Thermodynamic Properties of the Adsorbate for High-Pressure Multilayer Adsorption Yoshio Hori' and Riki Kobayashi* Department of Chemical Engineering, William ,Marsh Rice Cniversity, Houston, Texas 77001
Calculated values for the entropy and enthalpy of adsorbed methane on fused silica beads from - 19.9 to - 80°C under elevated pressures are presented. The entropy at low coverage follows the two-dimensional free gas theory of Kemball. At higher coverage the entropy and the enthalpy approach the same values as the compressed gas values at the molar volume of the adsorbed phase. The entropy value at the lowest isotherm (-8O.O0C), only 2.3" above the critical temperature of methane, i s essentially constant for coverage from 0.7 to 2.9 layers. This value i s close to that for saturated liquid methane at - 103.8"C, which has the same molar volume as the adsorbed phase. The persistence of liquidlike behavior i s seen considerably above the (normal) critical temperature. A discussion of the effects of ihese data on the potential theory for supercritical temperature and the adsorbed phase is given.
A d s o r p t i o n a t high pressure has been reported (Hori and Kobayashi, 1971) in terms of two definitions: abfolute adsorption and Gibbs adsorption. The adsorbed phase volume is determined by the surface area of the adsorbent and the intermolecular forces between the adsorbate and the adsorbent. Absolute adsorption is defined as the total amount of adsorbate in the adsorbed phase volume, while the differential adsorption, introduced by Gibbs (1961) and later defined as "Gibbs adsorption," is that excess of the adsorbate over that which would be in the adsorbed phase volume with no intermolecular force field of the adsorbent (von dntropoff, 1952). The two definitions are related.
ddsorpt'ion can be regarded as a phase equilibrium; almost all theoretical thermodynamic treatments lead directly to absolute adsorption. However, Gibbs adsorpbion is the only amount that can be measured by the traditional volumetric and gravimetric method. For instance, one can obtain Gibbs adsorption by means of a gravimetric method. In order to evaluate absolute adsorption, one has to make a buoyancy correction. L-nless one can measure the adsorbed phase volume, it' is impossible t o know the amount of buoyancy correction. Only series perturbation gas chromatography (Hori and Kobayashi, 1971; 1Iasukan-a and Kobayashi, 1968) can yield the value of V so that the experimental value of the absolute adsorption can be determined. The value of C, is small a t low pressures, and VC, is negligible in eq 1. Therefore, XG is nearly equal t o SAa t 1 0 ~pressures. At high pressures VC, becomes appreciably large and SGis quite different' from X.4 (von -Intropoff, 1952; llenon, 1968). An estimation of the absolute adsorptioii from the Gibbs adsorption was made by deBoer and Menon (1962), along n-ith a discussion of the entropy and mobility of the adsorbed molecules. The potential theory for adsorption below the critical temperature of the adsorbate was developed by Polanj-i (1916). The extension t o suporcritical conditions in various manners, as reviewed by Youiig and Crowell (1962), required assumpPresent address, Department of Industrial Chemistry, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo, Japan. 26
Ind. Eng. Chem. Fundom., Vol. 12, NO. 1 , 1973
tions for the properties of the adsorbed phase which were not verified experimentally. Values for absolute and Gibbs adsorption and the molar volume of the adsorbed phase have been discussed (Hori and Kobayashi, 1971) for the adsorption of methane on fused silica beads (Porasil) from -91.9' to 31.4OC at pressures up to 120 atm. The data are tabulated in Table I. The thermodynamic analysis of the data is presented here. The Thermodynamic Relationships for the Adsorbed Phase
The usual thermodynamic notation will be employed. Consider a system of a n absorbate gas in equilibrium with its adsorbed phase on a n adsorbent. The relationship for an infinitesimal change in the system conditions is (Hill, 1950)
The isosteric heat of adsorption qst is given by (Hill, 1950) 4.t = T(Sg
- 9,)= Hg - E t a
(3)
In this study the enthalpy of the adsorbed phase is defined as
Ha
=
Ea
+ PVa
(4)
Combination of eq 2 with eq 3 gives the exact relationship 9.t
=
H, - a,= T(Sg - Sa) =
The data of this investigation (Hori and Kobayashi, 1971) showed that the absolute adsorption us. pressure isotherms had a region of constant SA. This horizontal plateau did not occur for absolute adsorption vs. the gas phase fugacity f; therefore, the derivative in eq 5 can be more easily evaluated from
Table I.
-19.9
-40.2
-60.0
-80.0
-82.0
-91.9
a
Adsorption Data for Methane on Porasil (Fused Silica Beads)
Pressure, atm
Fugacity, atm
Gos phase density, mmoIes/cm3
Absolute adsorption, mmoIes/g
Gibbs adsorption, mmoles/g
10.0 20.0 30.0 50.0 50.0 80.0 100.0 5 0 10.0 20.0 40.0 60.0 80.0 90.0 110.00 10.0 20.0 40.0 40.0 60.0 80.0 90.0 95.0 100.0 5.0 10.0 20.0 30.0 40.0 60.0 80.0 90.0 100.0 110.0 5.0 10.0 20.0 40.0 45.0 50.0 60.0 80.0 100.0 110.0 120.0 10.0 20.0 30.0 40.0 40 . 0 45,o 50.0 60.0 80.0 100.0 110.0 118.13 118.20 3.0 5.0 7.06 9.26 13.21 15.96 20,07 22.94 26.62 31.20
9.87 19.46 28.78 46.67 46.67 71.78 87.52 4.92 9.70 18.80 35.32 49.75 62.30 67.97 78.27 9.61 18.45 33.92 33.92 46.63 56.87 61.19 63.14 65.10 4.87 9.49 17.97 25,47 32.01 42.26 48.97 51.49 53,79 56.01 4.83 9.32 17,28 29.11 31,ll 32.51 34.00 36,73 39.46 40.84 42.25 9.29 17.19 23.70 28.72 28.72 30.55 31.48 32.81 35.38 37.98 39,30 40.39 40.40 2.93 4.79 6.65 8.51 11.77 13.85 16.73 18.56 20.71 23,02
0 393 0 797 1 213 2 077 2 077 3 446 4 394 0 244 0 497 1 027 2 203 3 564 5 130 5 982 7 756 0 545 1 141 2 528 2 528 4 284 6 544 7 838 8 489 9 140 0 294 0 604 1 287 2 075 3 025 5 806 10 477 12 363 13 638 14 554 0 327 0 681 1 497 4 157 5 650 11 937 15 289 17 038 17 994 18 363 18 684 0 690 1 524 2 620 4 407 4 407 6 615 14 419 16 053 17 483 18 341 18 678 18 920 18 922 0 207 0 352 0 5062 0 6752 1 013 1 266 1 717 2 026 2 533 3 376
0.487 0,852 1.185 1.744 1.702 2.37 2.80 0.610 1.031 1.727 2.74 3.61 4.48 4.82 5.19 1.458 2.34 3.79 3.73 5.11 6.04 6.29 6.46 6.46 1,282 2.02 3.30 4.22 5.30 7.56 9.40 8.77 9.64 9.34 1.954 2.97 4.84 9.79 12.35 12.92 12.09 12.53 16.04 17.10 21.48 3.07 4.99 7.13 11.04 10.91 13.04 12.94 12.25 l5,20 19.09 21.18 26.46 27.06 1.824 2.46 3.00 3.54 4.50 5.12 6.24 7.15 8.61 12.39
471 816 117 494 492 060 420 600 006 618 409 004 334 418 080 406 18 22 21 78 81 59 61 23 266 952 04 77 45 5 28 4 09 3 29 2 73 1 88 1 931 2 86 4 47 7 83 8 32 4 52 2 77 1 74 1 30 1 12 1 04 2 98 4 62 6 16 8 57 8 56 8 10 3 17 2 28 1 45 0 91 0 55 1 04 1 22 1 802 2 41 2 92 3 39 4 24 4 78 5 67 6 35 7 39 10 16 0 0 1 1 1 2 2 0 1 1 2 3 3 3 3 1 2 3 3 3 3 3 3 3 1 1 3 3 4
Vg,a
cm3/g
2.213 2.204 2.196 2.133 2.151 2.141 2.130 2.213 2.196 2.141 2,099 2,077 2.025 2.014 1.978 2.155 2.104 2.025 2.041 1.938 1,903 1.925 1.901 1.906 2.188 2.140 2.044 2.025 1 953 1.884 1.831 ...
1.807 ...
2.174 2,088 1.997 1 .768 , . .
1.696 1.188 1.959 ... , . .
...
2.110 2.003 1.878 ... , . .
. . .
...
... ... ..
... . . .
...
2.138 2.110 2.088 2.033 1,992 1.983 1.907 1.861 1.787 1.610
V g (by He dissolution),o cm3/g
2 243 2 219 2 159 2 104 2 073 2 040 1 997 1 971 2 187 2 115 2 021 2 053 1 953 1 908 1 903 1 912 1 895 165 063 029 966 1 855 1 741 1 799 1 741 1 730 2 190 2 109 2 018 1 778 1 534 1 545 1 638 1 614 1 428 1 378 1 154 2 113 2 007 1 879 1 687 1 714 1 501 1 570 1 627 1 462 1 257 1 143 0 905 0 882 2 165 2 125 2 098 2 050 2 000 1 9i8 1 907 1 855 1 766 1 589
T h e distinction betw-een the two was deacribed in sections IVA-D and \’A in the paper by Hori and Kobayashi (1971)
2 2 2 1
+ 31.4
I "
'?-
EXPERIMENTAL -20.0 -40.2 I '
TEMPERATURE, 'C
-60.0
-80.0 I
-91.9
I
'
i
I,
f
E
l
2-a
tl
I
l
------
- - -/SbTURATEO - - _ _LlOUlD _ _AT _-1038.C
30
50
40
l i
10 mSOLUTE ADSORPTION
0 5 m molo/gm -
1 x)
15 NA mmim/qm
_1
4
------A 20
Figure 2. Entropy of adsorbed methane on fused silica beads. The data for NA = 16.0 and 20.0 mmoles/g were taken from the isotherms at -80.0 and -82.0"C
\\ a5
bT -80.C
1
1 50 60 RECIPROSAL ABSOLUTE TEMPERATURE, I/T X 10-4 e K-'
e
WEWE. 3.0 4.0
40
I
2.0 I
1.0
I
5.0
I
I
I
6.0 i
Figure 1. Temperature dependence of fugacity at fixed absolute adsorption. Only selected experimental data are shown for clarity
Basic thermodynamic relationships are (Lewis and Randall, 1961)
(7) and
The combination of eq 5-8 gives
0
5
10 b8Y)LUTE ADWRPTION,
I5
Nb
, mmoles/gm
20
Figure 3. Enthalpy of adsorbed methane on fused silica beads
mmoles/g. The B point method (Young and Croaell, 1962) gave 3.0-3.2 mmoles/g for the monolayer coverage. The coverage e is defined as
and
9 =
The more widely known expression for low-pressure adsorption states that
At low pressure, t, is much smaller than V,, and the adsorbate gas may be treated as an ideal gas, with no difference evident between eq 9 and eq 12. At the higher pressures of these studies the difference is quite considerable. Equations 9-11 form the basis for calculations. An equation of state for methane by Vennix and Kobayashi (1969) was used to compute (H, - H * ) and (S,- S*),with the ideal reference H * and S* taken from Tester (1961). The experimental data provided the fugacity-temperature values for [ b I n f / W / T ) INA. Entropy and Enthalpy of the Adsorbed Phase
Monolayer Coverage. The data a t -91.9OC were treated by the BET method for N A us. P/Po, where Po is the vapor pressure. A straight line was evident between 0.05 and 0.35 for P/Po, which gave the monolayer coverage NAO as 3.15 28
Ind. Eng. Chem. Fundam., Vol. 12, No. 1, 1973
NA/NAO
(13)
Using NAO = 3.15 mmoles/g, a coverage e = 2 was observed (Hori and Kobayashi, 1971) a t -40.2"C, some 40" above the critical temperature of methane, -823°C (Vennix and Kobayashi, 1969). Results
Figure 1 shows typical results of fugacity us. reciprocal temperature a t fixed absolute adsorptions obtained from the experimental results (Hori and Kobayashi, 1971). It is evident that the curve through each set of data is a straight line and is a constant. the partial derivative [bIn f/b(l/T)]NA,A Four isotherms from -19.9 to -8OOC for the differential entropy and enthalpy of methane on Porasil are shown in Figures 2 and 3. Shown as dashed lines are the computed values a t each temperature for the nonadsorbed phase. The molar volume was estimated (Hori and Kobayashi, 1971) to be 50.9 cm3/mole for -80 to -91.9OC and to be 54.0 em3/ mole for -19.9 to -6OOC. Saturated liquid methane has a molar volume of 50.9 cm3/mole a t - 103.8OC, and the corresponding values (Tester, 1961) of entropy and enthalpy are shown as dot-dash lines in the figures.
Entropy. From Figure 2, in the low coverage region well below monolayer (8 = 1) the differential entropy of the adsorbed phase decreases as the coverage increases. This decrease in entropy is ascribed t o the decrease in the mobility of the adsorbed molecules. I n this region the adsorbed molecule could be described by the two-dimensional mobile gas theory of Kemball (1946). At a n adsorption of 0.5 and 1.0 mmole/g (or up to e = 0.30), the vibrational frequency of the adsorbed molecules normal to the adsorbent surface was found to be practically constant (4.7-6.7 X lo1* sec-l) regardless of the temperature. However, as the coverage increases beyond monolayer, multilayer adsorption occurs and the entropy begins to increase. The entropy of the adsorbed phase approaches that of the highly cornpressed adsorbate gas a t the same molar volume, with the approach occurring a t lower coverage for the higher temperatures. The lowest isotherm, -8OoC, shows a n extensive region of constant entropy from 8 = 0.7 to 2.9, about 25.05 caljdeg mole, slightly greater than the 24.98 cal/deg mole entropy of saturated liquid methane a t the same molar volume. The increase toward the compressed gas value occurs a t a coverage from 3 to 4 times the monolayer value. Enthalpy. I n Figure 3 the differential enthalpy is seen to increase continuously as the coverage increases. This can be explained as a natural result of the heterogeneity of the surface. Again, the compressed gas value a t each temperature is approached a t high coverage. The -80°C isotherm eshibits a n additional effect; a n inflection is seen in the coverage region from 8 = 2-3, in the region of constant entropy. The inflection occurs close to the enthalpy value (1967 cal/mole) for the saturated liquid a t the same molecular volume. T h e Potential Theory for t h e Adsorbed Phase. The adsorbed phase a t supercritical temperatures was considered to be compressed gas in the early potential theory for adsorption by Polanyi (1916). Modifications t o the potential theory have been made for adsorption a t temperatures greater than the critical temperature of the adsorption a t temperatures greater than the critical temperature of the adsorbate. Dubinin (1960) defined the adsorption space (volume) by the van der K a a l s constant as
W
=
nb
(14)
The adsorption potential a t above critical temperatures mas given as E
=
RT In ( r n P c / P )
(15)
According to the theory, eq 14 and 15 describe a single characteristic curve for IV us. E . Using absolute adsorption N A for n, the present experimental data were used to test Dubinin's theory; no characteristic curve was found. Lewis, et al. (1950), tried to correlate the adsorption data of methane above the critical temperature. The experimental data were treated in terms of N V , and T / V , log (fo/f).The vapor pressure was extrapolated beyond the critical point for PO(and hence the fugacity fo a t that pressure). The molar volume of the adsorbed phase was assumed to be that of the liquid a t a temperature that would make the vapor pressure of the pure liquid equal t o the adsorption pressure. The present experimental data w r e relatively well correlated below monolayer by their method, but a systematic temperature-dependent shift was found above monolayer. In another analysis, Naslan, et al. (1953), treated the adsorbed film as a compressed gas. The vapor pressure was
'Tc
.J
i
i
-_L- . . ' - -Ul
1
0
l i
103 2co CORRELATION PARAMETER. T log (f./f)
J
xu
Figure 4. Experimental adsorption data for methane on fused silica beads plotted according to Lewis, et a/. ( 1 950), correlation with observed taken as V ,
v,
evaluated similarly. The molar volume V , was obtained from Poand the P-V-T relationship for the adsorbate. h plot after Maslan, et al., of nV, us. T / V , log (fo/f) of the present data give a single characteristic curve below e = 1, but a poor correlation was found above monolayer coverage. With the adsorbed phase taken as the same molar volume (50.9 and 54.0 cm3/mole) and fugacity fa as the compressed gas, a plot of NAV us. RT In (fa/f) gave a single curve for coverage above 8 = 3, but a poor correlation was found for lower coverages. Grant and Manes (1964) developed the method of Lewis, et al. (1950). They correlated adsorption data of methane on activated carbons a t - 195.8 and -78°C approximately from 0.006 to 100 Torr. The present data were treated by their method, using the molar volume of the adsorbed phase estimated by them (Grant and Manes, 1966). Their method, however, failed to give a characteristic curve. In another modification of the correlation of Lewis, et al. (1950), the observed value of (Hori and Kobayashi, 1971) was used for V , in N A V , us. T / V , log (fo/f) plot, with fo determined by the extrapolation as stated above. This treatment of the present data is shown in Figure 4 with V omitted since it is a constant (only one adsorbate, methane). The true meaning of the adsorption potential is lost when f exceeds fo and log (fo/f) becomes negative, but these values are given in the figure for comparison. The branching from the correlation for the various isotherms occurs a t higher absolute adsorption values as the temperature decreases: 4.4 mmoles/g a t - 19.9"C, 5.4 mmoles/g a t -4O.2"CJ 6.0 mmoles/g a t -6O.O0C, and 9.5 mmolesjg a t -8O.O"C. Examination of Figure 2 shom t,hat the differential entropy is approaching the compressed gas value a t these respective amounts of adsorption. These observations lead t'o the conclusion that the present method correlates esperimental data rather well until the adsorbed phase reaches the equivalent compressed gas state. In the region of applicability t,he extrapolation of the vapor pressure beyond the critical temperature implies that the adsorbed phase ' s in the liyuid'ike state. 'i'he absolute adsorption is requisite to correlate esperimental data a t high pressures by the potential theory. The present esperimental data, the only measured absolute adsorption, were not correlated by previous methods as discussed above. The reason would be given as follows. The molar
va
Ind. Eng. Chem. Fundam., Vol. 12, No. 1 , 1973
29
volumes of the adsorbed phase at supercritical temperatures were estimated in connection with bulk liquid by various authors. Most of these estimated values change so much with the adsorption pressure, not with adsorption temperature. However, the molar volume of the adsorbed phase is actually almost constant in the condition of +31.4" t o -91.9"C and up to 100 atm as determined by the present authors (Hori and Kobayashi, 1971). The -8O.O'C Behavior. As shown in Figure 2, the isotherm 2.3' above the critical temperature of methane has a wide range of adsorption with a constant partial molar entropy. This value is almost the same as t h a t for saturated liquid methane a t the same molar volume as the adsorbed phase: at -103.8"C, V = 50.9 cm3/mole, = 24.98 cal/deg mole. Figure 3 also indicates that the -8O.O"C isotherm approaches the molar enthalpy at the same conditions, and then a n inflection occurs. I n addition, in the development of their correlation, Grant and Manes stated that the liquidlike state might persist on the adsorbent a t supercritical temperatures. The present data verify this assumption. The behavior of the -8O.O"C isotherms strongly indicates that the adsorbed phase corresponds t o the adsorbate as a free liquid at a lower temperature than the adsorption temperature. The liquidlike behavior of the adsorbed phase occurs a t temperatures far above the critical temperature of the adsorbate methane. As even more methane is adsorbed, the adsorbate behavior changes t o that equivalent t o a highly compressed gaseous methane. The transition between the two types of behavior appears t o be continuous with temperature.
s
Acknowledgment
Tomoko Xakahara computed the thermodynam'c properties for gaseous methane. Nomenclature
b C
van der Waals constant, em31mole concentration of adsorbate] mmoles/cm3 E internal energy, cal/mole H molar enthalpy, cal/mole f - gas phase fugacity, atm -1 amount of adsorption, mmoles/g n = amount of adsorption, mmoles/g P = pressure, atm qat = isosteric heat of adsorption, cal/mole R = gas constant, cal/deg mole S = molar entropy, cal/deg mole =
= = = = =
30 Ind.
Eng. Chem. Fundam., Vol. 12, No. 1, 1973
T V V
= temperature,
"K
= adsorbed phase volume per = molar volume, cm3/mole
weight of adsorbent, cm3/g
W = adsorption space or volume, cm3/g GREEKLETTERS = coverage, as fraction of monolayer e = adsorption potential function] cal/mole 7 = reduced temperature
e
SUBSCRIPTS = area of adsorbent = adsorbed phase = absolute = critical property g = gas phase G = Gibbs 0 = saturation state
A a A c
SUPERSCRIPTS * = low-pressure ideal gas reference state = partial molar quantity
0
=
monolayer property
Literature Cited
de Boer, J. H., Menon, P. G., Kon. Ned. Akad. Wetensch. Proc., Ser. B 65, 17 (1962). Dubinin, M. M., Chem. Rev., 60, 235 (1960). Gibbs, J. W., ''The Scientific Papers of J. W. Gibbs," Vol. I, pp 235, 315, Dover, New York, N. Y., 1961. Grant, R. J., Manes, M., IND.ENG.CHEM.,FUNDAM. 3, 221 (1964). Grant, R. J., Manes, XI., IND.ENG.CHEM.,FUNDAM. 5 , 490 (1966). Hill, T. L., J . Chem. Phys. 18,246 (1950). Hori, Y., Kobayashi, R., J . Chem. Phys. 54, 1226 (1971). Kemball, C., Proc. Roy. SOC.London, Ser. A 187, 73 (1946). Lewis, W. K., Gilliland, E. R., Chertow, B., Cadogan, W. P., Ind. Eng. Chem. 42, 1326 (1950). Lewis, G. N., Randall, M., "Thermodynamics," revised b K. S. Pitzer, and L. Brewer, pp 155, 156, McGraw-Hilf New York, N. Y., 1961. Maslan, F. D., Altman, -"I., Aberth, E. R., J. Phys. Chem. 57, 106 (1953). Masukawa, S., Kobayashi, R., J . Gas Chromatogr. 6, 266 (1968). Menon, P. G., Chem. Rev. 68,277 (1968). Polanyi, RI., Verh. Deut. Phys. Ges. 18, 55 (1916). Tester, H. E., "Thermodynamic Functions of Gases," F. Din, Ed., Vol. 3, p 29 ff, Butterworths, London, 1961. Vennix, A. J., Kobayashi, R., A.Z.Ch.E.J. 15, 926 (1969). von Antropoff, A. Kolloid 2. 125,40 (1952). Young, D. XI., Crowell, A. D., "Physical Adsorption of Gases," pp 137. 189, Butterworths, London, 1962. RECEIVED for review January 25, 1971 ACCEPTED October 2, 1972 The National Science Foundation provided financial support for the work.
