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Adsorption thermodynamic functions and the mobility of SO2 on Aerosil
Adsorption Thermodynamic Functions and the Mobility of SO2 on Aerosil S E R G I O O. VASQUEZ AND LUIS A L Z A M O R A Departamento de Qufmica, Facultad de Ciencias Ffsicas y Matemdticas, Universidad de Chile, Santiago, Chile
Received June 23, 1986; accepted May 31, 1987 A study of the adsorption and thermodynamic functions of sulfur dioxide on Aerosil has been made, leadingto some conclusionsabout the mobilityof the SO2molecule.The differentialand integralenthalpies and entropies of adsorption, together with a statistical mechanical interpretation of the system, are discussed. Particularly,the statistical mechanical calculation of the integral entropy of adsorption allows a comparisonto be made betweenthe experimentalresultsfor the SO2-Aerosilsystemand those obtained for adsorption in two limiting cases: an immobile or localized model that can be associated with chemisorption, and a mobile film model that can be related to physisorption. The results confirm a weak gassolid interaction with a highly mobile adsorbed phase. © 1988AcademicPress,Inc. INTRODUCTION There is great interest in the investigation of the thermodynamic properties o f adsorption and the nature of the interaction of polar molecules with hydroxylated surfaces. Although numerous reports on the adsorption o f polar molecules on acidic solids have appeared, none seem to have been published on the SO2Aerosil system. This paper reports on a thermodynamic study of the adsorption of SO2 on Aerosil, with determinations of the isosteric heat and the integral enthalpy and entropy of adsorption. The latter parameter is alternatively calculated by a statistical mechanical treatment of the problem, originally developed by de Boer and Kruger (1), a theoretical approach that shows that the SO2-Aerosil interaction is of the mobile film type. EXPERIMENTAL The adsorption isotherms were determined in a conventional volumetric apparatus and with reproducible readings being taken at intervals that would allow equilibrium to be reached. The temperature of adsorption was kept within +0.1 K.
The experiments were performed using Aerosil (200 m2/g), which was outgassed overnight at 110°C and l0 -4 m m Hg as described earlier (2). Sulfur dioxide (Matheson Co.) was of anhydrous quality and was drawn directly from the cylinder, after line flushing, to a trap attached to the apparatus. It was then purified by alternate freezing and thawing in vacuo. RESULTS AND DISCUSSION The adsorption kinetics of the SO2-Aerosil system was studied prior to the determination of the different isotherms, since that information was needed for the experimental procedure that followed. Figure la shows the observed behavior, with an adsorption temperature of 25°C. For low absolute pressure values (curve 1), the adsorption equilibrium was reached in about 50 min, which is consistent with reported data (3). G o o d reproducibility was attained. The kinetic behavior was different when a higher pressure was used. At equilibrium values of about 100 Torr the process was m u c h slower, no less than 3 h being required to reach equilibrium (curve 2). In this case reproduc398
002 i-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
MOBILITY OF SULFUR DIOXIDE
399
a I Peq--98,4 mmHr
I
I
(2)
S
1
<[
<'l' I I
Peq=17,8 mm Hg
(~..4"5.....~
I
=, o
0
1
2
3 TIME, ( h )
4
5
G
b
8.0 _
7.C
t....u~
6.C
/
-
tam ~.,,
/ e
0
_
20
40
60 80 PRESSURE, mm Hg.
100
FIG. 1. A d s o r p t i o n kinetics (a) a n d adsorption isotherms (b) for sulfur dioxide on Aerosil.
ibility was less reliable, and at yet higher pressures reliability decreased even more. These results made it advisable to limit the study to the pressure interval between 0 and 100 mm Hg.
Adsorption Isotherms Figure lb shows the experimental results for the adsorption isotherms of the SO2-Aerosil system at 0.2, 25, 35, and 45°C. Within the relative pressure range under consideration, the SO2-Aerosil system shows as a characteristic the lack of large adsorbed volumes, while the shape of the isotherms shows that the monolayer region has not yet been reached.
Among the many known models, that of BET (4) has been classically accepted and used for the determination of surface areas, even though its validity decreases at low relative pressures because the energy homogeneity of the surface, which is one of its characteristic assumptions, is lost. In this study, a relative pressure range of 10-3 through 3 × 10-2 was covered, so that the BET model became inapplicable. Therefore, a different model was used, that of Kaganer (5), which is valid at low surface coverage; it takes into account the solid's energy heterogeneity and allows the determination of the monolayer volume I'm. Using the potential theory originally introJournal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
400
VASQUEZ AND ALZAMORA
duced by Polanyi, and Dubinin's method for the determination of the pore volume, Kaganer suggests a semiempirical expression that allows the adsorption phenomenon to be interpreted for a low range of surface coverage under relative pressures of the order of 10-4 to 10-2 , log Va = log Vm - D[log(po/p)] 2,
[1]
the manufacturers, Degussa (6), the value of aort (the number of silanol groups per 100 A 2 of surface) for the isolated type is 2.6. Since the surface area is 200 m2/g of solid, there are 5.2 X 1020 isolated O H groups per gram of solid. If the number of adsorbate molecules in the monolayer is B, and assuming that each of these molecules is joined to a silanol group by an hydrogen bridge, then B = 5.2 × l020 adsorbate molecules/g of solid, which results in an STP volume Vm = B(Vo/No) = 19.35 cma/g.
where Po is the adsorbate's saturated vapor pressure, Va is the adsorbed volume, and D is a parameter related to the mean value of the adsorption energy. (ii) Method based on the physical properties When log Va is plotted against [log(po/p)] 2, of the adsorbate. Once a monolayer condition Vm can be obtained from the log Vm intercept. has been achieved, the adsorbate can be viTable I shows the values obtained for this pasualized as a film of molecules having the rameter from the experimental results shown characteristic of the condensed liquid. If each in Fig. 2. In all these cases the relative pressure molecule occupies an area ~0 o f the monorange considered was 2 × 10-3 to 3 X 10 -2. layer, and the solid has a specific surface area The value that a given model yields for a A, the monolayer volume would be (7), parameter becomes significant when it is comparable to the value obtained from indeA pendent sources. In this paper two alternative Vm = 0.269~----~' [2] methods are used to determine the volume of the monolayer, one based on the chemical where a0 is 1.985, 2.012, and 2.042 at 25, 35, structure of the adsorbent, and the other based and 45°C, respectively. on the physical properties of the adsorbate. Table I shows the values for the monolayer, (i) Method based on the chemical structure Vm(F), for SO2 obtained by this method, using of the adsorbent. It is known that polar gas a value of 200 m2/g for the specific surface molecules, such as water and organic esters, area, A, of Aerosil. It can be seen that Kagainteract through hydrogen bridges with the ner's model yields values for Vm that are reasurface silanol groups. In this way, if the num- sonably close together. ber of isolate silanol groups on the surface is Considering the chemical structure of the known, a probable value for the volume of the adsorbent and the physical properties of the monolayer can be established. According to adsorbate, it can be concluded that the adTABLE I MonolayerCapacity, Vm,for SO2 on Aerosil from the Kaganer Method, Vm(K);Chemical Structure of the Adsorbent,Vm(Q);and PhysicalPropertiesof the Adsorbate, Vm(F) Monolayercapacity (ml S-1) T (*C)
V~(K)
0.2 25.0 35.0 45.0
16.62 16.73 16.18 15.96
Vm(Q)
Vm(F)
V~(K)/V~(Q)
V=(K)/Vm(F)
38.66 37.50 36.99 36.44
0.859 0.864 0.836 0.825
0.430 0.446 0.437 0.438
19.35
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
MOBILITY OF SULFUR DIOXIDE
401
o.
d
I,,i.I Q13
=,
2
3
~,
5
6
7
e
0
I
2
3
,~
5
6
7
8
tog(Polp)2
FIG. 2. Kaganerplots for sulfurdioxideon Aerosil. sorption of SO2 on Aerosil is more closely related to the occupancy of specific sites on the solid by the adsorbed phase, than to the formation of a condensed film. In fact, if the values obtained in both ways are compared with those derived from Kaganer's model, it is seen that the ratios are closer to unity using Vm from method (i) (Table I). Finally, it can be inferred that the monolayer condition would point to an occupancy of the order of 85% of the superficial silanol groups.
Heats and Entropies of Adsorption From the experimental data obtained at different temperatures it was possible to obtain the heats and entropies of adsorption, which
are extremely useful in the process of interpreting and analyzing the isotherms. One important aspect of this treatment is that it allows these thermodynamic parameters to be compared with those supplied by statistical mechanical models. Figure 3a shows the isosteric and integral heats, qisost and AH~s, respectively, as functions of the adsorbed volume obtained from isosteres and iso-II (spreading pressure) straight lines, respectively. Figure 3b shows the integral entropy of adsorption calculated from (7), A Sa,~s = (Sa - S °)
AHa~ - ~--
R ln(p/p°),
[3]
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
402
VASQUEZ AND ALZAMORA 8.0
\
7.5 E qisost 7.0
8 6.5
6.0
.....
/ _-~_ _
--~-~
AHads
o-~ --if---t-. . . .
OL
5.5 b -8 "-r.
~-1
~-~- o---c--o--
-20 ............................. -2t,
0
1
A$_~,
2 3 4 5 6 7 VOLUME ADSORBED, m| (STP)/g.
FIG. 3. Thermodynamicsfunctionsfor the adsorption of sulfur dioxide on Aerosil: (a) heats of adsorption; (b) integralentropy. where AHad~ is the integral enthalpy of adsorption and p0 = 760 m m Hg. These thermodynamic parameters, calculated from the experimental data, immediately show some peculiarities of the SO2-Aerosil system. The isosteric heat is relatively low, only slightly higher, by about 1 kcal/mole, than the heat of liquefaction of the adsorbate, pointing to a weak interaction of the physisorption type. Only at low surface coverage, lower than 1.5 cm 3 STP/g, does it show a tendency to increase, a result that was expected because, at low equilibrium pressures, the fraction of the surface that presents more active sites can adsorb the molecules liberating more energy. Figure 3a also shows a remarkable constancy in the value of the integral enthalpy of adsorption within the interval under consideration, and its agreement with the heat of liquefaction of the pure adsorbate QL. However, Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
this is just a peculiarity of the system, since at pressures so much lower than P0 as those that have been studied here, the adsorption mechanism bears no relation to that of the condensation of a gas. This is confirmed by the values obtained for the integral entropy of adsorption, Fig. 3b, since ASa~ is less negative than that of a simple condensation (ASL). This behavior indicates that the adsorbed phase is under an intermediate condition, between a gas phase and a condensed phase, a situation that has been already pointed out in this laboratory (8). The phenomenon is understandable if it is postulated that the adsorbed phase is a bidimensional gas with no restrictions to its motion in the plane of the adsorbent's surface, thus implying less mobility than that in the gas phase (tridimensional), but higher than that in the liquid phase. In this respect the variation of ASa~ with coverage indicates the change from a highly mobile phase at low pressures (therefore with a low entropy change) to an adsorbed phase whose mobility progressively decreases. At the limit, when the monolayer is reached, one would expect an entropy change similar to that of a condensation.
Statistical Mechanical Calculation of the Entropy of Adsorption The previously obtained results bring up, like every experimental work, the problem of their veracity. The question is, how can it be proved that they actually correspond to the real situation? Statistical mechanics is an important theoretical tool that allows the overall properties of a system to be known starting from the properties of the microsystems (in this case, the individual molecules). An outline of the calculation of the entropy follows. If a gas in its standard state (normal pressure) is adsorbed on a surface occupying a fraction 0s of the surface, the entropy change between these reference states would be s ASads = AS~r + ASCot + ASSb.
[4]
403
MOBILITY OF SULFUR DIOXIDE
Each of the terms of Eq. [4] can be evaluated from the respective partition function, considering the two extreme models of the adsorption mechanism: an immobile or localized model, and a mobile film model (9).
Immobile Adsorption The partition function, qtr, for a molecule with n degrees of translational freedom is
= [27rmkT~ ~/2 ~ h2 / tn,
qtr
[51
where L is the characteristic spatial parameter. The translational entropy is Str=Rln
No + -
qtr
~ cgZ]v,n
+ 1 .
[6]
Considering the difference between the adsorbed state, in which there are no translational degrees of freedom, and the gas state where L n = V (the molar volume in the reference state), and n = 3, then lo~AS~r = - 3 8 . 5 5 cal K -l mole -l. As to the rotational contribution, the calculations consider that the partition function is 1
qrot =
Ixy = 1.4911 ×
10 -39 g cm 2 molecule -l
and SSrot = 3.18 cal K -l mole -l. The difference between the two calculated types of rotation is small, but some considerations about the stability of the resonant structure of SO2 in case (a) make it preferable as a representative of the physicochemical situation. Finally, locSr~ot = - 1 5 , 2 4 cal K -l mole -1.
3
X I b" • • i~)l/n[n/2,'l rra+ [ h 2 kT (I~ J
[7] where a + is the symmetry factor; Ia, I s . . . . , IE are the molecule's m o m e n t s of inertia; and
a+b+
Therefore, Sr~ot= 20.24 cal K -1 mole -l for the gas phase. In the adsorbed phase, three rotational modes can be conceived, which are shown in Fig. 4. O f these situations, (c) can be discarded immediately, since it assumes two hydrogen bridge-type associations, which would lead to an interaction energy higher than the one found experimentally and to a rotational and location hindrance due to the size of the SO2 molecule. Case (a) has only one degree of rotational freedom around the axis y, leading to Sr~ot = 5.0 cal K -1 mole -I, while case (b) shows rotation around an axis that goes from the center of mass of the SO2 molecule to one of the oxygen atoms. In this case the m o m e n t of inertia is
... +e=n.
In order to determine the vibrational entropy, the molecule's vibrational frequencies in the adsorbed state must be known. An approximation that makes it possible to determine the frequency perpendicular to the surface, v±, consists in extrapolating the experi-
On the other hand, the rotational and vibrational entropies are derived from
S=R[Inq+T(O~ q
] V,n
[8]
For SO2, a + = 2, and the principal m o m e n t s of inertia are 1~ = 1.0505 × 10 -39 g cm 2 molecule -1
Iyy = 9.2261 × Izz = 10.2765 ×
10 -39 g cm 2 molecule -l
10 -39 g cm 2 molecule -1.
o~-~'~
o
o, 0"-.i B
i 0
I
- - S i - lal
f 0 --
I
Sl'-1b1
(el
FIG. 4. Geometry of the possible ways of rotation of the SO2 molecule in the localized model. Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
404
VASQUEZ AND ALZAMORA
mental data, according to the Hill-de Boer model (10). In this case, the constant K1 of the H D B model is, in the harmonic approximation,
K1
= [(21rMRT) 1/2] L ~ j × e-Qmr'
[9]
where M is the molecular weight of SO2, T0 is the average time for the vibration normal to the surface, an~ is the specific area available to each adsorbate molecule on the monolayer (obtained from the BET area and Vm), Q is the heat of adsorption, and T is the temperature. Since the dependence of K1 on the temperature is important only in the exponential term, when In K~ is plotted against T -~ a straight line is obtained having a slope -Q/R and an intercept of ln[(27rMRT)l/2/N':oam], from which one can calculate ~.L = T~ 1• In our case, considering the 25, 35, and 45°C isotherms, we obtained u~ = 6.16 × 1012 s-~ at a temperature of 307.44 K. According to Fripiat et al. (11), the vibrational frequencies parallel to the surface m a y be considered to be equal to the perpendicular vibration, so that
s
a~
Noh~,±
R ln[1 -
e(-h'~-/~n I
Standard Entropies of Adsorption at 307, 94 K
Translation
~.,S[ sS~ ASIr
Rotation
Immobile layer (cal K -t mole-t )
Mobile layer (cal K -t mole-t)
Term
20.74 38.55
0.0 38.55
-17.81
-38.55
.d~S~ot
20.24
5.0 ° 3.18b 20.24
gS~ot
20.24
ASCot
0.0
Vibration
AS~ib
2.14
6.43
Total
AS~
- 15.67
-47.36
- 15.24a
a.bValues accordingto Fig. 4. g-l. On the other hand, as has been calculated according to Law (12), giving mobS~r = 20.74 cal K -1 mole -l. From the viewpoint of the mobile film model, the molecule retains its three degrees of rotational freedom, as it is not attached to any specific center, whereby n~obAS~ot = 0. Finally, in this case there is only one degree of vibrational freedom, perpendicular to the surface, leading to
lo~,~b = ~[[eth,±/kr)_ 1] >~ T -
TABLE II
[101
and assuming that the adsorption does not modify the internal vibrations of either the adsorbate or the solid, lo~AS~b = 6.43 cal K -I mole -1.
mobAS~ib = 2.14 cal K -1 mole -1 which corresponds precisely to mobmSSib
=
~1( I o c A S vsi b ) .
[ l 1]
Summarizing, in the reference state 0s = 0.5, lo~AS~ds = --47.36 Cal K -1 mole -l
Mobile Adsorption The translational contribution must take into account that, for a mobile film, n = 2 and L n = a~No, where a~N0 is the free surface area per mole of a bidimensional gas in the reference state 0s = 0.5. This state is determined considering an average Vm for the 25, 35, and 45°C isotherms, Vm = 16.289 cm 3 g-i at STP, so that Nad (0 = 0.5) = 2.1875 × 1020 molecules Journal of Colloid and Interface Science, Vol. 122, No, 2, April 1988
and $
mobAS~,~ = - 1 5 . 6 7 cal K -l mole -l. Table II summarizes all the results. Figure 5 shows the entropy change with coverage, including the congregational molar entropy term for the mobile model (9) adsS ss = - R
lnl
[(1
0
-
/
0)/(1
Os
-
/
0s)J
[12]
MOBILITY OF SULFUR DIOXIDE
405
a n d c o m p a r e s t h e m with the e x p e r i m e n t a l data, a c o i n c i d e n c e b e i n g f o u n d b e t w e e n the latter a n d the values o b t a i n e d for a m o b i l e adsorption model. It is shown, therefore, that the g a s - s o l i d system a n a l y z e d certainly corres p o n d s to a m o b i l e phase.
-10
"~. -15
~..,~e
E xper imentol
Layer
ACKNOWLEDGMENT
z"
9 p. -20
\
This work was supported by the Departamento de Investigaci6ny Bibliotecas de la Universidad de Chile, Grant Q-2495-8613.
o ca -2~ < -3c
REFERENCES
m -3~
-4¢
-45
-5(
0
0,2
0,4
0,s
0,s
1.0
COVERAGE,t 0 )
FIG. 5. Comparison of experimental entropies of adsorption with theoretical entropies for mobile and immobile films.
a n d the configurational m o l a r e n t r o p y t e r m for the i m m o b i l e a d s o r p t i o n 0 (I 0) adsSfig = - R In ~ + - ~ l n ( l - 0)
(1-0s0S)ln(l_0s)), [13]
1. de Boer, J. H., and Kruger, S., Proc. K. Ned. Aka. Wet. 1355, 451 (1952); Scholten, I. J. F., and Kruger, S., "Physical and Chemical Aspects of Adsorbents and Catalysts" (B. G. Linsen, Ed.), Chap. 3. Academic Press, New York, 1970. 2. Alzamora, L., J. Colloid Interface Sci. 106, 513 (1985). 3. Jones, W. S., and Ross, R. A., J. Chem. Soc. A, 1021 (1967). 4. Brunauer, S., Emmett, P. H., and Teller, E. J., J. Amer, Chem. Soc. 60, 309 (1938). 5. Kaganer, M. G., Russ. J. Phys. Chem. 33, 352 (1959). 6. Degussa, "Technical Bulletin Pigments," No. I l, p. 9, Table 2. October 1982. 7. Young, O. M., and Crowell, A. D. "Physical Adsorption of Gases." Butterworths, London, 1962. 8. Alzamora, L., Contreras, S., and Cort6s, J., J. Colloid Interface Sci, 50, 503 (1975). 9. Ross, S., and Oliver, J. P., "On Physical Adsorption." Interscience, New York/London/Sidney, 1964. 10. de Boer, J. H., "The Dynamical Character of Adsorption." Oxford Univ. Press (Clarendon), Oxford, 1953. I I. Fripiat, J. J., Jelli, A., Poncelet, G., and Andre, J., J. Phys. Chem. 69, 2185 (1965). 12. Law, J. T., J. Phys. Chem. 59, 67 (1955).
Journal of Colloid and Interface Science, VoL 122, No. 2, April 1988
Received June 23, 1986; accepted May 31, 1987 A study of the adsorption and thermodynamic functions of sulfur dioxide on Aerosil has been made, leadingto some conclusionsabout the mobilityof the SO2molecule.The differentialand integralenthalpies and entropies of adsorption, together with a statistical mechanical interpretation of the system, are discussed. Particularly,the statistical mechanical calculation of the integral entropy of adsorption allows a comparisonto be made betweenthe experimentalresultsfor the SO2-Aerosilsystemand those obtained for adsorption in two limiting cases: an immobile or localized model that can be associated with chemisorption, and a mobile film model that can be related to physisorption. The results confirm a weak gassolid interaction with a highly mobile adsorbed phase. © 1988AcademicPress,Inc. INTRODUCTION There is great interest in the investigation of the thermodynamic properties o f adsorption and the nature of the interaction of polar molecules with hydroxylated surfaces. Although numerous reports on the adsorption o f polar molecules on acidic solids have appeared, none seem to have been published on the SO2Aerosil system. This paper reports on a thermodynamic study of the adsorption of SO2 on Aerosil, with determinations of the isosteric heat and the integral enthalpy and entropy of adsorption. The latter parameter is alternatively calculated by a statistical mechanical treatment of the problem, originally developed by de Boer and Kruger (1), a theoretical approach that shows that the SO2-Aerosil interaction is of the mobile film type. EXPERIMENTAL The adsorption isotherms were determined in a conventional volumetric apparatus and with reproducible readings being taken at intervals that would allow equilibrium to be reached. The temperature of adsorption was kept within +0.1 K.
The experiments were performed using Aerosil (200 m2/g), which was outgassed overnight at 110°C and l0 -4 m m Hg as described earlier (2). Sulfur dioxide (Matheson Co.) was of anhydrous quality and was drawn directly from the cylinder, after line flushing, to a trap attached to the apparatus. It was then purified by alternate freezing and thawing in vacuo. RESULTS AND DISCUSSION The adsorption kinetics of the SO2-Aerosil system was studied prior to the determination of the different isotherms, since that information was needed for the experimental procedure that followed. Figure la shows the observed behavior, with an adsorption temperature of 25°C. For low absolute pressure values (curve 1), the adsorption equilibrium was reached in about 50 min, which is consistent with reported data (3). G o o d reproducibility was attained. The kinetic behavior was different when a higher pressure was used. At equilibrium values of about 100 Torr the process was m u c h slower, no less than 3 h being required to reach equilibrium (curve 2). In this case reproduc398
002 i-9797/88 $3.00 Copyright © 1988 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
MOBILITY OF SULFUR DIOXIDE
399
a I Peq--98,4 mmHr
I
I
(2)
S
1
<[
<'l' I I
Peq=17,8 mm Hg
(~..4"5.....~
I
=, o
0
1
2
3 TIME, ( h )
4
5
G
b
8.0 _
7.C
t....u~
6.C
/
-
tam ~.,,
/ e
0
_
20
40
60 80 PRESSURE, mm Hg.
100
FIG. 1. A d s o r p t i o n kinetics (a) a n d adsorption isotherms (b) for sulfur dioxide on Aerosil.
ibility was less reliable, and at yet higher pressures reliability decreased even more. These results made it advisable to limit the study to the pressure interval between 0 and 100 mm Hg.
Adsorption Isotherms Figure lb shows the experimental results for the adsorption isotherms of the SO2-Aerosil system at 0.2, 25, 35, and 45°C. Within the relative pressure range under consideration, the SO2-Aerosil system shows as a characteristic the lack of large adsorbed volumes, while the shape of the isotherms shows that the monolayer region has not yet been reached.
Among the many known models, that of BET (4) has been classically accepted and used for the determination of surface areas, even though its validity decreases at low relative pressures because the energy homogeneity of the surface, which is one of its characteristic assumptions, is lost. In this study, a relative pressure range of 10-3 through 3 × 10-2 was covered, so that the BET model became inapplicable. Therefore, a different model was used, that of Kaganer (5), which is valid at low surface coverage; it takes into account the solid's energy heterogeneity and allows the determination of the monolayer volume I'm. Using the potential theory originally introJournal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
400
VASQUEZ AND ALZAMORA
duced by Polanyi, and Dubinin's method for the determination of the pore volume, Kaganer suggests a semiempirical expression that allows the adsorption phenomenon to be interpreted for a low range of surface coverage under relative pressures of the order of 10-4 to 10-2 , log Va = log Vm - D[log(po/p)] 2,
[1]
the manufacturers, Degussa (6), the value of aort (the number of silanol groups per 100 A 2 of surface) for the isolated type is 2.6. Since the surface area is 200 m2/g of solid, there are 5.2 X 1020 isolated O H groups per gram of solid. If the number of adsorbate molecules in the monolayer is B, and assuming that each of these molecules is joined to a silanol group by an hydrogen bridge, then B = 5.2 × l020 adsorbate molecules/g of solid, which results in an STP volume Vm = B(Vo/No) = 19.35 cma/g.
where Po is the adsorbate's saturated vapor pressure, Va is the adsorbed volume, and D is a parameter related to the mean value of the adsorption energy. (ii) Method based on the physical properties When log Va is plotted against [log(po/p)] 2, of the adsorbate. Once a monolayer condition Vm can be obtained from the log Vm intercept. has been achieved, the adsorbate can be viTable I shows the values obtained for this pasualized as a film of molecules having the rameter from the experimental results shown characteristic of the condensed liquid. If each in Fig. 2. In all these cases the relative pressure molecule occupies an area ~0 o f the monorange considered was 2 × 10-3 to 3 X 10 -2. layer, and the solid has a specific surface area The value that a given model yields for a A, the monolayer volume would be (7), parameter becomes significant when it is comparable to the value obtained from indeA pendent sources. In this paper two alternative Vm = 0.269~----~' [2] methods are used to determine the volume of the monolayer, one based on the chemical where a0 is 1.985, 2.012, and 2.042 at 25, 35, structure of the adsorbent, and the other based and 45°C, respectively. on the physical properties of the adsorbate. Table I shows the values for the monolayer, (i) Method based on the chemical structure Vm(F), for SO2 obtained by this method, using of the adsorbent. It is known that polar gas a value of 200 m2/g for the specific surface molecules, such as water and organic esters, area, A, of Aerosil. It can be seen that Kagainteract through hydrogen bridges with the ner's model yields values for Vm that are reasurface silanol groups. In this way, if the num- sonably close together. ber of isolate silanol groups on the surface is Considering the chemical structure of the known, a probable value for the volume of the adsorbent and the physical properties of the monolayer can be established. According to adsorbate, it can be concluded that the adTABLE I MonolayerCapacity, Vm,for SO2 on Aerosil from the Kaganer Method, Vm(K);Chemical Structure of the Adsorbent,Vm(Q);and PhysicalPropertiesof the Adsorbate, Vm(F) Monolayercapacity (ml S-1) T (*C)
V~(K)
0.2 25.0 35.0 45.0
16.62 16.73 16.18 15.96
Vm(Q)
Vm(F)
V~(K)/V~(Q)
V=(K)/Vm(F)
38.66 37.50 36.99 36.44
0.859 0.864 0.836 0.825
0.430 0.446 0.437 0.438
19.35
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
MOBILITY OF SULFUR DIOXIDE
401
o.
d
I,,i.I Q13
=,
2
3
~,
5
6
7
e
0
I
2
3
,~
5
6
7
8
tog(Polp)2
FIG. 2. Kaganerplots for sulfurdioxideon Aerosil. sorption of SO2 on Aerosil is more closely related to the occupancy of specific sites on the solid by the adsorbed phase, than to the formation of a condensed film. In fact, if the values obtained in both ways are compared with those derived from Kaganer's model, it is seen that the ratios are closer to unity using Vm from method (i) (Table I). Finally, it can be inferred that the monolayer condition would point to an occupancy of the order of 85% of the superficial silanol groups.
Heats and Entropies of Adsorption From the experimental data obtained at different temperatures it was possible to obtain the heats and entropies of adsorption, which
are extremely useful in the process of interpreting and analyzing the isotherms. One important aspect of this treatment is that it allows these thermodynamic parameters to be compared with those supplied by statistical mechanical models. Figure 3a shows the isosteric and integral heats, qisost and AH~s, respectively, as functions of the adsorbed volume obtained from isosteres and iso-II (spreading pressure) straight lines, respectively. Figure 3b shows the integral entropy of adsorption calculated from (7), A Sa,~s = (Sa - S °)
AHa~ - ~--
R ln(p/p°),
[3]
Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
402
VASQUEZ AND ALZAMORA 8.0
\
7.5 E qisost 7.0
8 6.5
6.0
.....
/ _-~_ _
--~-~
AHads
o-~ --if---t-. . . .
OL
5.5 b -8 "-r.
~-1
~-~- o---c--o--
-20 ............................. -2t,
0
1
A$_~,
2 3 4 5 6 7 VOLUME ADSORBED, m| (STP)/g.
FIG. 3. Thermodynamicsfunctionsfor the adsorption of sulfur dioxide on Aerosil: (a) heats of adsorption; (b) integralentropy. where AHad~ is the integral enthalpy of adsorption and p0 = 760 m m Hg. These thermodynamic parameters, calculated from the experimental data, immediately show some peculiarities of the SO2-Aerosil system. The isosteric heat is relatively low, only slightly higher, by about 1 kcal/mole, than the heat of liquefaction of the adsorbate, pointing to a weak interaction of the physisorption type. Only at low surface coverage, lower than 1.5 cm 3 STP/g, does it show a tendency to increase, a result that was expected because, at low equilibrium pressures, the fraction of the surface that presents more active sites can adsorb the molecules liberating more energy. Figure 3a also shows a remarkable constancy in the value of the integral enthalpy of adsorption within the interval under consideration, and its agreement with the heat of liquefaction of the pure adsorbate QL. However, Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
this is just a peculiarity of the system, since at pressures so much lower than P0 as those that have been studied here, the adsorption mechanism bears no relation to that of the condensation of a gas. This is confirmed by the values obtained for the integral entropy of adsorption, Fig. 3b, since ASa~ is less negative than that of a simple condensation (ASL). This behavior indicates that the adsorbed phase is under an intermediate condition, between a gas phase and a condensed phase, a situation that has been already pointed out in this laboratory (8). The phenomenon is understandable if it is postulated that the adsorbed phase is a bidimensional gas with no restrictions to its motion in the plane of the adsorbent's surface, thus implying less mobility than that in the gas phase (tridimensional), but higher than that in the liquid phase. In this respect the variation of ASa~ with coverage indicates the change from a highly mobile phase at low pressures (therefore with a low entropy change) to an adsorbed phase whose mobility progressively decreases. At the limit, when the monolayer is reached, one would expect an entropy change similar to that of a condensation.
Statistical Mechanical Calculation of the Entropy of Adsorption The previously obtained results bring up, like every experimental work, the problem of their veracity. The question is, how can it be proved that they actually correspond to the real situation? Statistical mechanics is an important theoretical tool that allows the overall properties of a system to be known starting from the properties of the microsystems (in this case, the individual molecules). An outline of the calculation of the entropy follows. If a gas in its standard state (normal pressure) is adsorbed on a surface occupying a fraction 0s of the surface, the entropy change between these reference states would be s ASads = AS~r + ASCot + ASSb.
[4]
403
MOBILITY OF SULFUR DIOXIDE
Each of the terms of Eq. [4] can be evaluated from the respective partition function, considering the two extreme models of the adsorption mechanism: an immobile or localized model, and a mobile film model (9).
Immobile Adsorption The partition function, qtr, for a molecule with n degrees of translational freedom is
= [27rmkT~ ~/2 ~ h2 / tn,
qtr
[51
where L is the characteristic spatial parameter. The translational entropy is Str=Rln
No + -
qtr
~ cgZ]v,n
+ 1 .
[6]
Considering the difference between the adsorbed state, in which there are no translational degrees of freedom, and the gas state where L n = V (the molar volume in the reference state), and n = 3, then lo~AS~r = - 3 8 . 5 5 cal K -l mole -l. As to the rotational contribution, the calculations consider that the partition function is 1
qrot =
Ixy = 1.4911 ×
10 -39 g cm 2 molecule -l
and SSrot = 3.18 cal K -l mole -l. The difference between the two calculated types of rotation is small, but some considerations about the stability of the resonant structure of SO2 in case (a) make it preferable as a representative of the physicochemical situation. Finally, locSr~ot = - 1 5 , 2 4 cal K -l mole -1.
3
X I b" • • i~)l/n[n/2,'l rra+ [ h 2 kT (I~ J
[7] where a + is the symmetry factor; Ia, I s . . . . , IE are the molecule's m o m e n t s of inertia; and
a+b+
Therefore, Sr~ot= 20.24 cal K -1 mole -l for the gas phase. In the adsorbed phase, three rotational modes can be conceived, which are shown in Fig. 4. O f these situations, (c) can be discarded immediately, since it assumes two hydrogen bridge-type associations, which would lead to an interaction energy higher than the one found experimentally and to a rotational and location hindrance due to the size of the SO2 molecule. Case (a) has only one degree of rotational freedom around the axis y, leading to Sr~ot = 5.0 cal K -1 mole -I, while case (b) shows rotation around an axis that goes from the center of mass of the SO2 molecule to one of the oxygen atoms. In this case the m o m e n t of inertia is
... +e=n.
In order to determine the vibrational entropy, the molecule's vibrational frequencies in the adsorbed state must be known. An approximation that makes it possible to determine the frequency perpendicular to the surface, v±, consists in extrapolating the experi-
On the other hand, the rotational and vibrational entropies are derived from
S=R[Inq+T(O~ q
] V,n
[8]
For SO2, a + = 2, and the principal m o m e n t s of inertia are 1~ = 1.0505 × 10 -39 g cm 2 molecule -1
Iyy = 9.2261 × Izz = 10.2765 ×
10 -39 g cm 2 molecule -l
10 -39 g cm 2 molecule -1.
o~-~'~
o
o, 0"-.i B
i 0
I
- - S i - lal
f 0 --
I
Sl'-1b1
(el
FIG. 4. Geometry of the possible ways of rotation of the SO2 molecule in the localized model. Journal of Colloid and Interface Science, Vol. 122, No. 2, April 1988
404
VASQUEZ AND ALZAMORA
mental data, according to the Hill-de Boer model (10). In this case, the constant K1 of the H D B model is, in the harmonic approximation,
K1
= [(21rMRT) 1/2] L ~ j × e-Qmr'
[9]
where M is the molecular weight of SO2, T0 is the average time for the vibration normal to the surface, an~ is the specific area available to each adsorbate molecule on the monolayer (obtained from the BET area and Vm), Q is the heat of adsorption, and T is the temperature. Since the dependence of K1 on the temperature is important only in the exponential term, when In K~ is plotted against T -~ a straight line is obtained having a slope -Q/R and an intercept of ln[(27rMRT)l/2/N':oam], from which one can calculate ~.L = T~ 1• In our case, considering the 25, 35, and 45°C isotherms, we obtained u~ = 6.16 × 1012 s-~ at a temperature of 307.44 K. According to Fripiat et al. (11), the vibrational frequencies parallel to the surface m a y be considered to be equal to the perpendicular vibration, so that
s
a~
Noh~,±
R ln[1 -
e(-h'~-/~n I
Standard Entropies of Adsorption at 307, 94 K
Translation
~.,S[ sS~ ASIr
Rotation
Immobile layer (cal K -t mole-t )
Mobile layer (cal K -t mole-t)
Term
20.74 38.55
0.0 38.55
-17.81
-38.55
.d~S~ot
20.24
5.0 ° 3.18b 20.24
gS~ot
20.24
ASCot
0.0
Vibration
AS~ib
2.14
6.43
Total
AS~
- 15.67
-47.36
- 15.24a
a.bValues accordingto Fig. 4. g-l. On the other hand, as has been calculated according to Law (12), giving mobS~r = 20.74 cal K -1 mole -l. From the viewpoint of the mobile film model, the molecule retains its three degrees of rotational freedom, as it is not attached to any specific center, whereby n~obAS~ot = 0. Finally, in this case there is only one degree of vibrational freedom, perpendicular to the surface, leading to
lo~,~b = ~[[eth,±/kr)_ 1] >~ T -
TABLE II
[101
and assuming that the adsorption does not modify the internal vibrations of either the adsorbate or the solid, lo~AS~b = 6.43 cal K -I mole -1.
mobAS~ib = 2.14 cal K -1 mole -1 which corresponds precisely to mobmSSib
=
~1( I o c A S vsi b ) .
[ l 1]
Summarizing, in the reference state 0s = 0.5, lo~AS~ds = --47.36 Cal K -1 mole -l
Mobile Adsorption The translational contribution must take into account that, for a mobile film, n = 2 and L n = a~No, where a~N0 is the free surface area per mole of a bidimensional gas in the reference state 0s = 0.5. This state is determined considering an average Vm for the 25, 35, and 45°C isotherms, Vm = 16.289 cm 3 g-i at STP, so that Nad (0 = 0.5) = 2.1875 × 1020 molecules Journal of Colloid and Interface Science, Vol. 122, No, 2, April 1988
and $
mobAS~,~ = - 1 5 . 6 7 cal K -l mole -l. Table II summarizes all the results. Figure 5 shows the entropy change with coverage, including the congregational molar entropy term for the mobile model (9) adsS ss = - R
lnl
[(1
0
-
/
0)/(1
Os
-
/
0s)J
[12]
MOBILITY OF SULFUR DIOXIDE
405
a n d c o m p a r e s t h e m with the e x p e r i m e n t a l data, a c o i n c i d e n c e b e i n g f o u n d b e t w e e n the latter a n d the values o b t a i n e d for a m o b i l e adsorption model. It is shown, therefore, that the g a s - s o l i d system a n a l y z e d certainly corres p o n d s to a m o b i l e phase.
-10
"~. -15
~..,~e
E xper imentol
Layer
ACKNOWLEDGMENT
z"
9 p. -20
\
This work was supported by the Departamento de Investigaci6ny Bibliotecas de la Universidad de Chile, Grant Q-2495-8613.
o ca -2~ < -3c
REFERENCES
m -3~
-4¢
-45
-5(
0
0,2
0,4
0,s
0,s
1.0
COVERAGE,t 0 )
FIG. 5. Comparison of experimental entropies of adsorption with theoretical entropies for mobile and immobile films.
a n d the configurational m o l a r e n t r o p y t e r m for the i m m o b i l e a d s o r p t i o n 0 (I 0) adsSfig = - R In ~ + - ~ l n ( l - 0)
(1-0s0S)ln(l_0s)), [13]
1. de Boer, J. H., and Kruger, S., Proc. K. Ned. Aka. Wet. 1355, 451 (1952); Scholten, I. J. F., and Kruger, S., "Physical and Chemical Aspects of Adsorbents and Catalysts" (B. G. Linsen, Ed.), Chap. 3. Academic Press, New York, 1970. 2. Alzamora, L., J. Colloid Interface Sci. 106, 513 (1985). 3. Jones, W. S., and Ross, R. A., J. Chem. Soc. A, 1021 (1967). 4. Brunauer, S., Emmett, P. H., and Teller, E. J., J. Amer, Chem. Soc. 60, 309 (1938). 5. Kaganer, M. G., Russ. J. Phys. Chem. 33, 352 (1959). 6. Degussa, "Technical Bulletin Pigments," No. I l, p. 9, Table 2. October 1982. 7. Young, O. M., and Crowell, A. D. "Physical Adsorption of Gases." Butterworths, London, 1962. 8. Alzamora, L., Contreras, S., and Cort6s, J., J. Colloid Interface Sci, 50, 503 (1975). 9. Ross, S., and Oliver, J. P., "On Physical Adsorption." Interscience, New York/London/Sidney, 1964. 10. de Boer, J. H., "The Dynamical Character of Adsorption." Oxford Univ. Press (Clarendon), Oxford, 1953. I I. Fripiat, J. J., Jelli, A., Poncelet, G., and Andre, J., J. Phys. Chem. 69, 2185 (1965). 12. Law, J. T., J. Phys. Chem. 59, 67 (1955).
Journal of Colloid and Interface Science, VoL 122, No. 2, April 1988