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Langmuir 1996, 12, 980-986

Sorption Isotherms of Methane, Ethane, Ethylene, and Carbon Dioxide on ALPO-5 and SAPO-5 Vasant R. Choudhary* and S. Mayadevi Chemical Engineering Division, National Chemical Laboratory, Pune 411 008, India Received April 26, 1995. In Final Form: October 20, 1995X The sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5 (temperature 305-353 K, and pressure 0-200 kPa) and the thermodynamics of sorption have been investigated under similar conditions using a gravimetric sorption apparatus. The Dubinin-Polanyi equation is found to fit the sorption of all the sorbates in both the sorbents except for carbon dioxide in ALPO-5. The Freundlich model fits the equilibrium data on the sorption of carbon dioxide in ALPO-5. The two sorbents differ widely in the isosteric heat of sorption and also in its variation with surface coverage of these sorbates. Entropy changes on the sorption have also been analyzed. The sorption of these gases in both the sorbents is found to be supermobile, the mobility being much higher in ALPO-5 than in SAPO-5.

Introduction ALPO-5 and SAPO-5 are crystalline microporous materials of similar structure (channel diameter 8.0 × 10-10 m). ALPO-5 has a neutral framework with no extra framework cations. However, it has a polar pore system consisting of unidimensional cylindrical channels of uniform cross section. It contains weak acid sites, both Lewis and protonic.1,2 It is moderately hydrophilic and has interesting water sorption properties.3 Water sorption in ALPO-5 (at 273 K) follows type V isotherm shape, unusual for microporous solids and zeolites. Hence, knowledge of sorption properties of ALPO-5 for various organic compounds is of great interest. However, only a few related studies have been carried out so far. Wilson et al.3 have measured the sorption isotherms of water (at 273 K) and oxygen (at 90 K) in ALPO-5. There have been a few reports2,4 on the sorption of alcohols and liquid hydrocarbons in ALPO-5 by gravimetric and GC methods. But studies on the sorption of gaseous hydrocarbons in ALPO-5 are scarce. Lok et al.5 first reported the synthesis of SAPO-5 which is a crystalline microporous silicon aluminum phosphate with structure similar to that of ALPO-5, having interesting unique properties for potential use in catalytic, adsorptive, and ion exchange applications. Pyke et al.5 have determined the single point adsorption of water, n-hexane, and p-xylene on SAPO-5 at 273 K. There have been some studies on the sorption of CO6,7 and argon7 on Rh and Pd catalysts supported on SAPO-5. However very little is known on the sorption properties of SAPO-5 for the sorption of gaseous hydrocarbons. Recently, we have compared6 the sorption of N2 and O2 in ALPO-5 and SAPO-5 at moderate pressures. We have * To whom correspondence should be addressed: e-mail, [email protected]; phone, (91)212-331453 extn 2023; FAX, 0212330233. X Abstract published in Advance ACS Abstracts, January 15, 1996. (1) Bond, G. C.; Gelstrope, M. R.; Sing, K. S. W.; Theocharis, C. R. J. Chem. Soc., Chem. Commun. 1985, 15, 1056. (2) Choudhary, V. R.; Akolekar, D. B. J. Catal. 1987, 103, 115. (3) Wilson, S. T.; Lok, B. M.; Messina, C. A.; Cannan, T. R.; Flanigen, E. M. ACS Symp. Ser., 1983, No. 218, 79. (4) Choudhary, V. R.; Akolekar, D. B.; Singh, A. P.; Sansare, S. D. J. Catal. 1988, 111, 23. (5) Pyke, D. R.; Whitney, P.; Houghton, H. Appl. Catal. 1985, 18, 173. (6) Choudhary, V. R.; Mayadevi, S. Ind. Eng. Chem. Res. 1994, 33, 1319. (7) Choudhary, V. R.; Mayadevi, S. Sep. Sci. Technol. 1993, 28 (13 & 14), 2197.

0743-7463/96/2412-0980$12.00/0

Figure 1. Schematic diagram of the experimental setup for gravimetric sorption: B, ball valve; M, fine metering valve.

also reported7 the heat of sorption at near zero coverage of methane, ethane, ethylene, and CO2 in ALPO-5 by GC pulse technique. The present investigation has been undertaken with the objective of thoroughly investigating and comparing the sorption properties of ALPO-5 and SAPO-5 for the sorption of these gases under similar conditions. The sorption isotherms at different temperatures have been measured by the gravimetric method and fitted to different isotherm equations, and the heat of sorption and entropy change due to sorption at different sorbate loadings have been evaluated. Experimental Section Materials. The gases, methane (99.995% pure), ethane (purity 99.95%), and carbon dioxide (purity 99.99%) were obtained from L’Air Liquide, France. Ethylene of high purity (>99.9%) was obtained from Airco Industrial Gases, U.S.A. ALPO-5 (Al:P ) 1:1) was crystallized from a gel composition of 1.5 Pr3N‚ 1.0Al2O3‚1.0P2O5‚4OH2O at 423 K over a period of 24 h in a stainless steel bomb. SAPO-5 (Si:Al:P ) 0.21:0.13:0.33) was synthesized from a gel composition of 1.5Et3N‚1.28SiO2‚ 0.39Al2O3‚1.0P2O5‚40-60H2O by hydrothermal treatment at 453 K over a period of 48 h. Both crystals were washed thoroughly with distilled, deionized water, filtered, dried in air (at 373 K for 16 h), and calcined (at 813 K for 12 h) to remove the organic template. The calcined materials were pressed binder-free and crushed to particles of 30-52 mesh. The crystal structure of ALPO-5 and SAPO-5 was confirmed by XRD. A detailed characterization of ALPO-5 is given elsewhere.2 Gravimetric Measurement of Sorption Isotherms. The schematic diagram of the experimental setup for the measurement of sorption isotherms is given in Figure 1. The sorption

© 1996 American Chemical Society

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Figure 3. Sorption isotherms of methane, ethane, ethylene, and carbon dioxide in SAPO-5.

Figure 2. Sorption isotherms of methane, ethane, ethylene, and carbon dioxide in ALPO-5. unit consists of a quartz sample cell (capacity 4 cm3) connected to the ball valve B4 using a stainless steel ultra-torr (0.635 cm) to Swagelok (0.32 cm) reducing union and a Swagelok double end shut-off quick connect system. The connection through quick connect permits the easy attachment/detachment of the sorbent sample cell to the unit and the cell is automatically sealed-off when detached from the unit. During sorption, the sample cell is kept inside a jacketed glass vessel, through the jacket of which thermostated water of the required temperature is circulated. During the pretreatment of the sorbent, the cell is placed inside a movable glass furnace. The temperature of the cell during sorption and pretreatment is measured using a thermocouple attached to the sorption cell. The detailed diagram of the sorption unit is given elsewhere.8 The four ball valves B1, B2, B3, and B4 are connected to one another through a stainless steel cross. Valve B2 is connected to a stainless steel Bourdon gauge (calibrated, pressure range 0-202 kPa), valve B1 to the vacuum pump through the fine metering valve M1, and B3 to the stainless steel intermediate reservoir (that provides the gas at the desired pressure) and stainless steel gas cylinder using metering valves M2 and M3 and ball valve B5. A pressure gauge is connected to the line between valves B3 and M2 to measure the gas pressure in the intermediate reservoir. The valves B1 to B4 and M1 are fixed on an aluminum panel and enclosed in a metallic casing which can be heated if required. About 2 g of the sorbent sample is accurately weighed into the sorption cell, and it is connected to the apparatus. Valve B3 is opened and the entire unit up to valve B5 is evacuated, by gradually opening valve M1 so as to avoid the carryover of solid particles. The sorbent in the cell is pretreated in situ at 673 K for 2 h under vacuum (0.67 Pa) using the glass furnace in place of the jacketed glass vessel. When the pretreatment is completed, valves B1, B3, B4, and M1 are closed, the cell is cooled, and its weight taken. The difference between this weight and the weight of the empty cell assembly is taken as the weight of the dry sample. After the pretreatment, the sorbent is heated to the sorption temperature by circulating water of the required temperature through the glass jacket. (8) Mayadevi, S. Adsorption and Mass Transfer in Solid Catalysts and Adsorbents; Ph.D. Thesis, University of Poona, Pune, 1991.

The intermediate reservoir is filled with the sorbate gas to the required pressure (indicated by the pressure gauge between valves M2 and B3) by opening valves M2, B5, and M3. Valves B5, M3, and M2 are then closed. Traces of air in the sorption cell are removed by repeatedly introducing sorbate gas (at about 0.67 kPa) in the cell and evacuating it to about 0.67 Pa. By this operation, traces of air present in the cell are carried away along with the sorbate gas during evacuation at the low vacuum (0.67 Pa) used, thus avoiding the necessity of a high vacuum (1.3 × 10-4 Pa) generally required for sorption studies. For the collection of sorption data, the sorption pressure at each point is varied by varying the gas pressure in the intermediate reservoir. Valves B4, B3, and B2 are opened and the sorbent is exposed to the gas (by slowly opening valve M2) for a period (more than 1 h) sufficient to establish the sorption equilibrium. Valve B4 is then closed, and the cell is allowed to attain room temperature and is detached from the unit for direct weighing. The increase in weight gives the amount of vapor sorbed at the sorption pressure and temperature. The experiment is then repeated for collecting isotherm data at different pressures, after changing the pressure of the gas in the intermediate reservoir. The weight of the sorption cell is measured using an electronic analytical balance with a sensitivity of 0.0001 g. Compared to other methods for the measurement of sorption, this method has the advantage that the measurement is made on a large (2.5-3.0 g) and, hence, representative sorbent sample. Also, this method of measurement requires neither a high vacuum system, nor any special expensive instrument for the sorption data collection. The sorption apparatus and the method used here are similar to that described earlier9 for measuring the sorption of liquid vapors in microporous solids, except that the vapor feed system is replaced by a gas reservoir. The maximum error in the measurement by this method is expected to be for the data on the sorption of methane in SAPO-5, which is estimated to be (3%. The other gases are sorbed to a larger extent on both the sorbents, and hence the error in the measurement is much less than that for methane in SAPO-5.

Results Sorption Isotherms. The isotherms of sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5 at different temperatures are presented in Figures 2 and 3, respectively. (9) Choudhary, V. R.; Mayadevi, S.; Singh, A. P. Ind. Eng. Chem. Res. 1995, 34, 413.

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Choudhary and Mayadevi

Table 1. Isotherm Models Giving the Best Fit for the Sorption of Methane, Ethane, Ethylene, and Carbon Dioxide in ALPO-5 and SAPO-5 (0-200 kPa, 305-353 K) adsorbent

adsorbate

best fitting model

% deviation of q

ALPO-5

methane ethane ethylene CO2 methane ethane ethylene CO2

Dubinin-Polanyi Dubinin-Polanyi Dubinin-Polanyi Freundlich Dubinin-Polanyi Dubinin-Polanyi Dubinin-Polanyi Dubinin-Polanyi

-6 to 6 -5 to 6 -5 to 5 -6 to 5 -5 to 5 -2 to 3 -7 to 5 -6 to 9

SAPO-5

regression coefficient 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.998

The isotherm data were fitted to the standard isotherm equations, viz., Langmuir,10 Freundlich,11 and DubininPolanyi12 isotherm models by linear regression. The discrimination of the model was mainly based on the regression coefficient and the percentage deviation of the amount sorbed (q) estimated using the model parameters from that measured experimentally. The DubininPolanyi model

log q ) C - D(log(Ps/P))2

(1)

was found to fit the experimental data of all the gases in both ALPO-5 and SAPO-5 except for CO2 in ALPO-5. The Freundlich equation

q ) kPc

(2)

was found to fit the sorption of CO2 in ALPO-5. In the Dubinin-Polanyi model, Ps, the saturation vapor pressure of the pure sorbate, was estimated using the generalized form of the Clapeyron.13 The best fitting isotherm model along with the percentage deviation of q and the regression coefficient for the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5 are presented in Table 1. The estimated values of the parameters of the best fitting isotherm models for the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5 are presented in Table 2. Isosteric Heat of Sorption. The isosteric heat of sorption and its variation with surface coverage can provide useful insight into the nature of the surface and the sorbed phase. Isosteric heat of sorption at different surface coverage was calculated from the sorption isotherms using the Clausius-Clapeyron equation14

Figure 4. Variation of isosteric heat of sorption (Qa) with sorbate loading (q) for the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5. Table 2. Constants of Best Fitting Isotherm Models for the Adsorption of Methane, Ethane, Ethylene, and Carbon Dioxide on ALPO-5, and SAPO-5 (Pressure, 0-200 kPa) Dubinin-Polanyi constants adsorbent

adsorbate

temp (K)

C

-D × 102

ALPO-5

methane

305 353 305 353 305 353 305 353 305 353 305 353 305 353

1.126 1.215 0.850 0.774 0.829 0.890 1.135 0.486 0.648 0.902 0.766 1.053 0.957 0.733

7.09 7.05 8.48 7.74 7.64 8.34 6.85 6.21 5.74 7.52 4.12 6.10 9.13 10.27

ethane ethylene SAPO-5

methane ethane

log P ) E - Qa/(2.303RT)

(3)

In zeolites, the isosteric heat of sorption generally depends upon the intracrystalline sorbate concentration. The variations of heat of sorption with surface coverage for the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5 are given in Figures 4 and 5. The isosteric heat of sorption was estimated from the adsorption data collected at only two temperatures. However, since the adsorption data are quite accurate, the error in the estimation of the isosteric heat of sorption is expected to be negligibly small. Figures 4 and 5 indicate that the variation of heat of sorption with the amount sorbed is strongly dependent (10) Langmuir, L. J. Am. Chem. Soc. 1918, 40, 1361. (11) Sips, R. J. Chem. Phys. 1948, 16, 490. (12) Bering, B. P.; Dubinin, M. M.; Serpinsky, V. V. J. Colloid Interface Sci. 1966, 21, 378. (13) Reid, R. C.; Praustnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill Book Company: New York, 1977. (14) Breck, D. W. Zeolite Molecular Sieves; John Wiley & Sons: New York, 1974.

ethylene CO2

Freundlich constants adsorbent

adsorbate

temp (K)

k × 103

c

ALPO-5

CO2

305 353

8.5 2.0

0.892 1.043

on the sorbate-sorbent system, and the heat of sorption is considerably influenced by the surface coverage. In general, an initial sharp decrease of heat of sorption with increasing the sorbate in the zeolite reveals site heterogeneity, whereas a small increase or decrease in the heat of sorption with increasing sorbate loading indicates attractive or repulsive sorbate-sorbate interaction, respectively, among the sorbed species. A sharp increase in the heat of sorption with increasing sorbate loading may also be due to an induced surface heterogeneity, probably due to increase in the energy of sorption sites. Sometimes sorbate-sorbate interactions manifest them-

Sorption of Gaseous Hydrocarbons

Langmuir, Vol. 12, No. 4, 1996 983 Table 4. Thermodynamic Data for the Sorption of Methane, Ethane, Ethylene, and Carbon Dioxide in SAPO-5 amount adsorbed, temp -∆G -∆S Sg Sa q (mmol/g) (K) (kJ‚mol-1) (J‚mol-1‚K-1) (J‚mol-1‚K-1) (J‚mol-1‚K-1) 0.05 0.10 0.15

0.20 0.30 0.40 0.50 0.60

Figure 5. Variation of isosteric heat of sorption (Qa) with sorbate loading (q) for the sorption of methane, ethane, ethylene, and carbon dioxide in SAPO-5.

0.20 0.30

Table 3. Thermodynamic Data for the Sorption of Methane, Ethane, Ethylene, and Carbon Dioxide in ALPO-5

0.40

amount adsorbed, temp -∆G -∆S Sg Sa q (mmol/g) (K) (kJ‚mol-1) (J‚mol-1‚K-1) (J‚mol-1‚K-1) (J‚mol-1‚K-1)

0.60

0.10 0.15 0.20 0.30

0.20 0.30 0.40 0.50

0.15 0.20 0.30 0.35

0.15 0.20 0.30 0.40

305 353 305 353 305 353 305 353

Sorption of Methane 2.88 8.9 2.07 10.0 1.79 10.4 0.88 11.5 1.01 10.8 0.04 12.1 -0.26 12.0 -1.15 12.9

305 353 305 353 305 353 305 353

3.82 2.73 2.70 0.69 1.79 0.19 1.13 -1.00

305 353 305 353 305 353 305 353

Sorption of Ethylene 4.11 24.2 2.22 26.3 3.31 28.5 1.42 30.0 1.92 36.2 -0.03 36.8 1.55 38.7 -0.67 39.7

305 353 305 353 305 353 305 353

0.70 186 192 186 192 186 192 186 192

177 182 176 180 175 180 174 179

230 239 230 239 230 239 230 239

200 210 195 202 190 199 186 194

220 227 220 227 220 227 220 227

196 201 192 197 184 190 182 187

Sorption of Carbon Dioxide 3.55 36.2 214 1.54 37.0 220 2.70 39.0 214 0.69 39.4 220 1.64 44.3 214 -0.50 44.3 220 0.76 50.0 214 -1.43 49.4 220

178 183 175 180 170 175 164 170

Sorption of Ethane 30.3 29.2 35.7 36.6 40.7 39.7 44.8 44.8

0.50

0.10 0.20 0.30 0.40

selves giving rise to a very complex trend for the dependence of heat of sorption on the sorbate loading. Free Energy and Entropy Changes in Sorption. The thermodynamic data for the sorption of methane, ethane, ethylene, and carbon dioxide at different sorbate loadings and temperatures are presented in Tables 3 and 4. The data were evaluated from the sorption isotherm

0.50

305 353 305 353 305 353

Sorption of Methane 5.31 63.3 3.57 59.6 3.31 67.8 1.42 64.0 2.12 67.8 -0.31 65.5

305 353 305 353 305 353 305 353 305 353

6.60 3.12 4.45 1.93 3.31 0.79 2.52 -0.17 1.67 -0.96

305 353 305 353 305 353 305 353 305 353 305 353

Sorption of Ethylene 7.63 71.4 4.42 70.8 6.60 71.8 3.12 71.9 5.31 71.3 2.07 70.8 3.82 69.9 1.00 68.4 3.09 65.8 0.04 65.5 2.20 62.3 -0.90 62.6

305 353 305 353 305 353 305 353 305 353

186 192 186 192 186 192

123 132 118 128 118 126

230 239 230 239 230 239 230 239 230 239

176 182 170 179 173 182 173 182 174 182

220 227 220 227 220 227 220 227 220 227 220 227

149 156 148 155 149 156 150 159 154 162 158 164

Sorption of Carbon Dioxide 5.87 53.7 214 3.83 52.2 220 4.45 52.4 214 1.79 52.8 220 3.31 54.7 214 0.52 55.2 220 2.36 57.8 214 -0.31 57.5 220 1.79 59.7 214 -1.09 59.7 220

161 167 162 167 160 164 156 162 155 160

Sorption of Ethane 54.4 56.9 60.5 59.4 57.5 56.8 57.0 56.9 56.7 56.4

data (Figures 2 and 3) using the following relations:

∆G ) RT ln P/p

(4)

∆G ) ∆H - T∆S

(5)

Sa ) Sg + ∆S

(6)

where ∆G, ∆H (which is equal to isosteric heat of sorption under isothermal conditions, neglecting gas imperfections), and ∆S are the standard free energy, enthalpy, and entropy changes in the sorption process, respectively; Sg is the entropy of sorbate at the standard pressure P; Sa is the entropy of the sorbed phase; and P and p are the equilibrium pressures of the sorbate phase in a standard state and the state at which the studies are conducted, respectively. The standard state pressure (P) is taken as 101.32 kPa. The values of Sg for the various sorbates were taken from the data given elsewhere.15 The results (Tables 3 and 4) reveal that in the sorption of methane, ethane, ethylene, and carbon dioxide, the free energy change (-∆G) decreases with increase in the sorbate loading and temperature. The entropy change (-∆S) shows a variation with sorbate loading but is influenced to a lesser extent by the sorption temperature. (15) Stull, D. R.; Westrum, E. F.; Sinke, G. C. Chemical Thermodynamics of Organic Compounds; New York, 1969.

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Choudhary and Mayadevi Table 5. Theoretical Entropy Changes in the Mobile and Localized Sorption of Methane, Ethane, Ethylene, and Carbon Dioxide entropy change (J‚mol-1‚K-1)

sorbate methane ethylene ethane CO2

Figure 6. Comparison of the observed entropy change, -∆Sm (solid line), at different sorbate loadings with the theoretical entropy change for mobile sorption (St3D - St2D) (dotted line) in the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5.

The entropy of the sorbed species (Sa) and, consequently, the mobility of the sorbed phase show a decrease with sorbate loading for the sorption of ethane, ethylene, and carbon dioxide in ALPO-5 and for the sorption of methane and carbon dioxide in SAPO-5. However, for the sorption of methane in ALPO-5, it passes through a maximum on increasing the sorbate loading. For the sorption of ethane in SAPO-5, the value of Sa passes through a minimum, whereas for ethylene in SAPO-5, it remains constant initially up to a sorbate loading of 0.4 mmol‚g-1 and then increases with further increase in the sorbate loading. In all the cases, Sa increases with temperature for the same sorbate loading. Figure 6 shows the comparison between the observed entropy change (-∆Sm) associated with the sorption (after correcting for the contributions for the entropy change in the vapor phase and in the sorbed phase) at the different sorbate loadings and the theoretical entropy change (St3D - St2D, where St3D and St2D are the translational entropies for the three-dimensional and two-dimensional sorbate vapors, respectively) for the mobile film model16 in the sorption of methane, ethane, ethylene, and carbon dioxide. The entropy change on sorption, ∆Sm at different sorbate loadings were obtained from the observed ∆S, averaged over the sorption temperature range, using the relation16

∆Sm ) ∆S + R ln(A*/A)

(7)

where A* is the standard molecular area (equal to 4.08T × 10-16 cm2) and A is the molecular area of the sorbate estimated using the relation suggested by Emmett and Brunauer.17 The values of the translational entropies of the threedimensional and two-dimensional sorbate at different temperatures are given in Table 5. These values were obtained from the expressions16,18

St3D ) R ln(M1.5T2.5) - 9.61

(8)

and

mobile localized temp St3D St2D sorption sorption -1 -1 -1 -1 (K) (J‚mol ‚K ) (J‚mol ‚K ) (St3D - St2D) St3D 305 353 305 353 305 353 305 353

144 147 151 154 152 155 156 159

99 101 104 106 104 107 107 110

44.8 45.4 47.1 47.7 47.4 48.0 49.0 49.6

144 147 151 154 152 155 156 159

in the sorption for the mobile and localized sorption models (with no loss of rotational degrees of freedom of sorbed molecules) is expected to be equal to (St3D - St2D) and St3D, respectively. The values of the entropy change for the two sorption models are included in Table 5. It may be noted that the influence of temperature on (St3D - St2D) and, consequently, on the entropy change in mobile sorption is very small, compared to its influence on St3D and St2D. The results (Figure 6) indicate that when the sorbate loading increases, the entropy change (-∆Sm) in the sorption of ethane, ethylene, and carbon dioxide in ALPO-5 increases. In the case of the sorption of methane in ALPO5, the entropy change increases up to a sorbate loading of 0.2 mmol‚g-1 after which there is a small decrease. The entropy change increases with the sorbate loading for the sorption of methane and carbon dioxide in SAPO-5, while for the sorption of ethylene it decreases with increase in the sorbate loading. The entropy change remains more or less constant for the sorption of ethane in SAPO-5. In all the cases, the entropy change is found to be much lower than the theoretical entropy change for a mobile sorption (St3D - St2D). However, in the case of the sorption of methane in SAPO-5, it approaches the theoretical value for mobile sorption on increasing the sorbate loading. The entropy of vibration and the corresponding frequency and wavelength for vibratory flight of the sorbed molecules at a given surface coverage (0.15-0.2 mmol‚g-1) for the sorption of different sorbates in ALPO-5 and SAPO-5 are given in Table 6. These have been estimated by the procedure given by de Boer19 using the following equations.

Svib ) Sa - St2D ) R(1 - ln(hν/kT))

(10)

where R and h are the gas constant and Planck’s constant, respectively, k is the gas constant per molecule R/N, T is the temperature, and ν is the frequency of vibration. The wavelength of vibrational motion, λ, can be calculated using the equation

λ ) u/ν

(11)

u ) (8RT/(πM))1/2

(12)

where

and M is the molecular weight.

St2D ) 0.667St3D + 2.76 ln T - 12.71

(9)

Discussion

where M is the molecular weight (the values of St3D and St2D are expressed in J‚mol-1‚K-1). The change of entropy

ALPO-5 and SAPO-5 are crystalline materials having one-dimensional channels of uniform cross section (8 ×

(16) Gregg, S. J. The Surface Chemistry of Solids; Chaman & Hall: London, 1961; p 74. (17) Emmett, P. H.; Brunauer, S. J. Am. Chem. Soc. 1937, 59, 1553. (18) Kemball, C. Adv. Catal. 1950, 2, 233.

(19) de Boer, J. H. Dynamic Character of Adsorption; Oxford University Press: London, 1953. (20) Stach, H.; Thamm, H.; Fielder, K.; Granert, B.; Weiker, W.; Jahn, E.; Oehlmann, G. Stud. Surf. Sci. Catal. 1986, 28, 539.

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Table 6. Entropy of Vibration and Frequency and Wavelength of Vibratory Flight of Sorbed Molecules in ALPO-5 and SAPO-5

sorbent

sorbate

ALPO-5

CH4 C2H6 C2H4 CO2 CH4 C2H6 C2H4 CO2

SAPO-5

sorbate loading (mmol‚g-1)

entropy of vibration of sorbed species (J‚mol-1‚K-1)

0.15 0.20 0.20 0.20 0.15 0.20 0.20 0.20

76.9 95.9 88.1 67.9 19.5 71.8 45.2 54.4

10-10 m). The kinetic diameters of the sorbates are as follows: methane, 3.8 × 10-10 m; ethane, 4.4 × 10-10 m; ethylene 4.2 × 10-10 m; carbon dioxide 3.9 × 10-10 m.13 The comparison between the pore size and the kinetic diameter indicates that the kinetic diameter of the sorbates is smaller than the channel diameter of the sorbents. Hence it is expected that the sorbate molecules can freely enter the sorbent channels. Sorption in ALPO-5. The results show the following order for the sorption of the different sorbates in ALPO-5: CH4 < CO2 ≈ C2H4 < C2H6. The fitting of the sorption data for methane, ethane, and ethylene to the DubininPolanyi model indicates that the sorption of these gases in ALPO-5 occurs by the pore volume filling mechanism. Interestingly, the sorption of carbon dioxide in ALPO-5 does not allow the pore filling mechanism; it follows the Freundlich sorption model. The variation of Qa with the surface coverage for the sorption of methane shows a trend different from that observed for the sorption of other sorbates (Figure 4). The observed initial sharp decrease in Qa for methane with increasing the surface coverage may be due to induced surface heterogeneity. Whereas the observed small increase of Qa for ethylene, ethane, and carbon dioxide with increasing the surface coverage is expected to be mostly due to attractive interactions between the sorbed species. It may be noted that the heat of sorption for all the sorbates in ALPO-5 is lower than that in SAPO-5 (Figures 4 and 5). This is because of the fact that ALPO-5 has a neutral framework and hence has weaker interactions with the sorbate molecules. For all the sorbates, the observed entropy change (-∆Sm) on their sorption in ALPO-5 (Figure 6) is appreciably smaller than the theoretical entropy change (St3D - St2D) for the mobile sorption (i.e., sorption with a complete loss of translation normal to the surface). This suggests that the sorption of all the sorbates in ALPO-5 at all the temperatures and sorbate loadings studied is mobile. The mobility is, however, strongly influenced by the sorbate loading. It is found to be decreasing with increasing the sorbate loading, except for methane at the higher sorbate loadings. The observed smaller entropy change on the sorption also implies that, in these cases, the translational motion normal to the surface is converted into vibration, and the entropy associated with the vibration normal to the surface (Table 6) is quite appreciable. It is interesting to note that the wavelength for vibratory motion of the sorbed molecules in all the cases (Table 6) is greater than even that of the channel diameter (8 × 10-10 m) of ALPO5. Thus in addition to the unrestricted translational motion in the two directions along the surface, the mobility of the sorbed molecules is greatly enhanced by the vibratory flight of the molecules in the channels, resulting into a supermobile sorption.18 Sorption of n-hexane, cyclohexane, and benzene in ALPO-5 at high temperatures (523-673 K) was also found to be supermobile.4

vibrational motion of sorbed species wavelength frequency × 109 m × 10-8 s-1 16.3 1.65 4.26 48.6 1.64 × 104 30.3 745 245

388 2810 1130 78.8 0.4 153 6.4 15.6

Sorption in SAPO-5. The sorption of methane, ethane, ethylene, and carbon dioxide in SAPO-5 shows the following order: CH4 < CO2 ≈ C2H6 < C2H4. The sorption data for all the four sorbates in SAPO-5 satisfy the Dubinin-Polanyi equation. This indicates that the sorption occurs by the pore volume filling mechanism. The variation of isosteric heat of sorption Qa with surface coverage shows different trends for the different sorbates (Figure 5). For the sorption of methane, Qa decreases slowly with increasing surface coverage initially, but the decrease is rapid above a surface coverage of 0.1 mmol‚g-1, indicating a possibility of sorption-induced surface heterogeneity. For the sorption of ethane and ethylene, Qa decreases with increasing the sorbate loading, suggesting repulsive interactions between the sorbed molecules. In the case of carbon dioxide sorption, Qa decreases initially and then attains a constant value with increasing the sorbate loading. The initial decrease in Qa is expected to be due to repulsive interactions between the sorbed carbon dioxide molecules. For all the sorbates, the observed entropy change (-∆Sm) on sorption in SAPO-5 (Figure 6) is less than the theoretical entropy change (St3D - St2D) for the mobile sorption. This suggests that the sorbed molecules of all the sorbates are mobile in SAPO-5 at all temperatures and sorbate loadings studied. However, the mobility of the sorbed methane molecules in SAPO-5 decreases and approaches the theoretical value for mobile sorption at higher sorbate loadings. The mobility does not change significantly with increasing the sorbate loading in the case of ethane sorption. Whereas, the observed entropy change (-∆Sm) increases with increasing the sorbate loading for the sorption of carbon dioxide in SAPO-5, suggesting a gradual decrease in the mobility of the sorbed molecules. Interestingly, the mobility of the sorbed ethylene molecules in SAPO-5 increases with increasing the sorbate loading as can be seen in Figure 6c. The results in Table 6 show that at a sorbate loading of 0.2 mmol‚g-1, the wavelength of vibratory flight for methane is somewhat greater than that of the atomic distances of SAPO-5. The wavelength of vibratory flight for ethane, ethylene, and carbon dioxide is even greater than that (8 × 10-10 m) of the channel diameter of SAPO5. This indicates that the mobility of these three sorbate molecules in SAPO-5 is greatly enhanced by their vibratory flight. The mobility of sorbed methane molecules is also enhanced by their vibratory flight, but to a smaller extent. Thus, because of the vibratory flight of the sorbed molecules, the sorption of all these sorbates in SAPO-5 is supermobile. A comparison of the entropy change on the sorption of the sorbates in SAPO-5 with that in ALPO-5 reveals that the mobility of the sorbed molecules in all the sorbates is much higher in ALPO-5 than in SAPO-5.

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Langmuir, Vol. 12, No. 4, 1996

Conclusions On the basis of the investigations carried out, the following conclusions have been arrived at on the sorption of methane, ethane, ethylene, and carbon dioxide in ALPO-5 and SAPO-5. 1. The equilibrium sorption of all the four sorbates in both ALPO-5 and SAPO-5 (except for carbon dioxide in ALPO-5) can be well represented by the Dubinin-Polanyi model, indicating that the sorption occurs by the pore volume filling mechanism. The Freundlich model fits the equilibrium sorption of carbon dioxide in ALPO-5. The order for sorption of these sorbates is CH4 < CO2 ≈ C2H4 < C2H6 in ALPO-5 and CH4 < CO2 ≈ C2H6 < C2H4 in SAPO-5.

Choudhary and Mayadevi

2. The isosteric heat of sorption and its variation with surface coverage for the sorption of methane, ethane, ethylene, and carbon dioxide are strongly dependent upon the sorbate and have different trends in ALPO-5 and SAPO-5. The heat of sorption of these sorbates in ALPO-5 is appreciably lower than that in SAPO-5. 3. The analysis of entropy change due to sorption reveals that the sorbed molecules of all the sorbates are supermobile in both the sorbents, the sorbate molecules being much more mobile in ALPO-5 than in SAPO-5. LA950333N