Znd. Eng. Chem. Res. 1996,34, 177-184
177
Adsorption of Branched and Cyclic Paraffins in Silicalite. 1. Equilibrium C6lio L. Cavalcante, Jr., and Douglas M. Ruthven" Department of Chemical Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
Gravimetric equilibrium isotherms are reported for adsorption of branched and cyclic c6 paraffins on silicalite. In addition to the isotherms, Henry constants and heats of adsorption are reported for 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-dimethylbutane, methylcyclopentane, and cyclohexane. Adsorption capacities are in the range of 4-7 wt %. All isotherms are of type 1 in Brunauer's classification. Adsorption saturation limits, estimated from the experimental results by Langmuir regression, show a decreasing trend with increasing temperature. Adsorption equilibrium constants follow the trend double-branched < singlebranched < cyclic paraffins. Heats of adsorption for the single-branched paraffins increase slightly with loading, but for the double-branched and cyclic paraffins the variation of heat of adsorption with coverage is more pronounced.
Introduction The potential applications of zeolites as shape selective catalysts and adsorbents have been widely studied during the past few decades. The first examples of the use of zeolites as molecular shape selective catalysts were given more than 30 years ago (Weisz and Frilette, 1960). Increased conversion in n-decane cracking for zeolites X (in Na+ and Ca2+forms), in comparison with a conventional silica-alumina catalyst, was observed. With the discovery of ZSM-5 (Kokotailo et al., 1978)and its pure silica form, silicalite (Flanigen et al., 19781, in the late 1970s, many new applications emerged (see, for example, Weisz, 1980; Csicsery, 1986). Shape selective separations with zeolites include the separation of close boiling isomers (e.g., p-xylene from mixed xylenes), separation of n-paraffins from isoparaffins, drying of hydrocarbon gas streams, and encapsulation of gases for long-term storage (Ruthven, 1984; Vansant, 1990). The adsorption of linear paraffins in ZSM-5/silicalite has been studied in detail (Stach et al., 1986; Doelle et al., 1981; Hufton and Danner, 19931,but the adsorption of branched and cyclic paraffins has received much less attention. Relatively minor differences in molecular size between cyclic, branched, and linear paraffins can significantly alter the adsorption properties of these components. The 10-ring pore opening of silicalite (ca. 6 A) may lead to shape selectivity for hydrocarbon molecules, especially those with six carbon atoms (c6) which have molecular dimensions close to those of the silicalite micropores. In this paper, we report the results of a detailed experimental study of adsorption equilibrium for several branched and cyclic c6 components. Kinetic data for the same sorbates are reported in part 2 (Cavalcante and Ruthven, 1995).
Experimental Section The silicalite crystals used in this study were kindly supplied by Prof. David Hayhurst (formerly of Cleveland State University, now with the University of South Alabama) and by Union Carbide. Different zeolite samples with different crystal sizes were used, mainly in order to establish the rate controlling diffusion step. Prior to use, the samples were pretreated in air at 0888-5885/95/2634-0177$09.~0f0
Table 1. Dimensions of the Cyclic and Branched Hydrocarbons Used as Sorbates (A) compd crit diama kinet diamb molecular lengthc 2-methylpentane 5.4 6.1 9.4 3-methylpentane 5.4 6.1 9.4 6.1 8.1 2,2-dimethylbutane 6.3 2,3-dimethylbutane 5.8 6.1 8.1 methylcyclopentane 5.9 5.8 7.4 5.7 6.9 cyclohexane 6.9/6.0d Diameter of smallest cylinder that circumscribes the molecule (estimated from bond angles and lengths). Estimated by WilkeLee method (Reid et al., 1987). Estimated from bond angles and lengths. From Breck (1974).
temperatures up to 550 "C in order to burn off the templates incorporated during synthesis. Gravimetric uptake measurements were carried out using a Cahn vacuum electrobalance (Model 2000 RG), and the data were collected by means of a data acquisition system (ADC-1, from Remote Measurement Systems). Sorbate partial pressures were monitored through a Datametrics transducer with a range of 0-100 Torr absolute. Before each set of experimental runs (increasing sorbate partial pressures at a given temperature), the sample was regenerated under vacuum at approximately Torr and temperature of 350 "C for at least 12 h. Such a procedure should desorb the sample fully, and the weight should return to its original value. When this did not occur, the gain of weight was attributed to coke formation. The sample was then reexposed to air at 480 "C and, afterward, regenerated in the normal way. The original weight was generally regained. This procedure was often necessary, particularly with some of the slower diffusing species, such as cyclohexane and dimethylalkanes. Reversibility of the isotherm was confirmed by comparing the data from adsorption and desorption measurements. The sorbates used in this study are listed in Table 1, with their relevant molecular dimensions. It can be seen that the critical diameters, defined as the diameter of the smallest cylinder that can circumscribe the molecule in its equilibrium conformation, are independent of the length of the main carbon chain, and depend solely on the number of methyl groups attached to the main carbon chain and their positions. For example,
0 1995 American Chemical Society
178 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
F]
2Me 100 c
.....0.‘
6.00
9 3
c0
200 c
150 C 4.00
.................. 200
c
2.00
.... .... .... .... .... .... 5
0
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I
I
15
20
25
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.sa
‘$8.’
......
.......-6”
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.
Figure 2. Langmuir plot of equilibrium isotherms for !&methylpentandsilicalite.
.A“
! -
1
4.0
i/p (TOIT)-’
)”“
h
’
..............A 200
c
. . . . I .... .... ....I ...., l
P (Ton)
Figure 1. Equilibrium isotherms for 2-methylpentane and 3methylpentane in silicalite. The curves are calculated from the Langmuir expression (eq 1)with the values of b and qa listed in Table 3. Open symbols: adsorption. Filled symbols: desorption. Table 2. Comparison of Equilibrium Data for Single-BranchedHydrocarbons in Silicalite weight sorbed (% g/g) this study Arbuckle et al. (1987) P(Torr) temp(’%) 2MP 3MP 2MP 3MP 7.5 8.4 15 22 50 6.6 7.9 100 5.8 6.5 6.0 5.9 150 5.5 5.1 200 2.5 2.3
2,2-dimethylbutane clearly has a larger critical diameter than 2,3-dimethylbutane. On the other hand, the molecular length depends only on the number of carbon atoms in the main chain. The sorbates were obtained from Aldrich o r Anachemia, with specified purities over 99%, and were used without further purification.
Results and Discussion In general the data obtained are self-consistent and in reasonably close agreement with the limited published data for these systems. The isotherms are reversible and show the expected favorable form with saturation loadings in the range 5-7 wt %. Single-BranchedParaffins. The isotherms for the singly-branched components (2-methylpentane (2MP) and 3-methylpentane (3MP) are shown in Figure 1. In Table 2, values reported by Arbuckle et al. (1987) are compared with those obtained in this study. The
Table 3. Summary. of Langmuir Fitted Parameters for Branched and Cychc Paraffine in Silicalite
n-hexanea 2MP 3MP
22DMB 23DMB cyclo-c6
MCP
30 100 150 200 100 125 150 200 150 175 205 110 150 200 120 150 200 250 300 150 175 205
10.0 5.95 6.33 6.29 6.75 5.95 6.06 5.40 5.6 5.2 3.6 4.8 5.8 2.3 6.8 5.8 5.6 5.4 6.5 6.0 5.1
22.22 2.73 0.28 20.83 4.83 2.02 0.25 0.50 0.16 0.092 1.63 0.39 0.062 6.4 1.7 0.20 0.051 0.024 3.24 1.68 0.61
16.7 16.2
15.0
13.0 13.0
15.1
12.2
Data of Stach et al. (1986). The saturation limit reported by Richards and Rees (1988) is similar although these authors report a lower limiting AH value (-14.5 kcaVmo1). The data of Wu et al. (1983) suggest higher values for both q s (12 w t %) and -M (20 kcdmol).
isotherms are of “type I” form (in Brunauer’s classification). The fit of the data to the ideal Langmuir model, is shown in Figure 1, as well as in Figure 2, in which the data for 2-methylpentane are plotted in accordance with the reciprocal relation:
It is evident that the plots are closely linear and the Langmuir parameters qsand b may be calculated from the slopes and intercepts (Table 3). Even though a good fit of the experimental data is generally obtained, it
Ind. Eng. Chem. Res., Vol. 34,No. 1, 1995 179
I
00
.
I
2.0
.
I
4.0
7
-
1
.
6.0
1
8.0
,
.
1.00E+03 2.0
.
,
.
I
2.2
,
.
2.6
2.4
.
2.8
0
1OOOrr 0.01
I 0.0
1
1
1
2.0
4.0
6.0
Figure 4. Temperature dependence of equilibrium constants for 2-methylpentane and 3-methylpentane in silicalite.
8.0
100.00
P(%PiP)
~
Figure 3. Virial plots of equilibrium isotherms for 2-methylpentane (a) and 3-methylpentane (b) in silicalite. Open symbols: adsorption. Filled symbols: desorption.
must be pointed out that the parameters derived from the Langmuir model may lack physical significance (Ruthven, 1984). Nevertheless, since the fits are so good, the correlated isotherms were used in the analysis of the equilibrium data and for estimation of the thermodynamic correction factors for the measured diffisivity values (part 2). Such fits are also useful for a first estimate of the Henry's law constant (K= bq,). Another way of plotting the equilibrium data t o extract the Henry's law constant makes use of the virial form of the thermodynamic equilibrium relation (Barrer and Davies, 1970):
It is evident that a plot of ln(plq) versus q should approach linearity a t low loadings, thus providing a straightforward extrapolation to determine the Henry constant K (as in Figure 3). The K values so obtained, converted t o dimensionless form (moles of sorbate per unit volume in adsorbed phase divided by moles of sorbate per unit volume in fluid phase) are shown in Figure 4 plotted against the inverse of the absolute temperature. It can be seen that the experimental results follow the integrated form of the van't Hoff equation: (3) with the slope of the straight line yielding directly the limiting internal energy of adsorption (-AUo). The heats of adsorption, calculated from ( - A H 0 = -Avo
+
I
2.0
.
,
2.2
-
,
2.4
.
,
2.6
-
,
2.8
3
Figure 5. Calculation of isosteric heats of adsorption from equilibrium data (2-methylpentaneon silicalite).
RT), are approximately 16.2 kcaWmol for 2MP and 15.0 kcaWmo1 for 3MP. Elementary thermodynamics shows that the equilibrium vapor pressure, a t constant loading, should follow the Clausius-Clapeyron equation. A plot of logp versus 1IT should therefore yield a straight line with slope proportional to the heat of adsorption. This is shown in Figure 5, and the values for the isosteric heats of
180 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
i zo'o 6'oo 5.00
2.00
5.0
1
,,.**A '
0
2MP
2MP
-
0.00
van1 Hoff
1
0
m
2MP/3MP-June el
A
3MP
A
0 . 0 , . 0
16
, . , . , . , I
IO
i
.
1
.
20
, . , . 3
2
4.001
4 (Wg) Figure 6. Variation of heat of adsorption with adsorbed phase concentration for 2-methylpentane and 3-methylpentane in silicalite.
I
40
'
50
P (Torr)
3MP . van1 Hoff
.
1
30
22DMB
..--
*..Q
..-9 15OoC
-
P
c
0
Table 4. Adsorption of Single-BranchedParaffins in Silicalite: Comparison of Experimental and Molecular Simulation Data this study June et al. (1990) compd 2MP 3MP
a
temp("C) 100 150 200 100 150 200
K 1.2 105 1.8 x lo4 1.9 103 1.0 x lo5 1.1 104 2.2 103
madsa
K
madsa
16.2
1.0 105
15.0
1.0 104
15.0
0.4 x lo5 0.5 104
15.0
In kcavmol.
adsorption derived in this way are plotted against sorbate concentration (a) in Figure 6. It may be seen that the isosteric heat is almost independent of loading, as required by the Langmuir model. The values are in good agreement with the limiting values from the van't Hoff plots, which are also shown. This behavior is in marked contrast to the behavior of the linear paraffins in silicalite which show a rather pronounced increase of isosteric heat with loading: see data for n-butane (Shen and Rees, 1991; Thamm et al., 1983), n-hexane (Richards and Rees, 19881, and n-decane (Janchen and Stach, 1986). Molecular simulations have been developed to predict the equilibrium behaviour of n-hexane, 2MP, and 3MP (June et al., 1990). The equilibrium constants and heats of sorption so obtained are in reasonable agreement with the experimental values obtained in this study (see Table 4). It is of interest to note that the simulations suggest that the single-branched molecules 2MP and 3MP, with critical diameters of about 5.3 A, prefer to sit in the channel intersections, while n-hexane, with critical diameter of roughly 4.d,tends to reside in the channels (June et al., 1990). Double-Branched Paraffins. Equilibrium data were obtained for 2,2-dimethylbutane (22DMB)and 2,3dimethylbutane (23DMB). These molecules have substantially different critical molecular diameters (6.3 and 5.8 A, respectively).
P Van)
Figure 7. Equilibrium isotherms for 2,2-dimethylbutane and 2,3dimethylbutane in silicalite showing fit of Langmuir model to the experimental data. Open symbols: adsorption. Filled symbols: desorption.
The isotherms are shown in Figure 7 together with the theoretical lines calculated from the Langmuir equation with the "best fit" values for b and as. It may be observed that, under comparable conditions, the loading for 23DMB is somewhat smaller than for 22DMB. Equilibrium constants ( K ) obtained from the virial extrapolation procedure are shown in Figure 8. The heats of adsorption a t different sorbate coverages, estimated as previously described, are shown in Figure 9. Also shown are the values obtained for the limiting heats of adsorption from the van't Hoff plots of the Henry constants. It is interesting to note that for these components there is a substantial increase in heat of adsorption with increasing adsorbed phase concentration. Such an effect is quite common in zeolite systems, and it is normally attributed to sorbate-sorbate interaction. Only very limited sorption equilibrium data have been published for the double-branched compounds in silicalite. Voogd and van Bekkum (1991) reported isotherms for 23DMB in dealuminated silicalite at 100 and 200 "C. These data are in good agreement with our isotherms, as may be seen from Figure 7. Cycloparaffins. The isotherms for cyclohexane (cyclo-Cs)and methylcyclopentane (MCP)are presented in Figure 10. The best fit Langmuir isotherms, calculated
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 181 8.00
1
7.00 6.00
-I
l.OOE+W
e
-
5.00 4.00
....*-U"'
U
3.00
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2.00
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0
1.WEc03
P'
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-
60
100
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P CTon)
7.00
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......
2.0
1
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I
2.2
2.4
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2 0.
6.00
-
5.00
-
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1
.
.*--..e.. .........0 ----.c-""
1500~
,,,..*+e* A ..................... ,b' 1 7 5 0 k .............
i
.......
.+
3.00
....... 205's .......--x-
/.K ,,..*X'
1ooo/r
X"
Figure 8. Temperature dependence of equilibrium constants for 2,2-dimethylbutane and 2,3-dimethylbutane in silicalite.
2.00 I ,
1.00
20.0
v:
,
!&e
.... 0
0
I
I
I
I
10
20
30
40
P Van)
A
A 0
Figure 10. Equilibrium isotherms for methylcyclopentane and cyclohexane in silicalite. The curves are calculated from the Langmuir expression (eq 1) with the parameters listed in Table 3. Open symbols: adsorption. Filled symbols: desorption.
0 Q
A
Table 5. Adsorption Capacity of Cyclohexane in Silicalite (% g/g) (Comparison with Other Studies) temp P this Wuetal. Arbuckle Chonand ("C) (Torr) studs (1983) et al. (1987) Park (1988) 22 7.5 4.8 0
22DMB 22DMB-VantHoff
,
0
.
,
.
,
1
.
l
23DMB
A
23DMB-VantHoff
l
.
16
l
2
4 PWe) Figure 9. Variation of heat of adsorption with adsorbed phase concentration for 2,2-dimethylbutane and 2,3-dimethylbutane in silicalite.
in the same way as described previously, are also plotted, and the relevant parameters are given in Table 3. From the molecular dimensions listed in Table 1, which show a critical diameter of 6.9 A for CyClO-c6, it may be concluded that no adsorption would take place within the channels of silicalite (roughly 6 A). However, this is not true and it seems clear that the cyclohexane molecule is sufficientlyflexible to fit within the channels of the silicalite structure. Table 5 shows comparisons
5.0 5.8
16 7.5
22
A
.
100 104 120 200
6.0 1.0 2.4
0.7 1.5
of our adsorption results with previously published data for ZSM-5 or silicalite (Wu et al., 1983; Arbuckle et al., 1987; Chon and Park, 1988). It may be seen that, in general, the adsorption capacity is limited to 5-6 wt %, and this is confirmed by the data from the present study. Methylcyclopentane has the same molecular weight as cyclohexane, but, as can be seen from Table 1, the reduced ring size decreases the critical diameter considerably relative to cyclohexane. It is thus expected that MCP will show faster diffision and may also show a higher equilibrium capacity and a higher heat of adsorption than CyClO-c6. It is seen from Figure 10 that the silicalite adsorption capacity for MCP (about 6.5 wt %I is indeed slightly higher than for cyclohexane. Arbuckle et al. (1987) reported a value of 8.6 wt % at a sorbate pressure of 7.5 Torr and 22 "C. The temperature dependence of the equilibrium constants for cyclo-c6 and MCP, calculated using the virial
182 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
This sequence is consistent with simple geometric considerations. The n-hexane molecule is sufficiently flexible that all CH2< and CH3 groups can be accommodated in the region of low potential energy close to the channel wall. The situation for the terminal 2MP and for cyclohexane is almost as favorable but, with the more highly branched species, only some of these centers can sit in the low energy region with the other centers forced to occupy less energetically favorable positions further from the walls. However the affinity sequence (at the mean experimental temperature):
1 E 4 -,
IEM-.
Y IEi03 -,
MCP > 2MP > 3MP > cyclohexane > 22DMB > 23DMB
1842-
- _. 20
1 8
1 6
22
24
2 6
2 8
1O O O i T
Figure 11. Temperature dependence of equilibrium constants for methylcyclopentane and cyclohexane in silicalite.
A
I
lo.o]
I 0
1
2
/I
A
cyclo-C6
A
cyclo-C6 -v.ntHoff -v.ntHoff
#I
cyclo.C6 I S w h et al.)
3
4
5
II 6
q (a&/g)
Figure 12. Variation of heat of adsorption with adsorbed phase concentration for methylcyclopentane and cyclohexane in silicalite.
plots of the equilibrium data, are shown in Figure 11. The equilibrium constant for MCP is about 10 times greater than for cyclohexane (at the same temperature) although the heat of sorption (Figure 12) is greater for cyclohexane. This can only be an entropy effect; the rotation of the larger cyclohexane molecule must be suppressed to a greater extent than that of MCP more than compensating for the energetically more favorable adsorption of cyclohexane. Heats of Adsorption. The limiting heats of sorption for the CS isomers (included in Table 3) show a well defined variation with the skeletal structures in the sequence:
notably for methylcyclopentane does not exactly follow the sequence of sorption heats so it is clear that entropy considerations must also play a role. SaturationLimit. The variation of saturation limit (qs)with temperature is shown in Figure 13 for some of the sorbates studied. These data can be interpreted in two different ways. A saturation limit of one molecule per channel intersection corresponds t o a capacity of about 6 wt % which is quite close to the observed values. However the data suggest that the saturation limit decreases, modestly, with increasing temperature, which is of course inconsistent with a fixed limit of one molecule per channel intersection. Such a temperature dependence has been observed previously for the adsorption of linear and cyclic paraffins (Barrer and Sutherland, 1956) and for large aromatic molecules (Ruthven and Kaul, 1993) on NaX zeolite. These results were interpreted on the assumption that the saturation limit corresponds to complete filling of the intracrystalline micropore volume by the adsorbed phase. The decrease in saturation limit with temperature arises because the coefficient of expansion of the sorbate is much greater than that of the sorbent. Adsorbed phase densities calculated using specific micropore volumes of 0.19 and 0.56 cm3/gfor silicalite and NaX are shown in Table 6, for n-hexane, cyclohexane, and 3-methylpentane. The densities of the saturated liquid, at the same temperatures, are also listed. For the cyclic and branched species densities for the adsorbed phase are about 50-60% of the bulk liquid density, but the temperature dependence is very similar, so that the ratio of adsorbed phase densityiliquid density varies only slightly. The density values for cyclohexane are very similar to those reported earlier by Barrer et al. (1957) for cyclohexane in NaX. The density ratio for n-hexane is substantially larger, reflecting the better packing of the more flexible molecule. The large size of the molecules of the present study (compared to the pore diameter of silicalite) greatly reduces the contact and the extent of interaction between neighboring molecules. This would explain the conformity of our experimental results with the ideal Langmuir model, as previously observed for large aromatic hydrocarbons on NaX zeolite (Ruthven and Kaul, 1993), another system with severe steric restrictions for diffusion and adsorption. In contrast, much greater sorbate-sorbate interaction is possible for nhexane leading to significant deviation from the ideal Langmuir model and a pronounced variation of heat of sorption with loading.
Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995 183
8.00-
8
22DMB
o 6.00-
0.
4.00
2.00
0.00
x
"
8
A
8
1
X
X
MCP
A
I
-
1
350
Cyclo-C6
I
1
5
1E+Ol
1E46 1E+05
'
IE+M
1E+03 400
500
450
550
IE+M
T (K)
Figure 13. Variation of saturation limit with temperature for cyclohexane, 3-methylpentane, and 2,2-dimethylbutanein sili-
calite.
Table 6. Densities of Cyclohexane and 3-Methylpentane in Adsorbed Phase in Silicate and in Saturated Liquid Phase compd n-hexane cyclohexane
3MP
temp ("C) 30
adsorbed phase 0.53
40 50 120 150 200 250 300 100 125 150 200
saturated liquid
density ratio
0.66
0.80
0.42" 0.41" 0.360 0.307 0.296 0.285 0.058
0.76 0.74 0.677 0.643 0.575
0.55 0.55 0.53 0.48 0.51 0.59
0.357
0.568 0.539 0.507 0.421
0.63 0.58 0.63 0.68
0.315 0.321 0.285
0.480 (T> TJ
aData o Barrer BI titude and Sui--erland et cyclohexane-NaX.
L.
(1957) .,r
Conclusions The equilibrium constants K for similar hydrocarbon structures are summarized in Figure 14. We have included here data available in the literature for nbutane (Hufton and Danner, 1993) and n-hexane (June et al., 1990)to help evaluate how the addition of methyl groups affects the sorption of the different paraffins in silicalite. The equilibrium constants for these CScompounds are evidently sensitive to minor differences in their critical molecular diameters. In particular, for the double-branched and the cyclic compounds, the effect of steric hindrance on the diffusion of these compounds in silicalite is severe and their adsorption equilibrium depends on how well each molecule can adjust its shape to fit the narrow channels andor intersections of the silicalite framework. It is expected that these molecules will probably prefer to reside in the intersection (-9 A) rather than in the channels (-6 A). In general, it may be concluded from our experimental results that the equilibrium constants follow the trend cyclic > singlebranched > double-branched paraffins. Heats of adsorption for the single-branched paraffins were essentially independent of coverage, whereas for
1.5
2.0
2.5
3.0
3.5
1000rr
Figure 14. Comparison of equilibrium constants for paraflins in silicalite. (n-C1 data from Hufton and Danner (1993); n-Ce data from June et al. (1990)J
the double-branched and cyclic paraffins an increase was observed for the values of heats of adsorption with increasing adsorbed phase concentration. In general, limiting heats of adsorption a t low coverage obtained from the van't Hoff plots of the equilibrium constants are in good agreement with the extrapolation of the values derived, at higher loadings, from the equilibrium data. The ideal Langmuir model provides a good representation of the equilibrium data, and saturation limits, estimated from the Langmuir fits, show a decreasing trend with increasing temperatures, as observed previously for other sterically hindered systems.
Nomenclature AI, Az, ..., A, = virial coefficients (eq 2) b = Langmuir constant H , Hg, H, = molar enthalpy of gaseous and adsorbed phases - M a d , = heat of adsorption - A H 0 = limiting heat of adsorption at low coverage K = dimensionless Henry's law equilibrium constant KO= preexponential factor in van't Hoff equation (eq 3) p = sorbate partial pressure q = adsorbed phase concentration q 0 = adsorbed phase concentration at time zero qs = saturation concentration in adsorbed phase R = gas constant T = absolute temperature T, = critical temperature
184 Ind. Eng. Chem. Res., Vol. 34, No. 1, 1995
AUo = internal energy change on adsorption at low concentration
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Received for review January 24, 1994 Revised manuscript received August 25, 1994 Accepted September 1,1994@ IE9400381 Abstract published in Advance A C S Abstracts, November 1, 1994. @
