ADSORPTION ISOTHERMS BY FRONTAL ANALYSIS CHROMATOGRAPHY
1009
Adsorption Isotherms and Heats of Adsorption by Frontal Analysis Chromatography
by R. A. Beebe, P. L. Evans, T. C. W. Kleinsteuber, and L. W. Richards Department of Chemietry, Amherst College, Amherst, Massachusetts 01002
(Received July 16, 1966)
Adsorption isotherm down to low coverages have been determined by frontal analysis chromatography for systems containing the carrier gas, one of the gases Nz, Ar, 02,CO, or C2Fe,and either carbon black or bone mineral. Isosteric heats of adsorption qat have been calculated from these isotherms. The same systems have been studied previously by the pulse method in this laboratory and thus the qBt from the two methods can be compared. It is found that the pulse method gives values of qat which are too low for Type I1 isotherm and too high for Type 111 isotherms, and an equation is derived which explains these results. The pulse method should give correct results for linear isotherms. The frontal analysis data were taken in such a way that lack of instantaneous equilibrium or temperature fluctuations of moderate duration at the adsorbate front, or a strongly nonlinear isotherm, would not introduce errors into the results.
Introduction Gas-solid chromatography has been used by a considerable number of investigators as a means of determining heats of adsorption. In much of the work the pulse technique has been employed. Gale and Beebe’ applied this method to several gas-solid systems for which calorimetric data on the heats of adsorption were available from previous work in this laboratory. These authors, as well as others, have discussed some of the approximations which are necessary in using the method. A number of pertinent journal references to the pulse technique, for gas-solid systems, are given in the above publication; additional references are included here.2-6 A considerable body of work leading to heats of solution has been done for gas-liquid systems. Typical references are given here.’zs Because of the shortcomings of the pulse technique, especially for those systems in which the isotherm fails to obey Henry’s law at low coverage, it is important to survey the advantages of the frontal analysis method of chromatography. Pertinent references for this latter method are cited herein. g-ll In the present work, we have applied the frontal analysis method to some of the same gas-solid systems previously studied by Gale and Beebe using the pulse method. It then becomes possible to compare the
heats of adsorption obtained from both chromatographic techniques as well as from calorimetry for the same adsorption systems. In the frontal analysis method we obtain the adsorption isotherms at low coverage at several temperatures and from these data we calculate the heats of adsorption by means of the Clapeyron-Clausius relationship. Furthermore, a knowledge of the isotherms is useful in assessing the applicability of the pulse method because linearity of the isotherm is a major necessary condition
(1) R. L. Gale and R. A. Beebe, J . Phys. Chem., 68, 555 (1964). (2) H. W. Habgood, Ann. Rev. Phys. Chem., 13, 259 (1962). See ref 118-130 and 162 and the text accompanying them. (3) G. C. Chirnside and C. G. Pope, J . Phys. Chem., 68, 2377 (1964). (4) R. D. Oldenkamp and G. Houghton, ibid., 67, 597 (1963). ‘ 5 ) A. V. Kiselev, E. A. Paskonova, R. S. Petrova, and K. D. Shcherbakova, Z h . Fiz. Khim., 38, 161 (1964). (6) H. Knozinger and H. Spannheimer, J . Chromatog., 16, 1 (1964). (7) D. H. Everett and C. T. H. Stoddart, Trans. Faraday Soc., 57, 746 (1961). (8) D. L. Peterson and F. Helfferich, J . Phgs. Chem., 69, 1283 (1965). (9) S. J. Gregg and R. Stock in “Gas Chromatography 1958,” D. H. Desty, Ed., Butterworth and Co. Ltd., London, 1958, pp 90-98. (10) P. E. Eberly, Jr., J . Phys. C h a . , 65, 1261 (1961). (11) H. G. Lutriok, K. C. Williams, and R. W. Maatman, J . Chem. Educ., 41, 93 (1964).
Volume 70, Number 4
April 1966
1010
in deriving the heats of adsorption by the pulse technique. I n the present paper, we include a derivation of a modification of eq 4 to fit those cases in which the isotherms deviate from linearity. This modified equation should tell us the direction in which the heat of adsorption by the pulse method in nonlinear systems may be expected to deviate from the more accurate data of the frontal analysis method.
Experimental Section Procedure. There are two somewhat different procedures which have been used for obtaining adsorption isotherms from frontal analysis chromatography. One of these, which can only be used when the adsorbate front or the elution tail is not sharp, involves the quantitative measurement of the shape of the front or tail. It is then feasible to calculate a portion of the adsorp tion isotherm from a single chromatographic experiment.9JO The other procedure, which is used when the adsorbate front is relatively sharp, is to measure the retention time of the front and then calculate the corresponding point on the isotherm. The first of these methods is clearly dependent on the assumption that equilibrium is approached rapidly and that there are no import,ant temperature changes in the adsorption or desorption processes. Unless special care is exercised, the second method may be dependent on these assumptions though perhaps to a lesser degree.'? It is possible to take a point of view which renders such assumptions unnecessary and this is described in the following paragraphs. In the frontal analysis method which we used, carrier gas is passed through the column until a steady state is reached. Then a steady flow of adsorbate is introduced into the carrier, and since the flow rates are known, it is possible to calculate how much adsorbate is carried into the column in any time interval. Similarly, if the concentration of the adsorbate in the gas coming out of the column is measured as a function of time, the measured total flow rate can be used to calculate the amount of adsorbate which comes out of the column in any time interval. The amount of adsorbate remaining in the column is then the difference between these results. By doing a similar experiment with a nonadsorbed gas, it is possible to determine how much of the adsorbate in the column is in the gas phase. Then a subtraction gives the amount which is adsorbed on the solid surface. Since in the steady state the partial pressure of the adsorbate over the column is known, these experiments serve to determine a point on the isotherm. If these measurements are begun when the adsorbate The Journal of Physical Chembtry
R. BEEBE,P. EVANS,T. KLEINSTUBER, AND L. RICHARDS
flow is started and continued until the column reaches a steady state, then the details of the processes by which
the steady state is achieved are of no concern. Temperature fluctuations attending the passage of the adsorbate front through the column, a slow approach to equilibrium, a strongly nonlinear isotherm, or channeling, eddies, and diffusion in the gas flow can only serve to change the length of time required to reach the steady state. They cannot change the properties of this steady state. Therefore, in principle it is possible to determine points on adsorption isotherms by gas chromatography without making any assumptions about the importance of these effects. In practice, the detectors for measuring the concentration of adsorbate flowing out of the column are susceptible to drift, so there is a limit to the slowness with which the adsorbate concentration can change in the final approach to the steady state. However, in the work reported here the steady state was approached sufficiently rapidly that recorder drift was not a problem. For the adsorbate pressure we used the average of the partial pressure at the entrance of the column Pi and at the exit Po. In the case of a linear isotherm this can be shown to be a very good approximation even when the pressure drop down the column is large. With the aid of the expression of James and Martin*3for the pressure at any point in the column, an integration can be carried out to calculate the total amount of adsorbate in the column at the steady state. The result is that a uniform pressure P as given by
(which is also the familiar pressure correction to the retention time) will cause the same amount to be adsorbed in the steady state, and therefore is the correct pressure to use in the calculations. Materials. In the present work we have chosen three adsorbents as column materials; the one, bone mineral (Ossar-500"), typefies a strongly polarizing surface, and the others (Graphon and Sterling MT-G) have nonpolarizing surfaces. These materia.ls have been described in earlier publications from this laboratory. l The bone mineral (Ossar-500") was in all cases degassed in the column in a stream of dry helium at 500" before use. The degassing temperature was not at all critical in the case of the carbon dsorbents; the temperature (12) A. I. M. Keulemans, "Gas Chromatography," 2nd ed, Reinhold Publishing Corp.. New York, N. Y . , 1959, p 206. (13) A. T. James and A. J. P. Martin, Bwchem. J., 50, 679 (1952). (14) J. M. Holmes, D. H. Davies, W. J. Meath, and R. A. Beebe, ~ i o c h ~ i s3,2019 t ~ ~ , (1984).
1011
ADSORPTION ISOTHERMS BY FRONTAL ANALYSIS CHROMATOGRAPHY
used here was approximately 200". The columns were those which had actually been employed in the earlier work by the pulse method.' The helium carrier gas was purified by passage through a system of traps cooled in liquid air. All adsorbate gases were of prepurified quality supplied by the Matheson Co. Apparatus. In the chromatograph, a Gow-Mac katharometer was used with a Leeds and Northrup Speedomax recorder which at maximum sensitivity produced a full-scale deflection per millivolt input. Flow control of the helium carrier gas was maintained by a constant differential type flow controller (Moore Products Co.) in conjunction with a needle valve and the flow rate of the effluent helium or adsorbate-helium mixture was conveniently measured by a soap bubble flow meter. Hydrogen was used as a nonadsorbed gas in measuring the dead time of the chromatograph. The adsorbate gas was stored in glass flasks of large volume and a t a pressure sufficiently in excess of atmospheric pressure to produce the desired small rate of injection into the helium stream through the capillary tube indicated in Figure 1. The injector system was calibrated for each gas by measuring the flow rate of the adsorbate as a functionof the pressure head, between the two ends of the capillary, which was measured by means of a differential manometer. Capillaries of appropriate internal diameter and length were used for the different gases. The withdrawal of adsorbate gas during a single experiment led to a small decrease in the pressure in the bulb and to a correspondingly small decrease in the flow rate of the adsorbate during the experiment. We estimated the error introduced by this decrease. I n the least favorable case (strong adsorption, nonlinear isotherm), Nz on Ossar-500, the uncertainty in the partial pressure due to this decrease in the flow rate amounts to i1.5%. This would result in an error no greater than &0.7% for any single point on the isotherm. (See error discussion below.) In calculating the heats of adsorption qst from the isotherms this error is reduced to 0,2% due to the fact that all isotherms are affected in the same direction. The column temperature used in the present work for the several gas-solid systems ranged from -95" up to 5". These temperatures were produced and maintained by one of two methods. The first method employed a solid-liquid slush of organic substances of appropriate freezing points. A partial list of these coldbath liquids is given in Table I of the paper by Gale and Beebe.1 A second method made use of the cryostat described by Graham.16 This latter method had the advantage that any selected bath temperature below
Figure 1. Schematic diagram of the gas injection system (not drawn to scale): A, carrier gas stream; B, carrier plus adsorbate gas stream; C, capillary tube; D, special valve with no dead space between valve and capillary C; E, adsorbate gas storage volume; F, differential manometer.
that of the room could be realized without depending on the availability of an organic liquid of a specified freezing point. Sources of Errors. We carried out a thorough analysis of the errors involved, based on reasonable assumptions on the accuracy of our original measurements. As this is a conventional procedure, we do not feel that we ought to reproduce the calculations here. It seems worthwhile, however, to discuss the importance of the individual error sources and to point out some conclusions which may help to improve the accuracy of future similar experiments. The retention time measurements were, in almost all systems, the major source of inaccuracy in the isotherms. Because we obtain the retention time as the difference between the observed retention time and the dead time, it is of great importance to make the observed retention time large compared to the dead time. This objective can be attained most easily by selecting a low column temperature; this increases the observed retention time without increasing the dead time appreciably. The size of the difference between the temperatures Ti and Tj, at which the isotherms are measured, influences the accuracy of the heats of adsorption q in a twofold manner. First, the relative error due to the factor (l/Ti - 1/TJ decreases with increasing (Ti Tj); second, the relative error of In p i - In p j also decreases with increasing (Ti - Tj). The inaccuracies due to the measurement and varia(15) D. Graham,
J. Phys. Chem., 66, 1815 (1962). Volume 70, Number 4
April 1966
1012
tion of the column temperature and of the flow rate of the carrier gas plus adsorbate mixture becoqe important only if the error due to the retention time is small (e.g., less than 2%). At first sight it is surprising that the error due to the measurement of the flow rate of the adsorbate is of minor importance in most cases. The flow rate of the adsorbate enters as a factor into the computation of the partial pressure of the adsorbate, and this factorIs is also used in computing the volume of adsorbate adsorbed on the column. As a result of this, an error in the measurement of the adsorbate flow would affect the partial pressure and the volume adsorbed in the same direction. Consequently, the error cancels out if the adsorption isotherm is linear and its effect is greatly reduced if the isotherm is nonlinear. We found that the error introduced because of the water vapor pressure of the soap solution of the soap bubble flow meter is negligible. The most important consideration in achieving a minimum error in the pst value, obtained from the continuous flow data, is the selection of an optimum set of column temperatures. The temperature intervals should be as large as is practicable, and the highest temperature used should be low enough still to result in a large ratio of the retention time to the dead time.
R. BEEBE,P. EVANS,T. KLEINSTUBER, AND L. RICHARDS
r
P i 0.10
0.09
0.08 0.07 6
0.05
8
.I
c
0.04 Fr,
0.03 0.02
0.01 0
0
1
2
3
4 5 6 Pressure, om.
7
8
Figure 2. Type I1 isotherms at low coverage from continuous flow chromatography: NSon Ossar-500'. Inset gives plot of In p (ordinates) us. 10*/T (abscissas).
Results In the present work, adsorption data have been determined by the frontal analysis technique for nitrogen, argon, and carbon monoxide on Ossar-500°, for nitrogen, argon, and oxygen on the Graphon carbon black, and for nitrogen and C ~ F R on Sterling MT-G carbon black. T h Isotherms. The isotherms for N2 and Ar on Ossar-500" and CzFs on Sterling MT-G are plotted in Figures 2-4. These are representative of the three isotherm types encountered in the present work. The following observations can be made concerning the isotherms for the various gas-solid systems considered here. (1) The isotherms for Nz and for CO on Ossar-500" a t all temperatures and coverages studied show a marked deviation from linearity which is well outside the estimated limits of error. These isotherms are concave to the pressure axis (BDDT Type II).17 (2) For N2and Ar on Graphon carbon black, there is a small but demonstrable deviation from linearity (BDDT Type 11) in the isotherms a t the lowest temperatures employed in each case (-95.7 to -96.0°), but in the slightly higher temperature range from -76 to -85" any apparent deviation from linear isotherms is within the limits of error. The Journal of Physical Chemistry
(3) The isotherms for Ar-Ossar-500" and 02-Graphon all conform to linearity; ie., they obey Henry's law within the limits of error. (4) In the case of N2 and CzFson Sterling MT-G a t all coverages and temperatures studied there is a marked departure from linearity, well outside the limits of error. These isotherms are convex to the pressure axis (BDDT Type 111). The Heats of Adsorption. The isosteric heat of adsorption qat as defined by eq 2 has been calculated from the isotherm data. Plots of In p us. 1/T are given in
-R(-) b In P WlT) v Figure 5 and as insets in Figures 2-4, and the derived qat =
heats for the three Ossar systems are given in Figure 6. The heats of adsorption together with error estimates for all systems studied here are given in Table I. In the case of the system N2-Ossar, the conditions
+
(16) V d . = t~ X F[273.1/2'][(760 P/Z)/760], where V d s is the volume adsorbed (STP), F is the flow rate of the adsorbate, T is the temperature of the column in O K , and P is the pressure drop in the column. (17) S. Brunauer, L. S. Deming, W. E. Deming, and E. Teller, J . Am. Chem. SOC.,62, 1723 (1940).
ADSORPTION ISOTHERMS BY FRONTAL ANALYSISCHROMATOGRAPHY
1013
Table I
System
Nt-Ossar
196222
Ar-Ossar CO-Ossar
187-208 266-278
NrGraphon Ar-Graphon OrGraphon NrMT-G CzFcMT-G
178-197 179-197 177-197 172-1 89 22 1-26 1
-
Fronts1 analysis method Coverage. e
Temperature range, "K
kcal/mole
0.001 0.002 0.004 0.008 0.010 0.020 0.040 0.060 0.00251). 025 0.005 0.010 0.015 0.020 0.030 0.001-0.003 0.0003-0.003 0.003-0.015 0.02-0.15
0.45
0.09
0.40
-
0.07
0.35
-
0.03
E.
1
0.08
a
i
0.06
Po
3
0.02
2
B ld
$ 0.05 .f: P -e
,.
.-* e k
m 0.04 0
0 0.03
8 0.30 -
5 $ 0.25
n a
-3
0.20
0.15
0.01 0.02
0.10
0.01
0.05
5.3
Type I1
2.5
...
Linear Type I1
2.7 2.7 2.7 2.4 4.9
Type 11-linear Type 11-linear Linear Type I11 Type I11
r
'
P
2 2 1.4'K
E
P .er
Isotherm type
qat,
5.97 f 1.5% 5.95 f 1.5% 6.03 f 1.5% 5.97 f 1.5% 5.84 f 1.5% 5.52 f 1.5% 5.35 f 1 . 5 % 5.3 &2.5% 2.7 *9% 8.4 f 3 . 5 % 7.9 *3.5% 7.7 f 3 . 5 7 0 7.7 f 3 . 5 7 0 7.8 f 3 . 5 7 4 3.2 f 5 % 2.9 f 7 % 2 . 6 326% 2.1 f 12% 4.6 f 2 . 5 %
0.0005-0.004
6
Pulse method kcal/mole
qat,
0.8
0.5
a 0.4
5
3
2
0.1
0
0 0
1
2
3
4
Pressure, cm.
0
0 0
1
2
3
Pressure,
4 om.
6
6
Figure 3. Linear isotherms a t low coverage from continuous flow chromatography: Ar on Ossar-500'. Inset gives plot of In p (ordinates) us. 103/T (abscissas).
Figure 4. Type 111 isotherms from continuous flow chromatography: C ~ Fon O Sterling MT-G carbon black. gives plot of In p (ordinates) us. 10a/T (abscissas).
selected for the continuous flow study were particularly favorable; this is reflected in a low value of the estimated error of less than zt0.2'% in the resultant heats of
adsorption. It is seen from the inset of Figure 2 that the points read off the isotherms, at the arbitrarily selected coverages indicated, fall nicely on a straight Volume 70,Number 4
Inset
April 1966
1014
R. BEEBE,P. EVANS, T. KLEINSTUBER, AND L. RICHARDS
runs considerably higher than *0.2%; in fact, the error for NrMT-G is as high as 12%. As a result, there may be a considerable scatter of points in the In p vs. 1/T plot, as seen for instance in Figure 5 for the system NrGraphon. In this case the heats of adsorption ~ 1 QL, , and q a were calculated from the slopes of the dotted lines for the three temperature intervals indicated. The weighted mean value gatwas then found, with appropriate attention to the estimated errors El, Ez, and E3 in each of the values q l , pz, and q3. This procedure is based on the relationship
0
d.
3 -1
If the three points of a In p us. 1/T plot do fall on a single 5.0
5.6
5.4
5.2
10*/T.
Figure 5. Plots of In p us. 10a/Tfor Na on Graphon carbon black.
I-
I
to
Y
-
0
I
Ar 3 2
0
I
0
I
I
I
I
0.01
0.02 Fraction of a monolayer, 0.
I
I
0.03
Figure 6. Isosteric heats of adsorption derived from continuous flow gas-solid chromatography: N1,.4r, and GO on Ossar-500'.
line. The slope of this line bears a linear relation to qat, the isosteric heat of adsorption. In this case there was a marked variation in the slope as a function of coverage which was reflected in decreasing qat values as e increased. This relationship is brought out in Figure 6 and in Table I. A decrease in qst with coverage was shown also by the system CO-Ossar. In all other systems under consideration here, there was no significant change in qat with 0 outside the estimated limits of error. For this reason we have included in Table I only the range of c.overagerather than specific values of e, except in the cases of Nzand CO on Ossar. In all cases except Nz-Ossar the estimated error The Journal of Phueical Chenzislr?l
straight line, this may be merely fortuitous depending on how the isotherms were drawn through the experimental points. The important factor to bear in mind here is the final estimate of the over-all error in the qst determination. The most commonly used relation for calculating 4st from the dependence of the retention time tR of an adsorbate pulse on temperature is
Here t~ is the length of time it takes the maximum of the adsorbed gas pulse to be eluted minus the time required to elute a nonadsorbed gas pulse. All experiments are done at the same flow rate (or else the retention volume is used in place of t ~ and ) usually with the same size pulse of adsorbate. Equation 4 can easily be shown to be valid if the adsorption isotherm is linear. It is the purpose of this section to deduce the sign and estimate the magnitude of the error in the value of qat obtained from eq 4 if the adsorption isotherm is not linear. To help to visualize the problem, let us assume for the moment that a system with an isotherm like that shown in Figure 7 is being studied. When the adsorbate pulse first enters the column its pressure might be given by point a. As the pulse travels down the column it spreads out and therefore the pressure at the peak maximum becomes smaller. By the time the pulse leaves the column the peak pressure decreases to some value given by the point b. For the isotherm shown, the fraction of the adsorbate adsorbed is larger at point b than at point a, and therefore the pulse slows down as it moves through the column. It is this slowing down which makes the interpretation of the retention time difficult. However, it would be possible to find some point c such that the retention time for the front of a
ADSORPTION ISOTHERMS BY FRONTAL ANALYSIS CHROMATOGRAPHY
5iW
1015
This can be related to the isosteric heat of adsorption by a calculus identity, giving
m
a
0
a In t~ WlT) =
$
~
blnV
P
blnP
-(am)im)v
=
av
qat
v(@)T
(6)
where use has been made of the definition of qBtin eq 2. Equation 6 differs from eq 4 by the inclusion of the additional factor (P/V)(bV/bP),. If the adsorption isotherm is linear, this factor is unity and we have succeeded in deriving eq 4. If the isotherm is not linear, then the factor will be greater or less than unity and the qat determined by the pulse method will be correspondingly too large or too small. If the shape of the isotherm and the surface coverage at which the pulse experiments are being done are known, then the magnitude of the error can be estimated by taking the ratio of the slope of the isotherm (bV/bP). to the slope of the line from the isotherm to the origin V/P.
PARTIAL PRESSURE OF ADSORBATE Figure 7. A sample of adsorption isotherm.
Discussion
continuous flow of adsorbate at pressure c would be the same as the retention time for the pulse which starts at pressure a. This same thing can be done for other temperatures TI, T”, etc., obtaining points a’, b’, and c’; a”, b”, and c“; etc., where the points for each temperature are related as above. Now it is assumed that if the same size pulse is always used so that a = a’ = a” = . . ., then it is at, least approximately true that the same pressure c = c’ = c” = . . . should be used in each of the equivalent continuous flow experiments. To the extent that this assumption is weak, the following analysis is weak. (If the isotherm is linear, all fronts and peaks will have the same retention time at a given temperature and the following analysis becomes exact.) A series of experiments at several temperatures, but with one pulse size, would yield a corresponding series of retention times. The above assumption implies that the same retention times for each temperature could be obtained from a series of experiments using the frontal analysis technique and only one adsorbate pressure. Therefore, in the two cases a plot of In 1~ tis. 1/T would appear exactly the same. In the series of frontal analysis experiments, t~ is directly proportional to V, the volume of adsorbate adsorbed per gram of adsorbent. Furthermore, the experiments are done with the adsorbate gas pressure held constant. Therefore b In tR --
a(l/T)
=
In V (-)bWl/T)
P
(5)
In the systems under consideration here, there is no evidence for a slow approach to a steady state behind the adsorbate front, so the procedure described in the experimental section appears to be valid. However, since some of the isotherms are not linear, it is to be expected that the pulse and frontal analysis methods might give different heats of adsorption as predicted by eq 6 . To verify this, we shall compare18 data for the systems N2-Ossar, Ar-Ossar, and C2F~--Sterling MT-G as representative examples. The isotherms for these three gas-solid systems, shown in Figures 2, 3, and 4, are seen to be Type 11, linear, and Type 111, respectively. (18) In making this comparison of the qat values obtained by the two methods we must call attention t o certain qualifications. (1) The values of coverage B given in Table I may be accepted with considerable confidence since they depend on a direct comparison of the moles of gas adsorbed on the column with the moles of gas necessary to give an adsorbed monolayer on the column. This latter quantity is determined from the weight and specific surface area of the adsorbent in the column with the use of the accepted molecular cross section of 16.2 A* for nitrogen in the adsorbed monolayer. The BET method is employed here. Unfortunately, in the pulse method no such direct determination of B is possible. This problem is discussed in the earlier publication from this laboratory.1 It seems reasonable to take an average of the Ofmar and elmax values given in Table V of the above publication. As a result of this uncertainty in the e values of the pulse method, we cannot be sure that we are considering equal coverages in comparing the two methods. This problem is of importance only where there is B substantial change in qat with coverage as in Figure 6 for the systems N2 and CO on Ossar. (2) We have given estimates of the specific percentages of error in the isotherms and in the derived qst values of the present research. It is not practicable for us to make similarly detailed error analysis of the results obtained by the pulse method. In reviewing the earlier work we conclude that the upper limit of error was of the order of *5%.
Volume 70,Number 4
April 1966
1016
Since the isotherm in the case of Ar-Ossar is linear, we may expect that qat as derived by the pulse method' will be correct. The values 2.7 and 2.5 kcal/mole, as obtained by the two methods, are in agreement within the estimated limits of experimental error which in the case of this system is rather high. Thus eq 4 is satisfactory in this case. The isotherm for N2-Ossar is seen from Figure 2 to be distinctly nonlinear [Type 11). The correction term ( P / V ) ( b V / W ) Tin eq 6 would be greater than 1.0 in this case and thus the qat value of Gale and Beebe calculated without the correction would be too low. It is seen from Table I that the value of pat by the pulse method a t low coverage is 5.3 as compared with about 6.0, at t9 < 0.01, obtained in the present research. Fortunately, the error in the present determination of qat is very low (ca. 2%) for the N2-Ossar system. Thus the prediction of the relative values of qat obtained by the two chromatographic methods is substantiated here. The isotherm for CeFrSterling MT-G in Figure 4 is nonlinear in the opposite sense to that of Figure 2, being concave to the pressure axis (Type 111). I n this case eq 6 leads to the conclusion that the qat value of Gale and Beebe would be too high. From Table I we see that this is indeed true with 4.9 kcal by the pulse method and 4.6 kcal by the present method. Here again we have a relatively low error (2.6%) and the difference between the two above qat values is well outside the limits of error.16 The other gas-solid systems are not represented in Figures 2, 3, and 4,but the qat data are given in Table I. Among these systems, only in the case of 02-Graphon was a linear isotherm observed a t each of the three temperatures used. The nature of the isotherms is indicated in the extreme right-hand column of Table I. Where the isotherms were linear at certain temperatures but Type I1 at lower temperatures, the designation Type II-linear is given. The system CO-Ossar yields distinctly Type I1 isotherms and excessively high qat values. Unfortunately, we have no data for this system by the pulse method. When these data become available, we would predict that the resulting qat values would be too small by a sub-
The Journal of Physical Chemistry
R. BEEBE,P. EVANS, T. KLEINSTUBER, AND L. RICHARDS
stantial amount, unless one makes the correction given in eq 6. The significance of the variation in the heats of adand Ar sorption of CO and the elementary gases Nz,02, when adsorbed on polarizing surfaces such as the Ossar500' or on the nonpolarizing carbon blacks has been discussed by Gale and Beebe' and more recently by Smith and Ford.Ig It is rather remarkable to find, as we do, a qat value as high as 8.0 kcal/mole for CO on Ossar since Smith and Ford found by calorimetry the low value 2.4 for this gas on Sterling MT-G. This wide spread in the qat values on different adsorbents underscores the importance of the polarizability of the adsorbate in combination with a strongly polarizing surface. Of course CO, unlike N2, has a small permanent dipole and this contributes even more strongly to a higher pat value on the polarizing surface of Ossar-500". It is also noted that the qst value for CO obtained chromatographically may serve as a convenient and useful probe in assessing the polarizing power of a given surface. All the chromatographic data obtained in this laboratory by the two methods employing the pulse technique' and that of frontal analysis, give qualitative support to the prediction of eq 6 within the estimated error limits. However, it is noted that any differences in the two methods do not exceed a figure of approximately 15%. I n our opinion, the systems NrOssar and C2F6-MT-G represent rather extreme cases of Type I1 and I11 adsorption, respectively, at low coverage. Thus we may make the observation that the chromatographic pulse method of getting at qst data is not excessively in error even if one does not make the correction included in eq 6. Because of the convenience in operation, the pulse method still has merit as a means of getting rough qat values which may be useful in many situations.
Acknowledgments. Our gratitude is due to the National Science Foundation and to the National Institutes of Health for financial support of this work. (19) W. R. Smith and D. G . Ford,
J. Phys. Chem., 6 9 , 3587 (1965).
