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Adsorption Equilibrium of Binary Methane/Ethane Mixtures in BPL Activated Carbon: Isotherms and Calorimetric Heats of Adsorption Yufeng He, Jeong-Ho Yun,† and Nigel A. Seaton* Institute for Materials and Processes, School of Engineering and Electronics, University of Edinburgh, Kenneth Denbigh Building, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom Received December 22, 2003. In Final Form: May 2, 2004 The adsorption of pure methane and ethane in BPL activated carbon has been measured at temperatures between 264 and 373 K and at pressures up to 3.3 MPa with a bench-scale high-pressure open-flow apparatus. The same apparatus was used to measure the adsorption of binary methane/ethane mixtures in BPL at 301.4 K and at pressures up to 2.6 MPa. Thermodynamic consistency tests demonstrate that the data are thermodynamically consistent. In contrast to two sets of data previously published, we found that the adsorption of binary methane/ethane in BPL behaves ideally (in the sense of obeying ideal adsorbed solution theory, IAST) throughout the pressure and gas-phase composition range studied. A Tian-Calvet type microcalorimeter was used to measure low-pressure isotherms, the isosteric heats of adsorption of pure methane and ethane in BPL activated carbon, and the individual heats of adsorption in binary mixtures, at 297 K and at pressures up to 100 kPa. The mixture heats of adsorption were consistent with IAST.
1. Introduction Activated carbon is widely used in adsorption separation processes as a result of its attractive adsorption properties. There are correspondingly large amounts of data published for the adsorption isotherms of pure and multicomponent gases in activated carbon.1-7 In general, pure-gas adsorption isotherms are easy and straightforward to measure experimentally with a high accuracy. Multicomponent adsorption equilibrium data are much more time consuming and expensive to obtain because a further variable (gas-phase composition) is introduced;8 multicomponent data are, thus, much scarcer. Multicomponent adsorption equilibrium is a key factor in the design and operation of industrial processes based on the equilibrium separation, such as pressure swing adsorption (PSA) and temperature swing adsorption processes. In a PSA separation process, Hartzog and Sircar9 have shown that the accuracy of process simulation results depends heavily upon the accuracy of the multicomponent equilibrium data input, especially when stringent product specifications are imposed. They have concluded that the representation of the multicomponent adsorption equilibrium must be accurate within 2% to obtain an accurate process model. Therefore, accurately measured adsorption equilibrium * Corresponding author. † Present address: Aspen Technology, Ltd., Titan House, Castle Park, Cambridge CB3 0AY, United Kingdom. E-mail:
[email protected]. (1) Reich, R.; Zeigler, W. T.; Rogers, K. A. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 336. (2) Rudisill, E. N.; Jacskaylo, J. J.; LeVan, M. D. Ind. Eng. Chem. Res. 1992, 31, 1122. (3) Eissmann, R. N.; LeVan, M. D. Ind. Eng. Chem. Res. 1993, 32, 2752. (4) Russell, B. P.; LeVan, M. D. Ind. Eng. Chem. Res. 1997, 36, 2380. (5) Taqvi, S. M.; Appel, W. S.; LeVan, M. D. Ind. Eng. Chem. Res. 1999, 38, 240. (6) Costa, E.; Sotelo, J. L.; Calleja, G.; Marron, C. AIChE J. 1981, 27 (1), 5. (7) Salame, I. I.; Bandosz, T. J. Langmuir 1999, 15, 587. (8) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: London, 1997. (9) Hartzog, D. G.; Sircar, S. Presented at the AIChE Annual Meeting, St. Louis, MO, 1993.
data are essential for the prediction of the multicomponent adsorption equilibrium and the development of adsorption theory. In the case of activated carbon, the inherent heterogeneity of the material adds another dimension to the study of multicomponent adsorption.10 Reich et al.1 carried out multicomponent adsorption of binary methane/ ethane in BPL activated carbon and found that the methane/ethane/BPL activated carbon adsorption system behaves nonideally, in the sense of deviating strongly from ideal adsorbed solution theory (IAST); this would not have been expected on the basis of bulk thermodynamics as methane and ethane closely follow Raoult’s law in the liquid phase. This conclusion was supported by the measurements of Gusev et al.11 As well as isotherm data, heats of adsorption are required both to evaluate theories of adsorption equilibrium and to calculate energy balances for adsorption processes. Heats of adsorption for pure-component adsorption may be obtained from the Clausius-Clayperon equation by evaluating the adsorption isotherms at different temperatures at constant loading.12 For mixtures, Sircar13,14 proposed a Gibbs surface excess thermodynamic model for the calculation of “isoexcess heat of adsorption” of each component in a binary adsorption experiment. The data requirements for this model are substantial (the amount adsorbed for each species as a function of P at constant T and yi, the amount adsorbed for each species as a function of T at constant P and yi, and the amount adsorbed for each species as a function of yi, at constant P and T), and we are not aware of this method being used in practice. In contrast, multicomponent adsorption microcalorimetry15-17 provides a more direct route to measure the isosteric heat of adsorption in mixtures and it is this approach that we use in this work. (10) Nguyen, C.; Do, D. D. Langmuir 2001, 17, 1552. (11) Gusev, V. Y.; O’Brien, B. J. A.; Jensen, C. R. C.; Seaton, N. A. AIChE J. 1996, 42 (10), 2773. (12) Valenzuela, D. P.; Myers, A. L. Adsorption Equilibrium Data Handbook; Prentice Hall: Englewood Cliffs, 1989. (13) Sircar, S. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1527. (14) Sircar, S. Ind. Eng. Chem. Res. 1999, 38, 3670.
10.1021/la036430v CCC: $27.50 © 2004 American Chemical Society Published on Web 07/01/2004
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Figure 1. Schematic diagram of the microcalorimeter.
In this paper, we revisit the system methane/ethane/ BPL, using a combination of high-pressure adsorption measurements and microcalorimetry, for both pure gases and binary mixtures. By using these complementary methods, we hoped to better understand the origin of the nonideal adsorption in this system. In fact, we will demonstrate that our measurements are quite different from the earlier results of Reich et al.1 and Gusev et al.,11 showing a high degree of ideality in both the mixture adsorption isotherms and the heats of adsorption of the individual components in the mixture. We are, thus, reporting detailed measurements, using two different techniques, which substantially disagree with the earlier work. 2. Experimental Section 2.1. Materials. Microporous BPL activated carbon (6 × 16 mesh), supplied by the Calgon Carbon Corp., was used in this study. The specific BET surface area and average pore size for this sample are 1061 m2/g and 10.2 Å, respectively, obtained by evaluating the standard nitrogen adsorption isotherm at 77 K. The methane and ethane gases were supplied by BOC with a purity of 99.99%. The gases were dried with 5A molecular sieves packed in cylinders before they eventually enter the adsorption system. 2.2. Apparatus and Procedure. A bench-scale high-pressure open-flow adsorption/desorption apparatus was used to measure adsorption isotherms of pure methane and ethane in the BPL activated carbon, at temperatures from 264.6 to 373.2 K and pressures up to 3.3 MPa. The adsorption of binary methane/ ethane mixtures in BPL activated carbon was carried out at 301.4 K with pressure up to 2.6 MPa. This apparatus uses a static volumetric method to obtain the pure-gas adsorption isotherms and a flow-through method to measure the binary adsorption isotherms. A total of 5.61 g of BPL activated carbon was used in this study, and the samples were regenerated at 423 (15) Dunne, J. A.; Mariwala, R.; Rao, M.; Sircar, S.; Gorte, R. J.; Myers, A. L. Langmuir 1996, 12, 5888. (16) Dunne, J. A.; Mariwala, R.; Sircar, S.; Gorte, R. J.; Myers, A. L. Langmuir 1997, 13, 4333. (17) Parrillo, D. J.; Gorte, R. J. Thermochim. Acta 1998, 312, 125.
K under a vacuum of less than 2 × 10-4 kPa for at least 2 h before each measurement. More details of the description of the apparatus and operating procedures can be found in ref 18. The uncertainties of the pure and binary isotherm data in this study are less than 0.2 and 1.5%, respectively. A Tian-Calvet type microcalorimeter was designed and constructed in our laboratory following the original design of a microcalorimeter for chemisorption studies by Gorte et al.15,19 A schematic diagram of the microcalorimeter is shown in Figure 1. A cubic Pyrex glass cell, with a volume about 20 cm3, is used as the adsorber. The sample (1.40 g in this case) is placed on the bottom the cell. The cell is surrounded on the bottom and the four sides by five square thermal-flux meters. The cell and the flux meters are placed inside a large aluminum block to allow rapid heat dissipation while minimizing the temperature variation of the system. A total of 3.0 g of glass beads is placed on top of the samples to minimize the loss of heat in an upward direction. The flux meters, type C-702, supplied by the International Thermal Instrument Co., are connected in series and generate a voltage signal, proportional to the instantaneous heat flux, during an adsorption or a desorption process. The area under the signal, obtained by numerical integration using the trapezoidal rule, is proportional to the amount of heat absorbed or released. The output signal generated by the flux meters is collected by a personal-computer-controlled data shuttle from Omega, Ltd. The cell is connected to a gas dosing loop by a Valco six-way valve. An Omega PX425 pressure transducer is connected to the cell because the dead volume of the pressure transducer is small, so it does not add much of the dead volume of the cell. All the components just mentioned are placed in an isothermal calorimetric unit. The temperature inside the calorimetric unit is controlled by a heater connected to a K-type thermopile, supplied by RS Components, Ltd. The Valco six-way valves connect the cell, the dosing loop, and the reference cell. A MKS (type 626) absolute pressure transducer is used to measure the pressure in the reference cell and the dosing loop. In a binary mixture experiment, the gas-phase composition is determined (18) Yun, J.-H.; Duren, T.; Keil, F. J.; Seaton, N. A. Langmuir 2002, 18, 2693. (19) Parrillo, D. J.; Gorte, R. J. Catal. Lett. 1992, 16, 17.
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Table 1. Pure-Gas Adsorption of Methane in BPL Activated Carbon 264.2 K P (kPa)
n (mmol/ g)
0.60 1.08 3.04 3.93 6.65 15.89 22.56 39.87 63.07 108.00 160.13 244.39 471.85 865.45 1364.37 1878.49 2255.28 2681.67 3160.72
0.025 0.043 0.109 0.137 0.211 0.412 0.530 0.791 1.054 1.454 1.816 2.269 3.101 3.941 4.570 4.982 5.198 5.387 5.546
301.4 K P (kPa)
n (mmol/ g)
1.03 1.97 4.72 8.33 13.19 23.44 46.00 46.02 82.66 94.90 123.86 178.39 185.85 227.45 264.38 350.10 401.97 529.02 546.49 874.99 1285.76 1862.51 2536.59 3220.67
0.013 0.024 0.055 0.093 0.140 0.230 0.411 0.397 0.638 0.684 0.848 1.060 1.111 1.257 1.390 1.613 1.784 2.073 2.084 2.637 3.133 3.621 3.999 4.263
333.2 K
Table 2. Pure-Gas Adsorption of Ethane in BPL Activated Carbon
373.2 K
264.2 K
P (kPa)
n (mmol/ g)
P (kPa)
n (mmol/ g)
0.40 1.68 2.88 4.96 8.24 17.51 26.04 43.83 48.80 62.27 72.26 96.40 102.13 131.73 142.00 177.46 208.66 238.66 313.86 322.39 398.52 495.85 541.99 715.05 935.71 1239.84 1574.09 1900.22 2155.81 2342.74 2775.93 3244.32
0.002 0.009 0.016 0.027 0.044 0.089 0.129 0.205 0.230 0.278 0.324 0.402 0.436 0.535 0.545 0.662 0.731 0.820 0.989 0.997 1.162 1.345 1.403 1.681 1.943 2.295 2.543 2.774 2.929 3.031 3.233 3.419
0.96 1.21 1.88 1.96 4.28 4.52 8.00 8.12 13.09 13.51 15.28 24.78 38.58 52.17 54.49 66.57 84.10 100.13 104.15 105.91 135.72 157.99 196.92 285.31 358.77 392.23 435.56 639.68 1032.32 1347.36 2230.75 2979.35
0.002 0.003 0.004 0.005 0.010 0.011 0.019 0.019 0.031 0.032 0.037 0.059 0.090 0.120 0.124 0.151 0.187 0.217 0.217 0.230 0.290 0.324 0.397 0.524 0.653 0.678 0.706 0.950 1.282 1.537 2.069 2.396
by a Leybold Inficon TSP C100F residual gas analyzer, with trace amounts of gas introduced by a Granville-Phillips 203 leak valve. The pure-gas adsorption isotherm is obtained by a static volumetric technique. In this technique, the temperature, pressure, and volume of the gas are measured in the sample cell, the dosing loop, and the reference cell before and after the gas contacts the adsorbent. These data are then used to calculate the extent of adsorption, ni, by the gas equation of state:
PVyi ) niZRT
n (mmol/ g)
0.43 1.45 2.80 3.25 6.73 6.80 11.75 16.67 23.47 38.40 45.47 80.40 136.80 136.80 209.59 272.13 313.59 377.32 461.59 542.25 629.32 725.18 803.85 866.78 945.44 1038.91 1132.51 1221.70 1296.37
0.452 0.845 1.200 1.243 1.734 1.769 2.208 2.575 2.921 3.437 3.602 4.226 4.788 4.771 5.244 5.527 5.662 5.887 6.109 6.257 6.434 6.569 6.634 6.723 6.765 6.860 6.922 6.973 6.976
P (kPa)
n (mmol/ g)
0.11 0.32 0.73 1.08 1.72 2.23 3.21 4.48 7.67 8.35 12.57 12.80 16.56 24.19 41.07 88.53 90.37 164.00 188.80 211.86 402.39 520.12 568.39 791.98 877.31 1086.37 1170.10 1491.56 1901.55 2172.08 2376.74
0.045 0.110 0.181 0.256 0.349 0.389 0.517 0.600 0.846 0.862 1.104 1.116 1.253 1.539 1.972 2.759 2.772 3.432 3.576 3.718 4.406 4.673 4.785 5.095 5.207 5.427 5.444 5.654 5.794 5.818 5.852
333.2 K P (kPa)
n (mmol/ g)
0.29 0.35 0.91 1.65 3.33 6.79 9.67 13.51 23.11 24.55 37.84 46.83 56.93 94.26 149.46 305.73 341.32 501.32 762.91 799.05 1376.23 1497.16 1863.02 2019.95 2279.94 2562.87 2839.00 3151.39 3368.32
0.035 0.043 0.094 0.153 0.255 0.414 0.514 0.638 0.877 0.902 1.157 1.289 1.446 1.860 2.303 3.067 3.173 3.613 4.041 4.110 4.599 4.678 4.835 4.850 4.925 4.952 4.933 4.853 4.781
373.2 K P (kPa)
n (mmol/ g)
0.53 0.87 1.59 2.56 4.27 7.87 13.07 23.44 40.31 62.43 90.66 104.93 120.40 211.19 288.93 370.26 593.19 685.05 925.98 1206.10 1287.03 1603.69 1858.75 2080.08 2458.34 2907.26 3248.19
0.018 0.030 0.051 0.078 0.121 0.198 0.292 0.444 0.639 0.843 1.057 1.151 1.250 1.689 1.981 2.220 2.712 2.863 3.181 3.443 3.509 3.699 3.813 3.891 3.972 3.949 3.923
first to get the amount adsorbed and the differential heat of adsorption for this species; then the strongly adsorbed gas (gas 2) is introduced into the adsorber. The total amount adsorbed will increase, and the bulk-gas and adsorbed phase compositions vary. This process is repeated as successive doses of the two gases are added. For the addition of a dose of gas 1 in step i, the heat, Qi, generated in this step is related to the individual differential heat of adsorption of the two components by
Qi ) qd1,i∆n1,i + qd2,i-1∆n2,i
(3)
(1)
where P, T, V, and yi are the pressure; the temperature; the volume of the sample cell, dosing loop, and reference cell; and the bulk-phase composition, respectively. The compressibility factor of the bulk phase, Z, is calculated using the Peng-Robinson equation. R is the universal gas constant. yi becomes unity when eq 1 is applied in the calculation of a pure component. At the same time, the heat of adsorption is determined by evaluating the signal generated by the five flux meters. Before each adsorption measurement, the calorimeter is run for about 10 min, and the signal from the series of the flux meters is collected, recorded, and averaged. If the starting value, ending value, and average value of the signal in this 10-min period are consistent with each other, then the average value of the signal is assumed to be the baseline for the next adsorption or desorption measurement. After the baseline is equilibrated and recorded, an amount of gas is introduced into the glass cell. The heat of adsorption released generates a signal from the flux meters that is recorded until the value of the signal returns to the baseline. The isosteric heat of adsorption, qst, is the partial molar enthalpy change of adsorption and is widely used to characterize adsorption heterogeneity, as well as in enthalpy balances in industrial adsorption processes. In contrast, in this design of a calorimeter, the differential heat of adsorption, qd, is measured.15 These two quantities are related by
qst ) qd + ZRT
P (kPa)
301.4 K
(2)
In a binary-mixture adsorption experiment with the calorimeter, the less strongly adsorbed gas (gas 1) is introduced to the adsorber
where ∆n1,i and ∆n2,i are the incremental adsorption and desorption of the two gases, which are obtained by applying the gas equation of state, shown in eq 1; qd1,i is the individual differential heat of adsorption of component 1 in this step, while qd2,i-1 is assumed to be the value of the previous dose of the pure gas 2, because the incremental adsorption and desorption of the gas 2 is quite small in this step. Similarly, for the addition of a dose of gas 2 in step j, the heat, Qj, generated in this process is related to the individual differential heat of adsorption of the two components by
Qj ) qd1,j-1∆n1,j + qd2,j∆n2,j
(4)
Therefore, the individual isosteric heat of adsorption in a binary mixture adsorption experiment can be obtained by eqs 2-4. The sample regeneration procedure is the same as that for the high-pressure apparatus. The uncertainties in the pure-gas and binary isotherm data obtained with the calorimeter are less than 0.2 and 1.5%, respectively. The uncertainty in the isosteric heat of adsorption comes mainly from the stability of the baseline of the signal from the flux meters, which reflects fluctuations in the temperature of the calorimetric unit; this error is about 3%. The microcalorimeter was used to measure the isotherms and the heats of adsorption for pure methane and ethane and their binary mixtures in BPL at 297 K and at pressures up to 100 kPa. Prior to any measurements of the heat of adsorption with the microcalorimeter, the flux meters must be calibrated to convert the area under the signal to the amount of heat released or consumed during the experiment.15 We used a self-consistent method which involves evaluating the heat of adsorption of
Methane/Ethane Mixtures in BPL Activated Carbon
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Figure 2. Adsorption isotherms of pure methane in BPL activated carbon.
Figure 3. Adsorption isotherms of pure ethane in BPL activated carbon. adsorption of carbon dioxide in a series of pure-silica MCM-41 samples with different pore sizes. Adsorption isotherms of CO2 in MCM-41 at different temperatures were first obtained with the high-pressure volumetric apparatus, and the isosteric heat of adsorption of CO2 in MCM-41 samples was obtained by the Clausius-Clapeyron equation. Then the heat released in the adsorption process, Q, was calculated from
calibration constant, and Sarea is the area under the signal. The calibration constant for the calorimeter obtained in this way is 1.993 mJ/W. This constant was then used to measure the isosteric heat of adsorption of ethane in the same MCM-41 materials, with excellent agreement between the values obtained with the two methods (the Clausius-Clapeyron equation applied to the isotherm data and the microcalorimetry).
Q ) qst∆n ) KfmSarea
3. Results and Discussion
(5)
where ∆n is the incremental adsorption of CO2, Kfm is the
3.1. Experimental Data. The isotherms for the adsorption of pure methane and ethane in BPL, obtained
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Table 3. Parameters for the Jensen-Seaton Equations for the Isotherms of Pure Methane and Ethane in BPL species
temp (K)
R (mmol/g)
K [mmol/(g kPa)]
t
κ (1/kPa)
error (%)
methane (CH4)
264.15 301.35 333.15 373.15 264.15 301.35 333.15 373.15
14.61 10.56 8.461 3.628 14.49 15.40 14.39 16.38
5.560 × 10-2 1.422 × 10-2 6.031 × 10-3 2.546 × 10-3 8.392 9.839 × 10-1 2.054 × 10-1 5.716 × 10-2
0.3814 0.4776 0.5573 0.7715 0.2559 0.2773 0.3168 0.3292
-4.509 × 10-5 -2.736 × 10-5 -1.571 × 10-5 1.079 × 10-4 -6.131 × 10-5 -8.080 × 10-5 -8.945 × 10-5 -1.066 × 10-4
0.719 1.110 1.249 2.619 1.079 1.913 1.015 1.670
ethane (C2H6)
Table 4. Calorimetric Pure Methane Adsorption in BPL at 297 K
Table 5. Calorimetric Pure Ethane Adsorption in BPL at 297 K
P (kPa)
n (mmol/g)
qst (kJ/mol)
P (kPa)
n (mmol/g)
qst (kJ/mol)
P (kPa)
n (mmol/g)
qst (kJ/mol)
P (kPa)
n (mmol/g)
qst (kJ/mol)
3.21 3.75 7.77 13.32 13.37 19.07 25.21 28.91 32.01 35.07
0.044 0.051 0.100 0.163 0.162 0.220 0.277 0.312 0.337 0.365
22.48 22.36 22.68 21.81 22.57 21.82 21.52 22.03 21.57 21.79
38.97 46.80 48.78 54.07 62.38 63.69 71.02 80.46 89.30 97.80
0.394 0.453 0.472 0.505 0.563 0.576 0.619 0.677 0.729 0.777
20.87 20.90 20.50 20.77 20.70 20.31 19.97 20.08 20.82 20.12
0.08 0.11 0.18 0.25 0.32 0.45 0.46 0.68 0.71 0.93 1.02 1.24 1.39 1.57 1.80 1.99 2.30 2.45 2.92 3.02 3.56 3.65 4.18 4.42 4.94 5.35 5.67 6.39 6.58 7.35
0.031 0.044 0.077 0.096 0.126 0.153 0.169 0.224 0.217 0.279 0.280 0.336 0.344 0.391 0.407 0.451 0.475 0.511 0.548 0.579 0.635 0.625 0.696 0.699 0.764 0.778 0.823 0.858 0.892 0.946
38.14 32.86 33.70 32.00 32.46 32.09 32.87 32.71 31.54 32.11 30.80 29.86 30.35 30.49 30.44 30.07 29.06 29.77 29.28 30.82 29.39 29.26 30.14 27.87 29.83 27.21 27.68 29.03 29.48 28.38
7.54 8.41 8.77 9.66 10.17 10.91 11.50 12.43 12.91 14.01 14.55 16.31 18.04 19.96 22.20 24.52 26.97 29.60 32.76 36.06 39.64 43.53 47.72 52.15 56.98 61.91 67.37 73.08 78.74
0.940 1.015 1.019 1.091 1.101 1.162 1.174 1.241 1.246 1.318 1.324 1.403 1.482 1.556 1.638 1.716 1.795 1.873 1.960 2.045 2.134 2.224 2.325 2.413 2.503 2.589 2.676 2.762 2.841
28.53
with the high-pressure apparatus at four different temperatures, are presented in Tables 1 and 2, respectively. The pure-gas isotherms were correlated with the JensenSeaton equation,20
[ (
n ) KP 1 +
KP R(1 + κP)
)]
t -1/t
(6)
The Jensen-Seaton equation allows for the compressibility of the adsorbed phase, κ; therefore, it gives an accurate fit to the adsorption isotherms at high pressures. Figures 2 and 3 show fitted Jensen-Seaton isotherms together with the experimental data for respectively pure methane and ethane. Clearly, the Jensen-Seaton equation fits the pure adsorption isotherms of methane and ethane in BPL quite accurately across the whole temperature and pressure range; the relative error is less than 2%. The constants for the Jensen-Seaton equations are shown in Table 3. Calorimetric isosteric heats of adsorption together with the adsorption isotherms of pure methane and ethane at 297 K are presented in Tables 4 and 5, respectively. The pure-gas isotherms were correlated with the JensenSeaton equation, but because the highest pressure is still quite low, κ was set to be 0 (in which case the JensenSeaton isotherm reduces to the Toth isotherm) without any significant reduction in the goodness of fit. The puregas isosteric heats of adsorption were fitted with the following virial equation:21
qst ) R(k1 + b1n + c1n2 + d1n3)
(7)
The average errors are about 0.2% for the fitting of the Toth equation to the low-pressure data, approximately the same as for the experimental data themselves, and 1.2% for the virial equation for the isosteric heat of adsorption, smaller than the experimental error. The fitting parameters are summarized in Table 6. The fits together with the experimental data are shown in Figure 4 for the isotherms and in Figure 5 for the isosteric heat of adsorption. The isosteric heats of adsorption of pure methane and ethane in BPL were also calculated from the Clausius-Clapeyron equation by evaluating the adsorption isotherms obtained with the high-pressure apparatus, shown in Figures 2 and 3, and the results are (20) Jensen, C. R. C.; Seaton, N. A. Langmuir 1996, 12, 2866. (21) Talu, O. Adv. Colloid Interface Sci. 1998, 76-77, 227.
29.02 28.45 28.21 27.65 28.58 27.28 28.54 27.21 26.98 26.67 27.50 27.35 27.15 26.94 26.80 26.79 26.64 26.12 26.29 25.74 25.70 25.83 25.45 25.53 25.53
Table 6. Fitting Parameters for the Toth and Virial Equations of Isotherms and Isosteric Heats of Adsorption of Pure Methane and Ethane in BPL at 297 K ethane (C2H6) methane (CH4)
amount adsorbed
