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795
HEATS OF ADSORPTIOX. IV
EKTROPY CHANGES IN ADSORPTION\ COSWAY PIERCE
AND
R. YELSOS SMITH
Department of Chemistry, Pomona College, Claremont, California Received A u g u s t 6 , 1949
I n recent papers by Davis and DeWitt ( 5 ) and Joyner and Emmett ( 7 ) , entropy changes are discussed for the process: Bulk liquid (vapor at p o )
+ solid surface = adsorbed film (vapor a t p )
The conclusions of these two papers appear at first sight to be contradictory. Davis and DeWitt find the entropy to increase at the start of adsorption and to become that of bulk liquid before a monolayer is adsorbed. Joyner and Emmett, on the contrary, show that for most of the adsorption in the first layer t'here is a decrease in entropy and that after completion of the first layer the entropy change approaches zero. For Graphon they find an initial region of entropy increase, but for carbon black they report no region of entropy increase. Seither paper considers the entropy changes in the region of multimolecular adsorption at high relative pressures. In connection with our adsorption studies me have experimentally obtained differential heats of adsorption over the entire relative pressure range for several systems. I n view of the apparent discrepancies betJyeen the tpvo papers cited, plus the fact that neither has considered the region of high relative pressures, we have used our heat data to compute entropy changes for several adsorption systems and we find v h a t Tye believe to be relations of general applicability, which are herein reported. EXPERIMENTAL
Ethyl chloride isotherms were determined at temperatures of 0°C. and -78°C. for Carbolac I. This is presumably a nonporous black2 of surface area near 1000 sq. m.ig. The amount adsorbed was followed gravimetrically by weighing the sample bulb after each addition. Details are given in previous papers (8, 11). A hlcLeod gage \vas used to determine vapor pressures for the -78OC. isotherm. Water isotherms for temperatures of 0°C. and 28.6"C. were determined for Graphon.? This is a partially graphitized carbon black of surface area near 80 sq. m./g. I t appears to be completely nonporous (10). Before use, it was treated with hydrogen a t 11OO"C., to eliminate the possibility that oxygen complexes on the surface might affect the water adsorption. The amount of xater adsorbed was determined gravimetrically. Pressures This is a progress report of work done under Contract N8 onr 54700 with the Office of Saval Research, United States Navy Department. We desire to thank Dr. W.R . Smith of the Godfrey L. Cabot Company, Boston, Massachusetts, for furnishing the samples. The properties of the two samples have been described by Smith, Thornhill, and Bray (12).
796
COXTVAY PIERCE A S D R . NELSOX SMITH
were read on silicone-filled manometers. These were freshly pumped before each reading, since it was found that if allowed to stand in contact with water vapor the readings slowly changed. A po reading was taken immediately follov4ng each adsorption reading; constant PO values were found. The Graphon sample was of the same lot used by Joyner and Emmett (7) and by Beebe, Biscoe, Smith, and Wendell (3). The nitrogen isotherm given by Joyner and Emmett for Graphon shows an unusual hump in the multilayer region, starting at about 0.3 PO. This hump has been observed by others for low-temperature adsorption of small molecules3 but did not show up in various isotherms determined in this laboratory, with large organic molecules. The hump does not seem to be the cause of the unusual entropy change a t 1-15 V , reported by Joyner and Emmett and discussed later, since its maximum occurs at about 2 V ,. To the best of our knowledge no other nonporous adsorbent has ever shown a hump of this type in its isotherm. We know of no satisfactory explanation to account for it. COMPUTATION O F EBTROPY CHANGE I N ADSORPTION
We have follolved the method used in the other papers cited for computation of T A S values in the adsorption process. The entropy change is given by the relation: T A S = A H - AF
(1)
Here A H is the measured quantity - ( E - E L ) or the differential heat of adsorption. Since E - EL is customarily given a plus sign when heat is evolved, it is necessary to use a minus sign when following thermodynamic conventions. The free energy change, A F , is computed by AF = R T l n p / p ,
(2)
Experimental A H and computed AF values are plotted as functions of relative pressure. Graphical subtraction then yields a T A S curve for the process. I n using this method certain precautions are necessary which are not explicitly stated in either of the other papers. I n order to make the computation of AF it is necessary to relate the A H values, which are computed for given volumes adsorbed, to relative pressure. This is done (approximately a t least) by using the average relative pressure for each volume. For example, 70 ml./g. is adsorbed by Carbolac a t relative pressures of 0.015 a t -78°C. and 0.07 a t O°C. The average relative pressure is 0.0425. This is the value used to compute AF’ for an adsorption of 70 ml. This pressure corresponds to an average isotherm determined a t the mean temperature, - 39°C. Therefore this mean temperature is used to compute A F . It is apparent that this method for computing the entropy change in adsorption neglects any change which may take place in the entropy of the surface itself as an adsorbed film is formed. This we believe to be proper, since the forces holding 3Private communicat~onsfrom Professor R A . Beebe of Amherst College and Dr. ,If. L. Corrin of the University of Chicago.
HEATS O F ADSORPTION. I V
797
surface atoms of a solid are very large in comparison to the forces between surface atoms and adsorbate molecules. In other words, it is reasonable to assume that the thermal vibrations of surface atoms are but slightly affected by the presence of an adsorbed layer on the surface. We are therefore assuming no change in entropy for the surface itself and computing only the entropy changes for adsorbed molecules as they pass from bulk liquid to adsorbed film. Differential A H , AF, and T A S values for the adsorption of ethyl chloride by Carbolac 1 are plotted as functions of relative pressure in figure 1. The isotherms from which the values are computed are given in Figure 2. 600
1
,
.E
’
P”.
.I
.’
FIG.1 FIG.2 FIG. 1. Differential free energy, net heat, and entropy changes for adsorption of ethyl chloride by Carbolac I. The approximate pressures are indicated a t which statistical first and second layers are completed. FIG.2. Isotherms of ethyl chloride on Carbolac I a t 0°C. and -78°C. .4t 0.995 P O the volume adsorbed a t 0°C. is 1650 ml. (S.T.P.). INTERPRETATION AND APPLICATIONS OF ENTROPY CURVE
We find for the Carbolac-ethyl chloride system some relations which we believe to be of general applicability for all physical adsorption. The T A S curve shows three separate regions, as follows: 1. At the start of adsorption there is an increase in entropy. That such must always be true is shown by equation 1. As pressure approaches zero, -AF approaches infinity; A H , however, must be finite for physical adsorption. Consequently, T A S must have a positive sign at the region near zero pressure and all T A S curves must tend tovards infinity a t zero pressure The region of entropy increase may or may not be found in experimental curves. Davis and DeWitt show only this region; Joyner and Emmett find it for one system but not for another. Whether or not the region can be experimentally observed depends upon the magnitude of AH a t low relative pressure. When an isotherm rises very steeply a t the start the AH curve may be so steep that it crosses the AF curve a t pressures too low for accurate measurement, and the positive T A S region is not observed. 2. Starting a t something less than 0.5 Ti, the entropy curve shows an abrupt
+
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COSJYAY PIERCE AND R. KELSON SMITH
change from positire to negative and it goes through a minimum somewhere near the point a t which a first layer is completed. 3. Sear the point a t which the first layer is completed there is an abrupt rise in entropy, which now approaches that of bulk liquid. There is, however, an entropy decrease throughout the region of multilayer adsorption and the entropy becomes that of bulk liquid only a t saturation. These three regions have been observed for the entropy changes in a variety of adsorption systems. There are, of course, variations in the magnitudes observed and in the pressures a t which the transition from positive t o negative entropies occur, but the general shapes of the curves are like that of the TAS curve of figure 1. -4mong the systems for which Tve have computed the entropy changes are the following: 1. Butane on glass spheres, using the data of Davis and DeWitt ( 5 ) Our numerical values are somewhat smaller than they give; apparently they did not use average relative pressures in relating adsorbed volumes to pressure. Rather, it appears that they used the relative pressures corresponding t o the isotherm a t the lower temperature in computing A F . 2. Ethyl chloride on Graphon. 3. Benzene on Graphon. 4. Cyclohexane on Graphon. 5. Methanol on Graphon. The isotherm for this system is Type VI (9). The results of Davis and DeWitt and of Joyner and Emmett are both in accord with the general entropy curve. The apparent discrepancies in their findings are due to the fact that each considered only narrow regions, Davis and DeWitt the initial region where there is an increase in entropy, and Joyner and Emmett the second region where there is a decrease in entropy (for one system they did note part of the first region). Both Davis and DeWitt and Joyner and Emmett seem to have tacitly assumed that A S is zero in the region of multilayer adsorption. The three distinct regions of the general entropy curve are precisely \That one might predict in advance, from considerations of the relative degrees of order of molecules in adsorbed films and in bulk liquid. At the start of adsorption the first molecules are randomly distributed over the adsorbent surface, a t the most active sites. With respect t o one another, the adsorl)ate molecules are much less ordered than in bulk liquid and consequently the F rocess is accompanied by an increase in entropy. As more molecules are adso.bed in the first layer they begin to crowd together in a two-dimensional latt ce. The arrangement now is more ordered than in bulk liquid; surface forced hold the molecules rather tightly to the surface and they have less mobilit:: with respect to one another than in bulk liquid. This greater order leads to the entropy decrease found in the second portion of the TAS tun-e, with the minimum a t or near the point a t which the first layer is completed. As soon as adsorption begins in the second layer the degree of order is markedly decreased, for the situation is now more like that of bulk liquid. This is the point a t which the TAS curve rises rapidly to a value near zero. Finally, for adsorption in multimolecular layers, one would
HEATS OF ADSORPTION. IV
799
expect the degree of order to approach that of bulk liquid but that film molecules would, because of the influence of forces from the solid surface, be still slightly more ordered than in bulk liquid. This too is found in the TAS curve. THERMODYN.4iMICS O F WATER ADSORPTION BY CARBON
One of the puzzling phenomena of adsorption is the behavior of water on carbon surfaces. Coolidge (4)measured isosteric heats for charcoals and came to the conclusion that E - E L is zero for the first portions adsorbed but greater than zero for the bulk of adsorption. We have (figure 3) determined the isotherms of water on Graphon a t temperatures of 0°C. and 28.6"C. These isotherms show less adsorption per unit area than any previously reported water isotherms for nonporous carbon surfaces. We believe that this is due to the absence of oxygen complex. A relative pressure of 0.99 is required to form a statistical monolayer eo
8
I
1 "
6
eo
.
40
2
20
r
-
C
2
1
P,r,
6
1
FIO.3 FIO.4 FIO.3. Isotherms for water on Graphon: 0, at 28.6"C.; , a t 0°C. FIG.4. Differential free energy, net heat, and entropy changes for adsorption of water by graphite.
(30 ml.) and a t 0.997 PO only two statistical monolayers are adsorbed-quite in contrast t o the behavior of other adsorbates on this sample, which holds some 32 statistical layers of ethyl chloride a t 0.997 PO. We believe that the isotherms at 0°C. and 28.6"C. are identical up to about 0.93 PO.I n other words E - EL = 0 for this region. Above 0.93 p , the 0°C. isotherm is definitely displaced to the left of the 28.6OC. isotherm, or E - EL is positive. Thus our findings in this temperature range are in agreement with those of Coolidge for an activated charcoal. We find it necessary, therefore, to modify our previously stated view that adsorption occurs only when E > E,. For the most part this view is correct, but apparently some water does adsorb with zero net heat. An explanation is suggested by the general shape of the entropy curve for adsorption. Water is, in comparison to other adsorbates, poorly adsorbed and the region of entropy increase extends to much higher relative pressure than for other adsorbates. At 0.93 PO less than one-tenth of a statistical monolayer is held. Up to this relative
800
COXWAY PIERCE A K D R. KELSOK SMITH
pressure, therefore, we may have spontaneous adsorption ivith zero net heat, since the increase in entropy permits a free energy decrease. Above 0.93 p , the isotherm for 0°C. lies to the left of that for 28.G°C., or E > EL.It is illogical to assume that now a portion of the surface can adsorb with positive net heat, which could not adsorb a t lower relative pressure. Rather one is forced to the conclusion that the increased heat of adsorption above 0.93 po is due to lateral interactions with previously adsorbed molecules, as discussed by Barrer (1) and by Halsey ( G ) , and that the net heat of interaction of water molecules with surface atoms remains zero. When cooperative adsorption sets in the entropy becomes negative in sign, but now the net heat is positive and a spontaneous process is still possible. The AH and TAS curves for water (figure 4)are in line with this interpretation. The region of entropy decrease is confined to the relative pressure region 0.931.0, but it is in this region that 95 per cent of the adsorption occurs. Thus, while some adsorption can occur with zero or negative net heat, because of the contribution of the entropy term to the free energy of the process, the bulk of the adsorption must occur when E > E L . The incidence of cooperative adsorption when less than 10 per cent of a statistical monolayer has formed is indirectly further evidence for our previously stated view (11) that water adsorption on carbon occurs only a t the most active sites and that probably the entire surface is never covered. The small adsorption a t saturation also favors this view. We think that a t saturation there are multilayer clumps of adsorbate at the more active sites while other portions of the surface hold no adsorbate. In connection with the AH and TAS curves of figure 4,it should be noted that the small adsorption of mater at low relative pressures makes the experimental precision poor. I t is not absolutely certain that the isotherms for the two temperatures coincide up to 0.93 po, but this is the best interpretation we can give our data. Certainly one is not justified in saying that the 0°C. curve is displaced to the left of the 28.G"C. curve below 0.93 po or that for this region E > EL.Actually, it is for the present discussion immaterial Tvhether there is a small positive net heat or a zero net heat in the lower pressure region. I n either case it is possible to have a spontaneous adsorption only because there is a large increase in entropy for the region. I t is significant that such an increase in entropy is of general occurrence in all adsorptions and need not be specifically invoked to explain the water-carbon system. The interpretation of this system now falls into the general theory which holds for all adsorption systems. On the basis of heat of emersion measurements Basford, Jura, and Harkins (2) concluded that there is an initial high heat of adsorption for water on graphite and that even a t as much adsorption as 0.18 V mthere is a net heat of some 20,000 cal./mole. Such cannot betrue forthe sample we used. If there were a net heat of even a few hundred calories per mole, the lower pressure portion of the isotherms of figure 3 mould show a marked displacement for the two temperatures. Within experimental limits we find no displacement in this region. Even on an expanded scale (left-hand curve) the two isotherms are identical.
HEATS OF ADSORPTION. IV
801
ISOSTERIC HEATS OF ADSORPTIOX
The preceding discussion of the three general regions for the entropy of adsorption is based largely upon isosteric measurements of heats of adsorption. Calorimetric measurements are usually possible only up to V, or a t best 2 si,, because of the small net heat effects after the first layer is completed. In the region of multilayer adsorption the net heat can be measured only by application of the Clapeyron equation to isotherms at two different temperatures. This procedure has led to the conclusion that E - E L is positive up to saturation, and to the generalizations we have made concerning entropies of adsorption. It is important then to reexamine the validity of using the Clapeyron equation. The basic equation
is undoubtedly rigorous when applied to vapor pressures of adsorbed films. I n practice, however, one uses the approximate integrated form
and AH is computed from the vapor pressure a t T I and T1 of a given weight of adsorbate. If the N molecules of adsorbate occupy the same surface sites a t the two temperatures equation 4 should apply, a t least as a good approximation, but if the situation is such that the given N molecules do not occupy the same sites at two temperatures, there may be doubt as to its applicability. Such a case is found just after completion of the first layer. If the N molecules just cover the surface a t the lower temperature Tn they cannot all be held in the first layer a t the higher temperature 7'1. As the temperature rises the area per molecule must increase and a t T I some of the molecules must be in a second layer, where they are less tightly held than in the first layer. For such molecules dp/dT may have a different value than for first-layer molecules. So we question the exact validity of the isosteric heat values just past sim. It is possible that this effect has caused the very peculiar entropy values reported by Joyner and Emmett (7) for adsorption of nitrogen by Graphon. Just past V , they find a small region in which the calculated AS values are positive. As pointed out in their paper, this is difficult to explain. I t seems highly improbable that there is greater disorder in this adsorption region than in bulk liquid, and that a region of entropy increase from 1 to 1.5 V , could then be followed by a region of entropy decrease. Another region in which the Clapeyron equation must be used with caution is near saturation for porous adsorbents whose isotherms are type I. At the lower temperature Ti, is greater than for the higher and the isotherms tend to become parallel and nearly horizontal a t high relative pressure. I n such a situation it is customary to use vapor pressure ratios for equal fractions of saturation (equal pore volumes filled) in the application of equation 4.There may be some doubt as
802
CONWAY PIERCE AND R. NELSON SMITH
to the validity of this procedure, but it does lead to what appear to he selfconsistent heat values. I n isotherms for nonporous solids the Clapeyron equation seems to be applicable right up to pa if the isotherm is Type 11. For several such isotherms Fve have found that the V,value is almost independent of the temperature, or the isotherms for two different temperatures converge as p o is approached. This is not true for the Type I11 water isotherm of figure 3, hovever. The Ve adsorption a t 0°C. is considerably greater than that for 28.6"C. This indicates that the last molecules are held differently at the two temperatures, and raises a question as to the validity of isosteric heats a t high relative pressures. We believe that the separation of the two isotherms above 0.93 pa does indicate a positive net heat, but we do not consider the heat values reliable except as to order of magnitude. In the low-pressure region of an isotherm isosteric heats seem theoretically sound, since if the surface is only partially covered a given S molecules should occupy the same sites, regardless of the temperature. Another difficulty arises in this region. At very low relative pressures the ratio of pressures at TI and T B is more difficult to measure accurately than at higher pressures and any error introduces a corresponding error into the computed net heat. Therefore values in this region are less reliable than in the higher pressure regions of multilayer adsorption. To illustrate, at -78°C. p o for ethyl chloride is only 3.44 mm., while a t 0°C. it is 471 mm. (mercury manometer, not corrected for temperature). At an adsorption of 70 ml. per gram of Carbolac the actual pressures at 0" and -78°C. are respectively 33 and 0.0517 mm. Obviously any error in the measured pressure at -78°C. would have a large effect on the computed net heat. Because of experimental uncertainty in isosteric heats at low relative pressures we have indicated the lower end of the AH curre of figure 1 by a dotted line. Whether or not this represents the true heat is, however, immaterial insofar as the general shape of the entropy curve is concerned. In any event, the AF curve must cross the AH curve and a positive value of A S must result. Bnother point which we have considered is whether the minimum of the AH curve of figure 1 is real or not. We have found a similar minimum in all the Type I1 isotherms cited above. It corresponds to the maximum in the E - EL curve found calorimetrically by Beebe and associates (3) and isosterically by Joyner and Emmett for nitrogen on Graphon. But no other calorimetric heat curves show this minimum AH near V,,,, If real it is readily accounted for by the cooperative effect of neighboring molecules, vhich should be most pronounced in the region 0.5 V, to V,. But there exists the possibility that this minimum is in some way associated with a defect in the isosteric heat values. There again, however, it is immaterial, insofar as the entropy curve is concerned, whether the minimum is real or not. In either case the entropy curve shows a minimum near V,. It is hoped that as more calorimetric data are obtained it will be possible to find whether the minimum is real. Despite the various uncertainties that are possibly inherent in the measurements of isosteric heats, it appears that in the main these are quite reliable, at least as to order of magnitude. The excellent agreement obtained by Joyner and
HEATS OF ADSORPTIOX. IV
803
Emmett with the calorimetric values previously reported for the same systems lend confidence to the use of isosteric heats. SCMMARY
Entropy changes for the adsorption process are computed by the relation TAS = AH - A F . I t is found that the TAS cs. relative pressure curve is characterized by three regions. First there is a region of entropy increase as the first molecules are adsorbed in a disorderly array. This is folloved by a region of entropy decrease and very orderly arrangement of molecules as the surface becomes covered by a monolayer. Finally, in the region of multilayer adsorption there is a small entropy decrease which approaches zero as p approaches p,. Xn interpretation is suggested for the isotherm of ivater on a plane carbon surface, the only knolvn example of a Type I11 isotherm. The first molecules are adsorbed at the most active sites with zero or very small net heat,s but with a large increase in entropy. On further adsorption there is a larger net heat, due t o lateral interactions, and a decrease in entropy. The limitations which may apply. to use of the Clapeyron equation for computing heats of adsorption are discussed. REFERESCES (1) BARRER: Proc. Roy. Sac. (London) 161A, 476 (1937). (2) BASFORD, JKRA,A N D HARKISS:J . Am. Chem. Sac. 70, 1444 (1948). (3) BEEBE,BISCOE,SMITH,ASD WENDELL: J. Am. Chem. SOC.89, 95 (1947). (4) COOLIDGE: J . Am. Chem. SOC. 49, 708 (1927). (5) DAVISA N D DEWITT:J. Am. Chem. Sac. 70, 1135 (1948). (6) HALSEY: J. Chem. Phys. 18, 931 (1948). (7) JOYNER A N D EMUETT: J. Am. Chem. Sac. 70, 2353 (1948). (8) PIERCE ASD SXITH:J. Phys. & Colloid. Chem. 62, 1111 (1948). A N D SMITH: J. Phys. & Colloid Chem. 64, 354 (19%). (9) PIERCE (IO) PIERCEA N D SMITH:J. Phys. & Colloid Chem. 64, 784 (1959). (11) SMITHAXD PIERCE:J. Phys. & Colloid Chem. 62, 1115 (1948). (12) SMITH,THORNHILL, . ~ N DBRAY:I n d . Eng. Chem. 33, 1303 (1941).
