 3.704 3.766 3.935 4.064 4.117 4.205
0.0 0.143 0.122 0.229 0.204 0.296 0.279 0.350 0.458 0.439 0.481 0.562 0.547 0.583 0.617 0.607 0.639 0.664 0.655 0.671
69.2 71.7 87.1 92.0 110.7 119.9 134.1 147.3 178.9 204.0 227.2 291.7 334.5 383.6 438.7 495.8 569.9 636.2 724.7 781.0
2.506 2.677 2.787 2.956 3.028 3.198 3.354 3.439 3.581 3.637 3.754 3.813 3.929 3.974 4.082
0.0 0.072 0.070 0.134 0.130 0.191 0.243 0.237 0.284 0.280 0.318 0.314 0.352 0.349 0.385
209.7 226.6 250.6 275.5 297.6 332.5 370.7 416.0 463.6 505.0 554.2 614.3 674.7 737.1 801.7
CO2 (1)-C2H6 (2) in NaX at 28.94 °C 237.0 0.0 0.0 277.8 0.002 0.0025 310.9 0.001 0.0026 377.2 0.003 0.0058 413.4 0.003 0.0058 526.4 0.006 0.0098 682.9 0.008 0.0140 826.0 0.007 0.0137 1134 0.011 0.0176 1363 0.010 0.0171 1876 0.016 0.0196 2458 0.013 0.0185 3518 0.021 0.0202 4621 0.016 0.0186 6633 0.024 0.0195
5. Results for Mixtures of Carbon Dioxide and Ethane in NaX This system of a quadrupolar (CO2) and nonpolar (C2H6) mixture in an adsorbent with a strong electric field (NaX) is expected to show strong deviations from ideality. The
IAS
exptl
IAS
30.9 30.9 31.2 31.2 31.9 31.9 31.0
31.2 31.2 31.2 31.2 31.2 31.2 31.2 31.2
20.2 20.2 21.1 21.1 20.9 20.9 21.0 21.0
21.0 21.0 21.0 21.0 21.0 21.0 21.0 21.0
qst1, kJ/mol IAS
CO2 (1)-C2H6 (2) in NaX at 29.4 °C 67.8 0.0 0.0 72.1 0.002 0.0030 87.6 0.002 0.0027 95.3 0.005 0.0063 114.1 0.004 0.0058 128.8 0.008 0.0106 144.4 0.007 0.0102 166.1 0.011 0.0158 221.4 0.024 0.0298 252.1 0.023 0.0286 292.1 0.033 0.0359 417.7 0.053 0.0536 484.7 0.049 0.0512 600.0 0.070 0.0594 739.8 0.085 0.0673 851.0 0.073 0.0642 1062. 0.101 0.0707 1251. 0.109 0.0758 1459. 0.098 0.0714 1647. 0.121 0.0740
and C3H8 in silicalite at 298 K using the method of isosteres. Their pure-component heats of adsorption for C2H6 (31 kJ/mol) are in excellent agreement with our calorimetric heats, but Hampson and Rees reported heats of adsorption of C2H6 from mixtures much lower than the values for pure C4H6, even at low coverage. In summary, the system of C2H6 and CH4 mixtures on silicalite at low coverage was selected specifically for its expected ideal behavior. Experimental data for loading and selectivity confirmed that the adsorbed solution is ideal. Quantitative agreement of the calorimetric heats of adsorption with values predicted by IAS theory confirms the accuracy of the experimental procedure for measuring heats of adsorption from mixtures.
qst2, kJ/mol
exptl
exptl
49.4 49.5 47.7 47.7 46.8 46.8 45.6 44.3 42.9 42.2 41.4 40.5 40.6 40.5 41.3
51.8 51.8 50.0 50.2 49.0 48.1 47.5 47.5 46.5 46.7 46.2 46.3 46.8
qst2, kJ/mol
IAS
exptl
IAS
48.2 47.7 47.7 47.1 47.1 46.2 46.2 45.4 43.0 42.9 41.8 39.3 39.0 38.0 37.1 37.0 36.4 36.1 36.1 36.0
27.9 27.9 28.1 28.1 28.2 28.2 28.7 28.7
28.2 28.1 28.4 28.4 28.8 28.8 29.0 29.0 28.5 28.6 28.3 27.1 27.0 26.3 25.6 25.5 25.0 24.8 24.7 24.6
49.0 48.3 48.4 46.9 46.8 44.8 42.6 42.0 39.8 39.2 37.7 37.2 36.5 36.4 36.3
31.1 31.1 31.3 31.3 32.6 32.6
28.8 28.8 30.7 30.7 30.1 30.1 32.8 32.8
32.6 32.6 32.6 32.6 33.2 33.2 33.6 33.5
31.4 31.6 32.0 31.8 32.0 31.3 30.2 29.9 28.3 27.9 26.6 26.1 25.3 25.2 25.2
degree of nonideality in the adsorbed phase should increase with loading. Low Preloading of Ethane. The loci traversed in the adsorbed phase are shown in Figure 9. In the first run (points designated by •) the adsorbent was preloaded with 0.98 mmol/g of C2H6. Doses were then alternated between pure CO2 and pure C2H6 until CO2 began to displace C2H6 from the adsorbed phase. The amount of ethane in the adsorbed phase was held approximately constant by manipulating the size of the doses. For the last 15 experimental points, the loading of C2H6 is constant (1.431 ( 0.055) mmol/g. The experimental points are given in Table 1. The experimental points are compared with the predictions of IAS theory in Table 2. Independent variables for the IAS calculations are T, nt, and x1. The selectivity s12 ) (x1/y1)/(x2/y2) of NaX for CO2 (1) relative to C2H6 (2) is plotted (n2 ≈ 1.4 mmol/g) on Figure 10. Comparison with IAS (dashed line) shows substantial deviations from ideality. Since s12 ) (P2°/P1°)(γ2/γ1), at low mole fractions of CO2, γ2 approaches unity and γ1 < 1, so the experimental
Heats of Adsorption and Selectivity of Mixtures
Langmuir, Vol. 13, No. 16, 1997 4339
Figure 6. Locus for adsorption of mixtures of C2H6 and CH4 in silicalite at 25.29 °C, amount of CH4 in adsorbed phase versus amount of C2H6 in adsorbed phase.
Figure 8. Isosteric heats of adsorption of C2H6 and CH4 in silicalite at 25.29 °C: (O) C2H6 in mixture; (0) CH4 in mixture; (dashed lines) IAS calculation.
Figure 7. Selectivity s12 ) (x1/y1)/(x2/y2) of silicalite for mixtures of C2H6 (1) and CH4 (2) at 25.29 °C: (b) experimental data; (dashed line) IAS calculation.
value of selectivity is higher than that of the IAS prediction (γ1 ) γ2 ) 1). At the equimolar concentration x1 ) 0.5, the activity coefficients are equal and the IAS predictions intersect the experimental data. The activity coefficient at infinite dilution of CO2 obtained by extrapolation of the selectivity to x1 f 0 is γ1∞ ) 71/88.5 ) 0.80. Thus the deviations from Raoult’s law are negative (ln γ < 0), which is the usual behavior discussed previously. The isosteric heats of adsorption for low preloading of ethane (1.4 mmol/g) are shown in Figure 11. The heat of adsorption of CO2 decreases with coverage from an infinitedilution value of 49 to 40 kJ/mol at a CO2 loading of 2.5 mmol/g. The IAS prediction agrees with experiment at low loading of CO2. At a CO2 loading of 2.5 mmol/g, the experimental heats are 5 kJ/mol higher than the IAS predictions. The heat of adsorption of C2H6 is nearly constant until the loading of CO2 is above 2 mmol/g. At a CO2 loading of 2.5 mmol/g, the heats of adsorption of C2H6 are 8 kJ/mol higher than those of the IAS predictions. High Preloading of Ethane. For the second run, the preloaded amount of ethane was maintained constant at 2.57 ( 0.04 mmol/g. The experimental points are given in Table 1, and IAS calculations are summarized in Table
Figure 9. Locus for adsorption of mixtures of CO2 and C2H6 in NaX: (b) low preloading of C2H6, 29.4 °C; (O) high preloading of C2H6, 28.94 °C. Amount of C2H6 in adsorbed phase versus amount of CO2 in adsorbed phase.
2. Independent variables for the IAS calculations are T, nt, and x1. Values of P and y1 calculated for the last seven points in the table are uncertain due to extrapolation for the standard-state pressure P2°. The calculated isosteric heats are, however, insensitive to this extrapolation. Since the second run has a higher loading of ethane, the deviations from ideality are larger than those in the first run. Figure 12 shows that the ideal selectivity of 33 at infinite dilution is much smaller than the experimental value of 60, indicating an activity coefficient at infinite dilution γ1∞ ) 33/60 ) 0.55. The accuracy of the experimental selectivity below x1 ) 0.1 is poor because of uncertainty in the composition of the equilibrium gas phase. The isosteric heats of adsorption for high preloading of ethane (2.57 mmol/g) are shown in Figure 13. The isosteric heats of CO2 and C2H6 are about 10 kJ/mol higher than the IAS predictions at high loading of CO2. 6. Conclusions Adsorption isotherms and heats of adsorption have been measured simultaneously in a microcalorimeter designed especially for mixtures. A key design feature is a short diffusion path (
