T H E ADSORPTION OF CERTAIN VAPORS BY ACTIVATED CHARCOAL. 111. BY J. N. PEARCE AND A. L. TAYLOR’
All experimental research on adsorption, hitherto, has been directed, for the most part, to the solution of two closely related fundamental problems. These problems involve, (I) the determination of the nature, the extent and range of the forces which are instrumental in producing concentration changes in the gas phase a t the solid-gas interface, and ( 2 ) the determination of the physical states and of the chemical relationships existing in the adsorption system. Whenever adsorption is mentioned we naturally think of the monumental work of Langmuir.* He has shown that in many cases, especially on plane metallic surfaces, the adsorbed layer is but one molecule thick, often only partially covering the adsorbing surface, and that the adsorbed molecules are highly oriented with respect to the adsorbent. With him adsorption is distinctly a chemical phenomenon. The whole problem of adsorption becomes much more complicated when the adsorbent present,s a rough uneven surface, like amorphous charcoal. Here we not only have the possibility of an increasing preferential adsorption as we pass from surfaces to edges to points,s but also the influence of capillarity. The complete solution of the adsorption problem will require an accurate knowledge not only of the physical properties of the adsorbent, but also of the adsorbate as well. Among the latter are surface tension, capillarity, compressibility, and the heats of condensation, of wetting and adsorption. I n case of the highly porous bodies which possess fine capillaries the geometrical configuration of the adsorbed molecules, their size and structure, the chemical and electrical nature of the molecules and of the substituents in these molecules,-all of these must exert a pronounced influence upon the energy and the magnitude of the adsorption of vapors. In any heterogeneous system in which one phase is rigid and one mobile there will always be, according to G i b b ~ a, ~change in concentration of the mobile phase a t the interface, if such a change in concentration will result in a decrease in surface energy. Langmuirj has shown that in forming films on liquids the molecules of the paraffm hydrocarbons arrange themselves in such a way that the methyl group (CH,) forms the surface layer. No matter how An extract of a thesis presented by A. L. Taylor in partial fulfillment of the requirements for the Ph.D. in Chemistry a t the State University of Iowa. Langmuir: Phys. Rev. ( z ) , 6, 79 (191j); 8, 149 (1916); J. Am. Chem. Soc., 38, 2221 (1916); 40, 1361 (1918). Taylor: J. Phys. Chem., 30, 1 4 j (1926). Gibbs: “Scientific Papers,” 1, 219 (1906). 5 Langmuir: ,Met. Chem. Eng., 1 5 , 468 (191j). J
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J. N. P E A R C E AND A. L. TAYLOR
long the chain may be the surface energy of the series from hexane to the molten p a r a f i s is practically the same. The surface energies of the alcohols are practically the same as those of the hydrocarbons. Further, a bulky end group, like “I” or “ S O ” , greatly increases the surface tension of the paraffins just as the substitution of an “OH” group, by orientation, increases the surface energy of benzene. He was able to show conclusively that the molecules are highly oriented in these surface films. We have been working for some time upon a systematic study of the relation between adsorption magnitudes and the various physical and chemical properties of the vapor molecules. To this end the vapors studied have been taken up in a definite order, viz., the order in which they occur in an homologous series, or in the order of increase in the number of a substituent atom or group in a given molecule, and, finally, from the standpoint of isomeric modifications, involving straight and branched chain compuunds. Our first contribution6deals with the adsorption of water, methyl alcohol, ethyl alcohol, ammonia, and methylamine vapors by activated charcoal; the second7 presents the results of a study of the adsorption of methane and its chlorine derivatives. In these we have assumed that it is the oxygen, the nitrogen, and the chlorine atom, respectively, that is most strongly attracted by the carbon atoms in the surface lattice of the adsorbent. The chlorine derivatives of the hydrocarbons are particularly interesting in the study of adsorption in that the chlorine atom possesses a large number of valence electrons. The force fields a b m t this: atom, and hence its residual valence, should be large. Moreover, the chiorine atom is usually considered to be highly electronegative, and hence. the substitution of a chlorine atom for hydrogen must increase the electronegativity of the molecule. The present .;Tork presents the results of the study of the adsorption isotherms of two series of vapors. These series are closely related in adsorptive forces and each offers special opportunities for the study of the structure of surface films and of the forces involved in the formation of these films. The isotherms of methyl chloride,7 ethyl chloride, n-propyl chloride and n-butyl chloride make available data on four alkyl chlorides of an homologous series in which the lengths of the carbon chain of successive members differ by a constant increment, CH,. By including the study of the vapors of isopropyl chloride and tertiary butyl chloride we have a second series in which one, two and three of the hydrogen atoms of the methyl radicle are replaced by methyl groups. If we remember that these molecules are orienteci with the chlorine atom toward the surface of the charcoal, it is evident that we have a series in which the cross-sectional area of the molecule, in a plane parallel to the surface of the adsorbent, is increased by characteristic increments. We may thus produce a crowding effect on the immediate surface, but at some distance from the surface. Pearce and Knudson: Proc. Iowa ticad. Sei., 34, 197 (1927). Pearce and Johnstone: J. Phys. Chem., 34, 1260 (1930).
ADSORPTION O F VAPORS B Y ACTIVATED CHARCOAL
‘093
Materials and Apparatus The “acid-washed”, “acid-free”, steam-activated charcoal used in this work was taken from the same large supply as that used in the previous researches6,’. It was specially prepared for us from coconut shell by the Carbide and Carbon Chemicals Corporation, under the direction of Dr. N. K . Chaney. The loss in weight on outgassing was found to be 2 . j percent; the These values were always employed density of the outgassed charcoal is 1.80~. in calculating the actual weight of the charcoal used and in calculating the volume of the dead “space.” All samples of charcoal used were outgassed mm. and the charcoal a t j z j ’ until the pressure dropped to about o.5.10-~ was then allowed to cool to room temperature where the pressure was too small to be measured on a McLeod gage. The liquid alkyl chlorides used in producing the vapors were of the highest quality obtainable from the Eastman Kodak Co. Each liquid was further purified by careful repeated fractionation. The last three or four fractionations were carried out in an air-free apparatus of such design that the vapor never came in contact with air before it was brought’ in contact with the charcoal. The boiling points of the purified alkyl chlorides were: ethyl chloride, 1 2 . j ’ at 7 5 5 mm.; n-propyl chloride, 46.j’ at 7 5 3 mm.; iso-propyl chloride, 34.6j’ at 748.6 mm.; n-butyl chloride, 77.0°-77.zo a t 745 mm; terbutyl chloride, 50.1’ at 740.45 mm. The apparatus and the experimental procedure was the same as that employed in the work of Pearce and Johnstone.’ The apparatus was, however, carefully recalibrated. Adsorption equilibrium was assumed when the pressure of the vapor above the charcoal remained constant for at least 30 minutes. I n those cases where equilibrium was only slowly attained a much longer time was allowed. Each pressure reading recorded is the mean of a t least two or three readings and is corrected to o’, sea level and 4 j’ latitude. Each isotherm plotted represents at least two different series of measurements on different samples of charcoal. An isotherm was considered as definitely established when the points of successive series were found to lie on the same smooth curve. To furnish a better basis of comparison the isotherms of the five alkyl chlorides were determined as nearly as possible at the same temperatures. The lowest temperature employed for each vapor was 0’;the highest temperature used depended upon the stability of the vapor in contact with the charcoal. The temperature of each isotherm was frequently checked by raising or lowering the temperature until it corresponded with that of an adjacent isotherm and then by adjusting the volume of vapor in contact with the charcoal so that the point representing equilibrium would fall in the region of high pressures. The equilibrium points thus obtained were in excellent agreement with the isotherm previously determined on a fresh sample of charcoal. Only in one case did we observe any evidence of decomposition. This was for the tertiary butyl chloride at 99.5’.
I094
J. N. PEARCE AND A. L. TAYLOR
Natural Isotherms The adsorption isotherms obtained in this series have the usual characteristic forms. At all temperatures the curves are concave toward the pressure axis throughout the entire pressure range. Attempts to determine the isotherms at temperatures above those for which data were obtained failed because of the occurrence of decomposition as indicated by a progressive increase in pressure over a long period of time. The temperatures a t which decomposition of the alkyl chlorides first appeared are: methyl, 236' (rapid); ethyl, 236'; n-propyl, 182'; iso-propyl, 137'; n-butyl, 140'; tertiary butyl,
FIG.I 99.5'. Thus, the stability of the alklyl chlorides in contact with our charcoal decreases with increase in molecular complexity. It is lower for the secondary and tertiary forms than for the corresponding normal compounds. From the reproducibility of their results Lamb and Coolidge* conclude that previous contact with ethyl chloride does not alter the adsorption capacity of activated charcoal for subsequent determinations. Our experience has been exactly the opposite. I n no case have we found the activity the same after outgassing at 5 2 5 ' . The various isotherms for the individual vapors were carefully plotted separately and from these were read the data for the isobars and isosteres. For purposes of illustration we are presenting in Figs. 1-4the natural isotherms of the alkyl chlorides at oo, 40°, 77,s' and 99.5', respectively. The plots of the higher pressures have been purposely omitted to save space. While these temperatures cannot in any way be considered as corresponding adsorption temperatures of the vapors the plots show the characteristic *Lamb and Coolidge: J. Am. Chem. SOC.,46, 1146 (1920).
ADSORPTION O F VAPORS BY ACTIVATED CHARCOAL
1095
trends of the various isotherms. They show also the influence of temperature upon the relative amounts of the different vapors adsorbed at the various pressures. At oo the adsorption isotherms break very sharply away from the 3,;\I axis. With rise in temperature the break becomes less pronounced and it should completely disappear in the vicinity of the critical temperature. For a given temperature also the sharpness of the break increases as the boiling point of the liquids increases, but it occurs a t lower values of S 11. The isotherms at oo (Fig. I ) , may be somewhat complicated because of the fact that four of the vapors reach saturation at relatively low pressures.
I
'
-p-_---p-i._L
20
do
-11 i 60
80
roo
FIG.2
The tendency for the isotherms to intersect upon variation of pressure is obvious from the plot given. The rapid increase in the adsorption of methyl chloride with increase in pressure is also particularly interesting. For pressures between I O mm. and 20 mm. the volume of the normal alkyl chloride vapors adsorbed, (cc. per gram), decreases in the order ethyl, n-propyl, n-butyl, methyl. At pressures above I O O mm. the order becomes methyl, ethyl, n-propyl. Above this pressure the magnitude of the adsorption decreases with increase in the length of the carbon chain. With rise in temperature the tendency for the isotherms to intersect becomes markedly less. For pressures below 60 mm., (Fig. 4) the volumes of vapor adsorbed at 99. j' increases as the length of the normal chain vapor molecule is increased. I t is very probable that this relation is completely fulfilled at sufficiently high temperatures. This is also the order of increase in boiling points, critical temperatures and other physical properties of the
1096
J. S . PEARCE AND A . L . TAYLOR
liquids. At all temperatures the isotherms of the iso-propyl and tertiary butyl chlorides lie below those of the corresponding normal compounds. The volume of each of the alkyl chloride vapors which had to be admitted to the charcoal at oo before an equilibrium pressure could be detected is large. The volume of vapor adsorbed at low pressures (below 0 .j mm.), is greater the greater the molecular weight of the vapor. Thus, at oo and under an equilibrium pressure of 0.45 mm. one gram of charcoal adsorbs 33.65 cc. of the tertiary butyl chloride and 12.99 cc. of ethyl chloride, while at the same temperature, but under 1.39 mm. only 7.85 cc. of methyl chloride are ador bed.^ These observations are even more striking when we take into
consideration the fact that the total amount of vapor capable of being adsorbed decreases with increasing molecular weight. Further, the amount of vapor adsorbed at oo under one mm. pressure is equal to or exceeds one-half of the total amount adsorbable at the same temperature under a pressure just short of saturation. This relation holds without exception for the five vapors studied. It has been interesting to observe that the time necessary to attain adsorption equilibrium at a given temperature differs widely corresponding to different points on the isotherm. The time required is greatly increased in the pressure interval including the “break” of the isotherm; it is much greater for the iso-propyl and the tertiary butyl chlorides than for the normal compounds. I n fact, it is difficult to reproduce the 0’-isotherm of the tertiary buty! chloride either in the pressure range including the break, or just below condensation. One illustration of the slowness of the pressure variation observed a t the break point of the tertiary butyl chloride may not be amiss. Two and one-half hours after the admission of the vapor to the bulb the pressure over the charcoal was 30.65 mm. The pressure decreased slowly and
ADSORPTIOS OF VAPORS BY ACTIVATED CHARCOAL
I09 7
regularly without exhibiting any sign of equilibrium even after 119 hours when the pressure was 19. j o mm. I t was observed also that when the adsorption equilibrium was approached from the side of high pressure, especially, if the butyl chloride had been previously condensed on the charcoal, the values of X/M were always too high. It is evident that the sluggishness in the attainment of adsorption equilibrium in this instance is due to steric hindrance. When the vapor is first admitted to the gas-free surface of the charcoal the molecules will be adsorbed on those points and areas most accessible to the vapor molecules. This will include also the most easily accessible points and areas on the capillary walls.
PO
60
80
FIG.4 JVith increase in the concentration and pressure of the vapor above the adsorbent there will be a crowding and a readjustment of the adsorbed molecules on the surface. These readjustments will require time and they will be most easily made on the more exposed charcoal surfaces; they will be more difficult within the capillaries where the influence of the size and shape of thp vapor molecules will be more pronounced. We have then the phenomenon of a “drift,” similar to that observed by Cude and Hulettg when thoroughly outgassed charcoal is immersed in liquids for long periods of time. The validity of the Freundlich equation, X / m = CY.^"^, requiresa constant value for the exponent I/n. The plot of the double-log isotherms should, if the equation applies to these vapors, give perfectly straight lines. The behavior of these isotherms is to be seen in Fig.5. In general, the slopes, I/n, of these isotherms tend to become more constant the lower the temperature a t which they are determined, and to a less pronounced extent also a t 9Cude and Huletr: J. Am. Chern. SOC.,42, 391
(1920).
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J. N. PEARCE AND A. L. TAYLOR
higher pressures. The values of r/n becomes smaller as the number of carbon atoms in the chain is increased. Further, the flaring of the isotherms, that is the variation of the log X/m values of the chain compounds with decreasing pressures, decreases with increase in the molecular weight of the vapor. This is exactly the same order as that previously observed for methane and its chlorine derivatives'. Further discussion of these isotherms will be left for a later paper. The effect of temperature on the adsorption of the monochlor alkyl derivatives is also shown by their isosteres. If the well-known relation,
0
/O
30
/O
20
30
FIG.5
applies to adsorption phenomena, the slope of these isosteres should be proportional to the negative value of the heat of adsorption. Further, unless the heat of adsorption is dependent upon the temperature the isotherms should be parallel straight lines. Within limits of experimental error the isosteres are both parallel and rectilinear throughout the temperature range. Since they have the usual characteristic form we are omitting the graphs in order to save space. The heats of adsorption calculated from the mean slopes of all of the isosteres of each vapor are given in Table I.
I099
ADSORPTIOS OF VAPORS BY ACTIVATED CHARCOAL
TABLE I Heats of Adsorption of the Vapors of Alkyl Chlorides on Charcoal Vapor
CHsC1 CzHsCl C3H;Cl
AH cals.
- 8300
- 10060 -12300
Vapor
AH cals.
i-C3H7Cl n-C4H9C1 ter-C4HsC1
-12250
- I3400
-II ~ O O ?
Upon the basis of theoretical considerations Coolidge1ohas justified the use of the Clausius-Clapeyron equation in the calculation of the heat evolved in the adsorption process. However, it has usually been found that the heat effect calculated in this way is lower than that experimentally determined. Pearce and McKinleyll have determined the heat of adsorption of ethyl chloride and methyl chloride a t 2 j o ;the vaIues obtained for AH were - I j 4 0 0 and - I 1600 cals., respectively. The liquids from which they obtained their vapors were those purified for the present work; their charcoal was taken from the same container and subjected to the same treatment in outgassing. The difference between the observed and calculated heats of adsorption may be due in part to the fact that in determining the heats of adsorption experimentally the vapors are not admitted to the charcoal under the equilibrium pressure. Lamb and Coolidge6 have shown that the heats of adsorption differ from the heats of vaporization by constant amounts. This they attribute to the compression caused by the adsorption forces. According to the Polanyi theory, however, the surface of the adsorbed layer increases in distance from the surface of the adsorbent as more and more vapor is adsorbed until, finally, it reaches the edge of the adsorption space. The potential and, therefore, the compressive forces decrease very rapidly very near the edge of the adsorption space, and hence the heat of compression must also decrease rapidly. In this range, therefore, the heat of adsorption should change very rapidly with the concentration until it becomes equal to the heat of vaporization. Application of the Polanyi Theory I n his earlier work Polanyi12 attempted to explain the forces existing between the adsorbent and adsorbed molecules. He assumed that the adsorption forces act through distances which are large compared with molecular diameters. Also, that the force exerted upon a molecule a t a given distance from the surface of the adsorbent is independent of the temperature and independent of whether or not other molecules exist between the molecule and the surface. He has shown that for temperatures below 0.8 TCrbt. of the vapor the adsorption potential a t any point in the adsorption space is given by the relation, E , = RT In E , P, '"Coolidge: J. Am. Chem. Soc., 48, 1795 (1926). Pearce and McKinley: J. Phys. Chem., 32,360 (1928). l* Polanyi: Ber. deutsch. physik. Ges., 12, I O I Z (1924);Yerh. deutsch physik. Ges., 18, jj (1916); 2. Elektrochemie, 26, 370 (1920). l1
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J. N. PEARCE AND A. L. TAYLOR
where ps is the vapor pressure of the liquid in the free state and px is the equilibrium pressure in the adsorbed state. The potential ci is nothing more than the work done in transporting one mole of vapor from the saturation pressure, p. to the equilibrium pressure p.. All points possessing the same adsorption potential, ti, form an equipotential surface. This and the surface of the adsorbent inclose a definite volume, -the adsorption space, @i. Assuming the adsorbed substance to have the same density as the free liquid, for temperatures well below the critical temperature, we can calculate the volume of the adsorption space from the relation, +i = xt/6, where x’ is x/m and 6 is the density of the liquid. Thus, for every pair of px and x/m values we may calculate a pair of ci and Qi values, so that ei
=
f(4i).
The curves showing the potential distribution with the volume are given in Fig. 6. The (e 4) curve is then a characterFIG.6 istic adsorption curve for a given vapor and adsorbent. If we assume with Polanyi that the temperature coefficient of the adsorption potential is zero, and make the necessary corrections for the volume occupied by the adsorbed substance, the curve should be the same for all temperatures. In the vicinity of and above the critical temperature corrections must be applied for the density of the adsorbed substance. By means of the thermal dilatation formula of the adsorbed substance as a liquid and of its equation of state as a vapor it is possible to calculate the adsorption isotherm a t any other temperature from the (+@)-curve determined for a single isotherm. We have calculated the (€-@)-curvesfor propyl chloride and iso-propyl chloride from both the oo and 40’ isotherms. In making these calculations the densities were taken from the “International Critical Tables” and they are corrected for temperature by the dilatation formulas given in the “Physical Chemistry Tables.” The curves have been drawn for the 40’ isotherms and the points calculated from the o0 isotherms are indicated by double circles. The agreement is all that can be desired. BerenyiI3 has previously applied the method here used to the data of Titoff for the adsorption of carbon dioxide. The agreement in this case is also most excellent. The relative positions of the (e-Q)-curves of the two pairs of isomers is interesting. While they do not coincide the curves for either pair of isomers l3
Berenyi: 2. physik. Chem., 94,
628 ( 1 9 2 0 ) .
A D S O R P T I O S O F V.%PORS BY ACTIVATED CHARCOAL
I101
run practically parallel throughout their whole extent. Further, for a given adsorption volume, 4, the adsorption potential, E, of the normal compound, is greater than that of its isomer. Conversely, for equal adsorption potentials the adsorption space occupied is always greater for the normal compound. These curves show also the influence of lengthening the hydrocarbon chain by successive increments of CH,. For relatively high values of E , say E = 3000 cals., the values of 4 increase regularly from methyl chloride to n-butyl chloride. This relation disappears, however, as we approach saturation. I t is interesting to note also that at the limit of the adsorption space, where the adsorption potential is zero, the adsorption volume, 4.IO?, is practically the same for all of the vapors given, viz., about 39.5. This is almost identically the same value as that obtained by Pearce and Johnstone7 for the adsorption of the chlorine derivatives of methane on charcoal from the same stock supply. The coincidence is exactly what we should expect, if the Polanyi theory involved is correct. The maximum ralue of 4 would not necessarily be the same, however, on another sample of the same charcoal having a different degree of activation. I t is very probable that adsorption relations would be much more significant if comparisons were made at corresponding temperatures rather than at identical temperatures. We have in the 40' isotherms data which is quite suited for such a comparison. The boiling points of propyl chloride and tertiary butyl chloride are 46.6' and IO, respectively; their isotherms are very similar in shape. We have calculated the ratio of the volumes of the two vapors adsorbed under the same pressure at different pressures throughout the pressure range from 3 mm. to 300 mm. The values of the ratios were found to be practically constant: I cc. of propyl chloride vapor -~ = 1.285 cc. of ter-butyl chloride vapor 0.778
The molecular volumes of these chlorides as liquids a t their values at zoo, are in the ratio VI (propyl chloride) 90.7 T', (ter-butyl chloride) I12,z
4oo,
calculated from
0.823 I
If we now neglect the compressibility of the liquids, the small difference in boiling points, and also any possible blocking effect in the capillaries due to the larger cross-section of the tertiary butyl chloride molecules, we find that the ratio of the actual volumes of the adsorbed substances, considered as liquids, is TI (propyl chloride) I 06 =5, (ter-butyl chloride) I . 00 Taking into cocsideration the uncertainty of the density data, this ratio of approximately unity should indicate that the amounts of different vapors, possessing a common orienting atom, adsorbed a t identical, or nearly cor-
1102
J. N . PEARCE AND A. L. TAYLOR
responding temperatures, occupy a definite volume for a given equilibrium pressure. It is our intention to study this relation more fully in a forthcoming study of the adsorption of vapors a t their boiling points. In his calculations Polanyi has assumed that the density of the adsorbed vapor is the same as that of the free liquid a t the same temperature. Above the critical temperature the density of the adsorbed substance is no longer equal to that of the liquid. In order to apply the characteristic (e,-+,) curves for the determination of an isotherm, Berenyi" has shown that it is necessary to make corrections for the change of density a t the various levels in the adsorption space. The relation given by e, = g(6,), indicates that for every potential level, si, there is a corresponding density, &. Making use of the equation of s t a t e of t h e adsorbed vapor, Berenyi finds that the relation between the density distribution and the potential can be expressed by the equation: FIG.7
where a and b are the van der Waal constants and 6i is the density of the vapor a t the potential level, €1. Neglecting the last three terms on the right will introduce only a negligible error, since za8JRT and b6, become vanishingly small a t high temperatures. The application of this equation a t the temperatures which we have used may introduce error in calculating the density distribution of the vapors studied. The values obtained for the different vapors, however, should be, relatively a t least, of the correct order of magnitude. By elimination of ei between the two functions, ei = f(+i )and ei = g(6i), we obtain a relation between the density distribution and the volume, viz., 6i = h(+i). I n making these calculations we have taken the constants a and b of the equations of state of the three lower alkyl chlorides from the Landolt-Bornstein-Roth Tabellen, Ed. 5 . The constants for isopropyl chloride and the two butyl chlorides were not available in the literature. They were estimated from the values for similar compounds. The volume-density distribution relations thus obtained are shown graphically in Fig. 7 .
ADSORPTIOS O F VAPORS BY ACTIVATED CHARCOAL
I
103
summary The adsorption of the vapors of ethyl, n-propyl, isopropyl, n-butyl and tertiary butyl chlorides by charcoal has been determined a t temperatures ranging from oo to temperatures a t which the vapors become unstable when jn contact with charcoal. The stability of these alkyl chlorides toward heat decreases with increase in molecular complexity. The is0 and tertiary compounds decompose a t lower temperatures than do the corresponding normal compounds. 2. At low pressures and for all temperatures the volume of vapor adsorbed in the normal series increases with the molecular weight of the vapor. At oo the order of adsorbability is completely reversed a t sufficiently high pressures. At high temperatures (above 100') the magnitude of the adsorption a t all pressures increases with the length of the carbon chain. The adsorbability of the branch-chain compounds is a t all temperatures and pressures less than that of the corresponding normal compounds. The influence of the branching structure of molecules upon the time required for the attainment of pressure equilibrium, especially a t the break of the isotherm, is very pronounced. 3 . The heats of adsorption of these vapors have been calculated from the slopes of the isosteres and they have been found to be lower than the values experimentally determined. 4. The potential distribution and the density distribution of the vapors in the adsorption space have been calculated according to the method of Polanyi. I.
T h e Physkcal Chemistry Laboratory, T h e State Unzverszty of Iowa.
