THE ADSORPTION OF THE HEAVIER RARE GASES BY MERCURY' HANS M. CASSEL AND KURT NEUGEBAUER Department of Chemistry, Stanford University, California, and Techniwhe Hochschule, Berlin, Germany
Received May 9, 10.96
Since the nature of the van der Waals forces was revealed as a consequence of the atomic zero point vibrations of the electrons, the adsorption as caused by such attraction fields of solid or liquid surfaces also became accessible to advanced theoretical treatment. The theory due to London (12) at first was applied to the simplest example, that of spherical symmetrical atoms and molecules which may be regarded aa spheres. Introducing certain further simplifying assumptions, London calculated the heats of adsorption by charcoal. Owing to a numerical erroz, the values so obtained seemed at iimt to be in excellent agreement with the experimental results. The correctly calculated values, however, are o d y one-tenth, or, if repelling forces are disregarded, nearly one-fifth of the observed amounts. Thus, although the right order of magnitude is attained, there exists a discrepancy, the reason for which must be sought in the nature of the experimental conditions rather than in the theory. As London has already pointed out, an increase of the attraction beyond that due to entirely plane surfaces is to be expected, owing to the porous structure of the crystalline adsorbent. Experimentally, it would seem possible to avoid these irregularities by using single crystals ria the adsorbent. This method, however, has the disadvantage of so limiting the surface that it would be difficult to obtain measurable adsorption. Measurement of the surface tension of liquid adsorbents may be a better procedure, for on this basis surface densities of the adsorbed gas atoms may be derived by the Gibbs thermodynamic equation. Though at first sight this method appears to be rather indirect, its advantage over the mere observation of adsorbed quantities is that it does not require a special measurement of the adsorbing surface area. The heats of adsorption are then derived from the determination of different isotherms. 1 The measurements were carried out in collaboration with K. Neugebauer in the Technische Hochschule, Berlin; see also the dissertation of H. Binne, Technische Hochschule, Berlin, 1932.
523
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HANS M. CASSEL AND KURT NECGEBAUER
Liquid mercury was used as the adsorbent in our experiments. This material proved to be well suited for checking the adsorption theory. Although in the earlier stage of our knowledge of the metallic state the application of London’s theory to metals was objectionable, now, on the basis of Bloch’s (2) ideas,2 it is justified by the new dispersion theory of metals advocated by Kronig (9). The experimental equipment was that previously used for the study of the adsorption of some polar and non-polar compounds by mercury (5) and was very similar to that of the capillary electrometer. In order to measure the surface tension, u, the height of a mercury column necessary to press a mercury droplet through a small hole was determined. This opening, about 0.1 mm. in diameter, consisted of a stainless steel nozzle such as is employed for the purpose of manufacturing artificial silk. It was sealed to the bottom of a vertical glass tube communicating with the container of the mercury, which was purified by vacuum distillation and lifted pneumatically to the desired level. The observations made by means of a cathetometer were in error by less than 0.05 mm., that is to say, they corresponded to the formula by less than 0.1 dyne per centimeter. In order to eliminate the uncertainty in the effective value of the curvatures, l/rl + l/r2, of the hole, the value 480.00 dynes per centimeter for the surface tension of mercury at room temperature (ZOOC.), as determined by Bircumshaw (l),was taken as a standard for calibration.3 Owing to the smallness of the radii, corrections for the influence of gravity could be neglected. The accuracy of f 0 . 0 5 dyne per centimeter thus obtained was, however, not sufficient to indicate any decrease of the surface tension by the action of argon at room temperature, even at a pressure of 100 mm. of mercury. To continue the investigation, therefore, the heavier rare gases, krypton and xenon, were brought into contact with the metal. In these cases also the observable effects at room temperature were rather small, although well-defined values of the decrease in surface tension could be measured on cooling the system. Particular care was taken to keep the temperatures constant. Here of course the freezing point of mercury determined the lowest temperature. The experimental results are given in the first and second columns of table 1. The corresponding figure (figure 1) shows the decrease in the surface tension, uo - u = F, as plotted against the gas pressure, p . 2 We are indebted to Dr. Felix Bloch of Stanford University for his kind suggestions. a With the value recently obtained by Bradley (3) our results had to be increased by 4 per cent.
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ADSORPTION O F HEAVIER RARE GASES BY MERCURY
In the range of lower pressures, the isotherms are approximately straight lines converging towards the zero point. Under these conditions dF/dp = F/p, so that the Gibbs relation, dF/dp = I’RT/p, yields the simple “two-dimensional” osmotic equation of state: F = FRT, where r denotes the number of adsorbed moles per unit area. TABLE 1
Isotherms for adsorption of rare gases by mercury a. Krypton
T
=
T = 253°K.
235°K.
mm. Hg
dynes per cm.
10-18 om.2
93 198 263 320
0.35 0.85 1.10 1.30
1.1 2.5 3.4 4 .O
mm. H g
dgnes per om.
GO
0.20 0.50 0.75 1.15
160 221 339
10-18
cm.2
0.G 1. G 2.2 3.4
b. Xenon
T
=
I1
237°K.
mm. Hg
dynes per cm.
50 89 198 331
1.65 2.85 6.05 9.10
T = 253’K. dynes per Cm,
10-13 cm.2
1.20 2.60
3.5 7.5 12 .o 15.5
50 130
4.40 25.0
295
5.50
.............. 11.50
Vapor density., . . . . . . . . . . . . . . . Liquid density,,. . . . . . . . . . . . . .
T 69 93 146 227 278
=
. . . . . . . . . . . . . 52.50
I/
273°K.
0.80 1.10 1.75 2.75 3.35
2.0 3 .O 4.5
7.5 9 .o
~~~~
T 40 91 149 205 280 355
= 293’K.
0.35 0.70 1.20 1.60 2 .oo 2.80
1.o 2.0 3 .O 4 .O 5.5 7.0
At higher pressures, the 237°K. and the 253°K. isotherm of xenon incline distinctly toward the p-axis. This curving, familiar from the Langmuir type of adsorption isotherms, in the case of mobile adatoms4 indicates a 4 The word “adatom,” as introduced by F. A. Becker, is here used t o designate the adsorbed particles according to Langmuir (10).
THE JOURNAL OF PHYSICAL C H m I a T R Y , VOL. 40, NO. 4
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HANS M. CASSEL AND KURT NEUGEBAUER
predominance of the vinal term which arises from the repulsion of the adatoms over that due to the mutual attraction (6). Let us suppose that the simple van der Waals equation holds true for the gaseous state (constants a and b) as well as for the adsorbed state (constants a! and 8). The c
20 MMHG FIG.1. The decrease of the surface tension, F, is plotted against the gas pressure. The observations are represented by vertical lines, the length of which corresponds t o the possible error. The drawn straight lines are the initial tangents of the isotherms corresponding t o the ideal two-dimensional gas law F = rRT.
critical temperature of the adsorbed state may then be estimated by means of the equation a*b Tkads = - Tkvai a.8
ADSORPTION OF HEAVIER RARE GASES BY MERCURY
527
Since, according to Volmer (19), B is equal to twice the moo88 section of the adatoms, b/@is given by 8/3r if z denotes the radius of the atom. The amounts of a and a on the other hand, as determined by the virial coefficients of the attracting forces, may be calculated from the inverse seventhpower law as derived by London (12). Thus, the ratio a / a is found to be the same as a/@. Hence, in the case of xenon the critical temperatures should be equal, namely, 289.6”K. This deduction, however, fails to agree with the experiments. The surface densities (number of atoms per unit area) of the liquid state and the coexisting vapor of xenon in bulk, as calculated from the measurements of Patterson, Cripps, and Gray (14), may be compared with the surface densities of the adatoms corresponding to the Gibbs equation M given in the third column of table 1. The values, although exceeding the vapor densities of 253°K. and 237”K.,do not reach those of the liquid state. It must be concluded, therefore, that the critical temperature of the adsorbed state lies below the range here observed. This behavior obviously corresponds to a very general rule (17) : condensation phenomena in adsorbed layers occur only at temperatures far below the critical point of the masses in bulk. In the case here studied, this may be due to the fact that the assumption of a free two-dimensional mobility is not quite justified, owing to distinct elementary spaces of adsorption. It was necessary to assume a semicrystalline structure of the mercury, as was suggested for the interior of the liquid by Debye and Menke (8) and observed by Bresler (4) for the reflection of electron beams from the surface of liquid mercury. There is, furthermore, reason to believe that an increase in B beyond the value employed above could be brought about in the electric field of the metallic surface by the polarization, which reinforces the mutual repulsion of the adatoms by induced dipole moments. For the purpose of further tests, the heats of adsorption on A, on the basis of the experimental results, were calculated for the m e r e n t isotherms according to the formula (7),
which corresponds to the statement that the “dividing surface” coincides with the surface of the adsorbent. The values thus obtained are given in table 2. The simplest method of checking these results, and one requiring a minimum of hypothesis, could be established by the knowledge of the binding energy, U,of the diatomic compounds between mercury and the rare gases. The existence of such molecules caused by polarieation forces was suggested by Oldenberg (13) in order to account for his spectroscopical
528
HANS M. CASSEL AND KURT NEUGEBAUER
observations. The heat of adsorption then may be calculated with satisfactory approximation, taking into consideration the attraction exerted only by the next neighbors of the adatom. This quantity, of course, depends on the type of arrangement of the atoms of the adsorbent. For hexagonal, spherical, close packing, corresponding to the work of Stranski and Kaischew (18), the inverse seventh-power law of attraction yields A = 4.35 U , as an average value of different possible surfaces (see table 3, A d ) . However, as the interpretation of the spectroscopic data is rather problematical, especially in the case of xenon, the complete requirement of the TABLE 2 Heats of adsorption
I
GhS
1
TEMPERATURS
Krypton Xenon
H E A T OF ADSORPTIOX
“K. 239
2700
245 263 283
3450 3350 3400
cal.
TABLE 3 Certain phusical constank I the rare gases and mercurq .~ __ ELEMENT
Keon. , . . , . . . . Argon. , . . . . . . Krypton.. , , , , Xenon. , . . , . . , Mercury.. . . , .
1
Ra
1
Rb
RC
a
I
____
cm.-a
cm.-8
cm.-8
X 10-2
kg-cat.
1.55 1.85 1.95 2.10 1.60
1.20 1.47 1.57 1.72
1 60 0 42 1 95 1 70 1 98 2 35 2 20 3 85 11 2
514 375 332 285 240
cat.
850 2300 2750 3750
1 cal. 1200 3250 3900 5200
cat.
1
cal.
cat.
cat.
800’ (500) 2100 2700 1500 2700 3700 3000 2300 3500 3700 3100
London theory has to be applied, represer ing the heat of adsorption by the equation:
A = -RN -CYCY’ - I.1’ 4 0 3 I + I’ where I and I’ denote the ionization potentials, a and a’ the atomic polarizabilities, N the number of mercury atoms per cubic centimeter, and D the distance of the adsorbate and the adsorbent, as given by the sum of the radii of the noble gas and the mercury atoms. Since this quantity enters with the third power, the results, of course, are greatly dependent upon the value chosen. The radius of the mercury atom was calculated
ADSORPTION O F HEAVIER RARE GASES BY MERCURY
529
from the density of the crystal, assuming spherical close packing. Consequently the radii of the noble gas atoms were determined on the same basis, according to the work of Simon (16) and Ruhemann (Ea). To obtain an idea of the possible limits of variation, the amounts derived from the critical volume (Rb) and from the liquid densities (R,) are also given in table 3, as well as the “spectroscopic” heats of adsorption ( A d ) , the heats of evaporation ( L ) (15), and the ionization potentials (I). The heats of adsorption found experimentally had to be extrapolated to the absolute zero point. This was done upon the supposition that the specific hcat of the adatoms equals that of the adsorbent (Ao). While the agreement between theory and experiment was satisfactory for charcoal only as regards the order of magnitude, the observed values for mercury tend to coincide with the lower theoretical limit, which might have been expected since, as a first approximation, the forces of repulsion were disregarded. SUMMARY
The surface tension of mercury in contact with krypton and xenon was measured at several temperatures and pressures. With the accuracy available (.t0.05 dyne per centimeter) the influence of argon could not be ascertained. The adsorbed quantities were calculated by means of the Gibbs equation, and the heats of adsorption derived from these isotherms were compared with the theoretical values according to the dispersion theory of the van der Waals forces.
We wish to express our thanks to Dr. Pollitzer, chief chemist of Linde’s Eismaschinen, Miinchen, Germany, through whose kindness we obtained samples of the noble gases, and to Professor J. W. McBain of Stanford University for his kind interest. REFERENCES (1) BIRCUMSHAW, L. L.: Phil. Mag. 12,596 (1931). F.: 2. Physik 62, 555 (1928). (2) BLOCH, R. S.: J. Phys. Chem. 38,231 (1934). (3) BRADLEY, (4) BRESLER,S. E. : Unpublished work, information concerning which was contributed by Dr. J. W. McBain of Stanford University. (5) CASSEL,H., AND SALDITT, F.: 2.physik. Chem. 166A, 321 (1931). H., AND FORMSTECHER, M.: Kolloid-Z. 61,18 (1932). (6) CASSEL, (7) CASSEL,H . : Physik. Z. 28,152 (1927). (8) DEBYE;P., AND MENKE,H.: Physik. Z.S1,797 (1930). (9) KRONIG,R. DE L.: Proc. Roy. SOC.London 1S3A, 255 (1931). (10) LANGMUIR, I.: J. Chem. Physics 1 , 3 (1933). I.: Nobel Lecture, 1933. (11) LANGMUIR, F.: Z. physik. Chem. 11B, 222 (1930). (12) LONDON,
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HANS Y. CASSEL AND KURT NEUGEBAUER
(13) OLDENBERQ, 0.:8. Physik 6 6 , l (1929). (14) PATTERSON, H. S., CRIPPS,R. S., AND GRAY,R. H.: Proc. Roy. SOC. London MA,579 (1912). (15) RABINOWITSCH, E.: Abeggs Handbuch der anorganischen Chemie, IV, 3 (1928). (16) RUEEMANN, B., AND SIMON,F.: Z. physik. Chem. 16B,389 (1932). N.: Z. physik. Chem. 7B,471 (1930). (17) SEMENOFF, I. N., AND KAISCHEW, R.: Z. Krist. 78, 373 (1931). (18) STRANSKI, M.: Z. physik. Chem. 116,253 (1925). (19) VOLMER,
