EDWINF. MEYERAND ROBERT E. WAGNER
3162
While the above sequence qualitatively describes the system, it should be emphasized that further study is required before the reaction sequence is accepted in detail. For example, the isotopic distributions of deuterium in digermane and trigermane products from the irradiation of the GeH4-GeD4 mixture strongly suggest formation via reactions 13 and 15. However, the abstraction reaction which produces Ge2H6 could involve GeH3 as well as the H atoms as suggested in reaction 14. Examination of the mass spectrum of GeH4-GeDl after irradiation should, in principle, permit a decision as to whether GeH3 radicals were involved in abstraction reactions. Because of the low conversions used
in these experiments and the large number of isotopes of germanium, we could not find evidence for GeH3D and GeD3H formation. Future experiments, utilizing a high-resolution mass spectrometer, may permit a conclusion regarding the participation of GeH4 in abstraction reactions. Acknowledgments. The authors wish to thank Mr. Eric Daby for assistance with some experiments and Mr. Wrbican for determining the mass spectra. The financial support of the U. S. Atomic Energy Commission (Contract No. AT(30-1-3007)) and the U. S. Air Force Office of Scientific Research is gratefully acknowledged.
Cohesive Energies in Polar Organic Liquids
by Edwin F. Meyer' and Robert E. Wagner U.S. A r m y Coating & Chemical Laboratory, Aberdeen Proving Ground, M a r y h n d
(Received M a y 8, 1966)
A method which allows quantitative estimation of the dipole-dipole (orientation), dipoleinduced dipole (induction), and dispersion energies in polar organic liquids is presented and illustrated with the methyl n-alkyl ketones. Use is made of the temperature variation of density and vapor pressure for homologous series of organic compounds. Data were obtained for the odd-numbered 2-ketones from Csto C13. As an example of the results, it is estimated that the cohesion in liquid 2-butanone a t 40" is comprised of 8% orientation, 14% induction, and 78% dispersion energies. The relatively high value for induction is surprising in view of the general opinion in the literature, but reconsideration of the usual expressions for these energies as applied to the liquids in question makes it not unreasonable. The contribution of induction to cohesion is larger than is generally appreciated.
A knowledge of the relative amounts of the different types of cohesive energies in liquids will lead to a better understanding of liquid Properties, Particularly sohbiljties, as well as provide necessary information for the development of a satisfactory theory of the liquid state. It can be shown that such knowledge is obtainable from the temperature dependence of vapor pressures and densities for homologous series of organic compounds.
Theoretical Section We assume herein that the cohesive energy (the energy required to separate the component molecules to infinity without changing the average internal energy of
Y
The Journal of Physical Chemistrg
(1) Correspondence should be directed to Capt. E. F. Meyer, NAS-NRC Postdoctoral Research Associate, at the U. S. Naval Research Laboratory, Washington, D. C.
COHESIVE ENERGIES IN POLAR ORGANICLIQUIDS
the individual molecules), E,, may be approximated by the energy of vaporization. I n cases where appreciable forces of attraction remain in the vapor phase, the additional energy needed to separate the molecules to infinity may be calculated from appropriate compressibility data. Consider first a liquid composed of nonpolar molecules such as n-hexane. I t s cohesive energy results from the attraction of the individual atoms of one molecule for those of another, the so-called dispersion attraction. By increasing the length of the hydrocarbon chain, more atoms per molecule attract each other, with the result that the molecules are drawn closer together and the cohesive energy is increased. The increment in E , per CH2group inserted (the “CH2 increment”) is not constant for the paraffin series, since the energy of interaction depends heavily on the distances between interacting centers, and these decrease upon insertion of each CH2 group at constant temperature. The CH2 increment might be expected to be constant under the condition of constant time-average distances between interacting centers. This condition can be realized in two ways: by considering all molecules at absolute zero or by choosing a fixed molar volume per CH2 group and adjusting the temperature of each homolog until this molar volume is achieved. That the former produces a constant CH2 increment is knowni2 that the latter does the same is illustrated by the lower curve in Figure 1. The fixed molar volume per CH2 has been arbitrarily set at 19.08 cc/mole, characteristic of nhexane a t 0”. The value is calculated from the molar volume, 127.3 cc,”ole, and the relative van der Waals volumes for CHs and CH2 (13.67 and 10.23, respectively) given by Bondi3 The temperatures at which each member of the series displays 19.08 cc/mole of CH2 groups is calculated from thermal expansion data, and E , is calculated for each member a t its appropriate temperature. The contribution of each CH2 group to E , is given by the slope of the E, vs. n curve, where n is the number of CH2groups in the molecule. It should be pointed out that Hijmans4has developed a phenomenological approach to the principle of corresponding states for chain molecules, wherein thermodynamic properties may be expressed as linear functions of the number of segments in the chain. The results obtained with the simplified approach used here agree with those obtained with his more elaborate scheme. For example, his molecular units for volume as a function of chain length are compared in Table I to analogous figures obtained as described above. In addition, of course, the temperaturesat which the alkanes display our values for the volumes correspond to the same reduced temperature in Hijmans’ scheme. Thus a
3163
m
Figure 1. Paraffin densities from “International Critical Tables,” vapor pressures from API Project 44.
fixed volume per CH2 group puts the alkanes in “corresponding states,” and addition of a CH2 group under this condition increases E , by a fixed amount.
Table I: Ratio of Molar Volume to That of n-Hexane for n-Alkanes in Corresponding States V(n)/V(6)-
r
7
n
Hijmans
This work
5 6
0.858 1.000 1.144 1.292 1.441 1.585 1.732
0.851 1.000 1.149 1.299 1.448 1.600 1.748
7 8 9 10 11
Consider now a liquid composed of polar molecules such as 2-pentanone. I n addition to the dispersion energy present in the paraffins, orientation and induction energies contribute to cohesion. Stipulating the same volume per CH2 group and assigning a consistent volume to the carbonyl group (11.70),3 how might we expect these energies to vary with insertion of successive CH2 groups to form higher 2-ketones? The contribution of dispersion to the CH2 increment. should be the same as in the paraffin series, even though the absolute value of the dispersion energy for a ketone (2) E. A. Moelwyn-Hughes, “Physical Chemistry,” The Macmillan
Co., New York, N. Y., 1964,p 702. (3) A. Bondi, J. phzls.chm., 68,441 (1964). (4) J. Hijmans, Physiea, 27, 433 (1961).
Volume 70, Number 10 October 1966
3164
will not be the same as in the corresponding alkane. That is, a plot of dispersion energy us. n for the ketone series should have the same slope as the plot of E, us. n for the alkanes. The Orientation energy depends on the proximity of two permanent dipoles. As the length of the hydrocarbon chain is increased, the probability that two carbonyl groups (or whatever the polar groups happen to be) will come close enough to interact decreases, and we expect that, a point will be reached beyond which interaction of permanent dipoles adds an insignificant amount to the cohesive energy. Insertion of successive CH2 groups should thus lead to a decrease in the contribution of orientation energy to total cohesion. The induction energy depends on the proximity of a permanent dipole and matter into which a dipole can be induced. The magnitude of the energy depends on the moment of the permanent dipole and the polarizability of the adjacent matter. Insertion of successive CH2 groups at constant molar volume per CH2 group should change the contribution of induction only insofar as it changes the average polarizability of the matter adjacent to the permanent dipole. Since the polarizability5 of the carbonyl group is very close to that of the methylene group (12.71 and 13.02 X cc/molecule, respectively),6the average polarizability of the matter adjacent to the dipole will be relatively insensitive to the ratio of carbonyl and methylene groups in the bulk of the liquid (This holds true in general; e.g., CHBand CN have very similar polarizabilities. The nitriles are presently under study in this laboratory.) The contribution of induction to total cohesion thus remains constant with extension of the hydrocarbon side chain. This approach allows separation of the component parts of the cohesive energy, since we have selected a variable (the number of CH2 groups) which causes each to change characteristically : dispersion increases, induction remains constant, and orientation decreases. I n practice, plots are made of E , us. m, the number of CH bonds in the molecule, for both the paraffin and polar series on the same graph. We choose to use the number of CH bonds rather than the number of CH2 groups simply for convenience in counting; the plots are not affected. The value of m for a member of the polar series is not the actual number of CH bonds, but the number of CH bonds a molecule would have in order to produce the same dispersion energy displayed by the polar molecule. It is necessary to establish a dispersion equivalence between the polar group and the CH bond, Le., the contribution of the polar group to dispersion relative to the CH bond. There have been several formulas put forth for the The Journal of Physical Chemistry
EDWINF. MEYERAND ROBERTE. WAGNER
calculation of dispersion energies;' we have chosen to use one due to Slater and Kirkwood Edisp
=
K
Lylff2
where K is a constant (assuming fixed separation), a is the polarizability, and N is the number of electrons in the outer shell. Pitzer has used this equation in a study of van der Waals energies in the paraffins& and obtained very good results for the isomerization energies of the butanes and pentanes using N equal to 4 and 1 for carbon and hydrogen. For larger atoms,*b he found that better results could be had using the mean of the total number of electrons and the number in the outer shell. I n the case of C, H, and 0, the values of N obtained either way do not lead to significantly different results. Using group polarizabilities, the ratio of dispersion energy for two CO groups to that for two CH2 groups is 1.26; the same ratio for CO and CHs is 0.850. We conclude that the dispersion energy for the CO group is 2.5 times that for the CH bond. Thus the value of m for a ketone is the number of CH bonds plus 2.5; for acetone, m = 8.5. There is some question regarding the accuracy of the available vapor pressure data for the higher 2-ket0nes.~ Reference to the original work is unavailable,'O so we obtained the necessary compounds and measured their vapor pressures and thermal expansion in order to test the above ideas.
Experimental Section Practical grade 2-heptanone was purified to 99.9% through its semicarbazide. *l Practical grades of the other 2-ketones, C5, Cs, CI1, and CI3,were fractionally distilled to 99.9% (punty by vpc) and dried over Linde 4A Molecular Sieve prior to use. Mercury was washed thoroughly with dilute nitric acid, rinsed with distilled water, and distilled. Thermal expansion measurements employed a dilatometer designed and built in this laboratory. The mercury expelled by the expansion of the liquid was weighed, as in the usual dilatometric technique. Temperature was controlled to 0.1O and measured with mer(5) We assume that the polarizability tensor may be replaced by a scalar average value. (6) See ref 2, p 385. (7) H. Margenau, Rev. Mod. Phya., 11, 1 (1939). (8) (a) K. S. Pitzer and E. Catalano, J. Am. Chem. SOC.,7 8 , 4844 (1956); (b) K.S. Pitzer, ibid., 78,4565 (1956). (9) D.R. Stull, I d . Eng. Chem., 39, 517 (1947). (IO) D.R. Stull, private communication. (11) Work was performed by Dr. M. Kolobielski.
COHESIVEENE.RGIES IN POLAR ORGANICLIQUIDS
3165
~~~
Table 11: Fit of Density Data to Power Series, d , = a
+ bt + ct2
Temp range, Compound
2-Pentanone 2-Hept anone ZNonanone ZUndecanone 2-Tridecanone
- 5 to 27 t o 26 to 25 to 31 to
100 151 163 160 159
Rms dev
a
b X 10'
x
0.82639 0.83162 0.83644 0.84060 0.84324
- 9.4379 - 7.9788
- 5.5030
O C
-6.7121 -4.4170 -2.9023 - 1.8485
-7.5953 -7.3296 -7.1567
Table 111: Fit of' Vapor Pressure Data to Antoine Equation: Log p
=
107
A
dza
dAPI
0.8025 0.8113 0.8172 0.8221 0.8252
0.8015 0.8111 0,8172 0.8220 0.8256
2-pent anon e
2-Heptanone 2-Nonanone 2-Undecanone 2-Tridecanone ~Propanorie~ 2-Butanone"
O C
-5 to 36 to 62 to 62 to 62 to
100 151 164 158 158
0 to 56 43 to 88
104
1.9 1.2 1.6 0.9
1.6
- B/(C + t)"
A
B
C
Rms dev x 108
6.13916 5.95166 6.21003 6.19289 6.87357
1379.06 1408.13 1697.25 1804.95 2313.06
221.41 194.84 198.44 185.57 202.50
2.2 4 1 5.2 4.7 6.0
6.35556 7.06376
1338.16 1261.45
242.92 221.98
1.0
Temp range, Compound
x
...
0 Pressure, p , is in centimeters a t 0" and standard gravity. b J. Timmermans, "Physico-Chemical Constants of Pure Organic Compounds,', Elsevier Publishing Co., Inc., New York, N. Y., 1950. e R. R. Collerson, et al., J. Chem. SOC.,3697 (1965).
cury thermometers calibrated against an XBS certified thermometer. Vapor pressure measurements were made using the Tobey modification of the classical Ramsey-Young apparatus. ** Mercury and butyl phthalate manometers were connected to the apparatus in parallel, allowing direct measurement of the conversion factor between the two pressure units. Pressures below 10 cm were read on the butyl phthalate manometer. Temperatures were measured to 0.1" with Anschiitz thermometers calibrated against an NBS certified thermometer. Because of its very low solubility and inertness, helium was used to apply the external pressure to the vaporliquid equilibrium.
Results The density data were fitted to second-order power series in temperature by least squares. The results are presented in Table 11. Our results at 25' are compared to the densities in the API tables. The large discrepancy for 2-pentanone led us to repeat our measurements after more thorough exposure of the compound to molecular sieve, but our results were duplicated. Colei3 reports a value at 20" of 0.8072; ours is 0.8073. The vapor pressure data were fitted to Antoine equations by least squares. The results are presented in Table 111. The root-mean-square deviation quoted is
for the logarithm of the vapor pressure. The reproducibility of the data was about 1% in the pressure. E, was calculated for the methyl n-alkyl ketones containing 3, 4, 5, 7, 9, 11, and 13 carbon atoms for five different "reduced temperatures," corresponding to nhexane at 0, 10, 20, 30, 40". It mas assumed that the vapor behaved ideally, allowing use of the equation =
2.303B T R T [ m - 11
where B and C are constants of the Antoirie equation log p
=
A - B/(C
+ t)
An example of the resulting plots is given in Figure 1. The plot for the paraffin seriesgives a straight line; that for the ketone series gives a curve which approaches linearity at higher values of m. The limiting slope is the same as that for the paraffin series, since the influence of 'the dipole-dipole interaction is eventually not felt. The linear portion of the latter curve is displaced upward by the induction energy, which persists at high na. Thus, drawing the asymptote of the ketone curve enables the estimation of the magnitudes of the three types of cohesive energy by inspection: at (12) F. Daniels, et al., "Experimental Physical Chemistry," McGrawHill Book Co., Inc., New York, N . Y., 1962, p 40. (13) R. H. Cole, J . Chem. Phys., 9 , 251 (1941).
Volume 70, Number 10
OLtober 1966
EDWIN F. MEYERAND ROBERT E. WAGNER
3166
Table IV: Contributions to Total Cohesion (in kcal/mole) Temp, Compound
OC
14 51 40 80 51 93 78 122 96 143 111 162 123 176
2-Propanone 2-Butanone %Pentanone 2-Heptarione BNonanone BUndecanone 2-Tridecanone
Eo
7.08 6.81 7.62 7.19 8.29 7.84 9.99 9.24 11.48 10.71 13.09 12.09 14.89 14.02
Edisp
Eind
Eorien
% diw
% ’ ind
% orien
5.04 4.68 5.91 5.49 6.79 6.29 8.53 7.90 10.27 9.51 12.01 11.13 13.76 12.74
1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1
0.94 1.03 0.61 0.60 0.40 0.45 0.36 0.24 0.11 0.10
71.2 68.8 77.6 76.4 81.9 80.2 85.5 85.5 89.5 88.8 91.6 91.0 92.6 92.0
15.5 16.2 14.4 15.3 13.3 14.0 11.0 11.9 9.6 10.3 8.4 9.0 7.4 8.0
13.3 15.0 8.0 8.3 4.8 5.8 3.5 2.6 0.9 0.9
the value of m corresponding to the ketone of interest, the dispersion energy is given by the paraffin curve; the induction energy is the vertical distance between the paraffin curve and the asymptote; and the orientation energy is the distance from the asymptote to the ketone curve. I t should be emphasized that each point of the graph corresponds to a temperature characteristic of the compound it represents; these are not isotherms in any sense. Some arbitrariness cannot be avoided in drawing the asymptote to the ketone curve, since the probable error is larger for the higher boiling compounds. It was decided, in the light of the rapid disappearance of curvature, to assume that there is no orientation contribution in the Cn and Cla ketones and to take as the induction energy the average of the difference between E, and E d i s p for these two compounds. This procedure gave 1.1 kcal/mole at all temperatures. The equations for E, for the paraffins at the lowest and highest temperatures are, respectively
E,
=
E,
=
+ 0.4357m 1.26 + 0.4028m 1.34
f
0.10
f
0.06
making the equations for the asymptotes Ediap+ind
=
Edisp+ind
=
+ 0.4357m 2.36 + 0.4028m‘
... ...
... ...
...
... ...
...
Discussion Estimates in the literature of the contributions of dispersion, induction, and orientation to cohesion in fluids are generally limited to very simple molecules in the gas phase.14 However, the conclusions drawn are frequently applied to the liquid state. For example, Hildebrand and Scott16 say, “. . .the induction forces are always small compared with the other two. . . ,” and Hirschfelder, Curtiss, and Birdla comment, “It is apparent that the induction effect is never important in the interaction of neutral molecules.” These statements are made subsequent to an examination of the theoretical expressions for each type of energy
where a is the polarizability, p is the dipole moment, I is the ionization potential, and r is the distance between interacting centers. Tables of calculated energieslb#la for some simple molecules with dipole moments show
2.44
Since the temperature dependence is slight for each type of cohesive energy, only the results for the lowest and highest temperatures are presented, with the temperature for each compound, in Table IV. The rootmean-square deviation in E, for the ketones whose properties we measured is indicated in Figure 1. The Journal of Physical Chemktry
(14) P. A. Small, J. Appl. Chem., 3, 71 (1953), however, has calculated a dipole contribution parameter for liquid acetone from heats of mixing with nonpolar liquids. He estimates the dipole contributes but 4% to cohesion, unrealistically low considering the 66O difference in boiling mint between acetone and isobutylene. (15) J. H. Hildebrand and R. L. Scott, “The Solubility of Nonelectrolytes,” Dover Publications, Inc., New York, N. Y., 1964, p 167. (16) J. 0.Hirschfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, Inc., New York, N. Y., 1954, p 988.
COHESIVE EKERGIES IN POLAR ORGANIC LIQUIDS
that induction is always less than the other two types of energy, but in the case of a molecule containing both polar and nonpolar segments, the significance of these expressions must be reexamined. Consider the acetone molecule in the liquid state. Its dipole contributes to cohesion in the three ways under discussion : dispersion, induction, and orientation. In the first two cases, attraction occurs independently of the nature of the segment of a neighboring molecule which finds itself adjacent to the dipole, but in the case of orientation, there is no interaction unless two dipoles are present. There are two equivalent ways of looking at this situation. First, consider the interaction of segments a fixed distance apart. If a represents a methyl group and b represents a carbonyl group, we can denote the specific interactions by aa, ab, and bb. All three types contribute to dispersion and induction, but only the last to orientation. Thus, when a molecule consists of a nonpolar segment as well as a polar one, the expression for orientation given above must contain a weighting factor to account for the reduced probability of finding two dipoles at a given distance. Second, we may consider average distances between two a’s, a an0 b, and two b’s in order to use the above equations to calculate the interactions between individual segments of different molecules. The average distance between b’s will be greatest, even in acetone, and will increase with the insertion of CH2 groups to form higher %ketones, while the other two distances remain constant. From this point of view, it is readily seen that orientation must fall off quite rapidly as the size of the molecule increases, because it depends on the inverse sixth power of the distance between b’s. The expressions for these energies are not expected to give quantitative values, but give a qualitative idea of their relative magnitudes. Typical values are obtained cc/molecule, and I if we use p = 2.9 D., a = 6 X = 10 ev (approximate values for acetone) for Er6 X 1060 erg cm6: dispersion, 450; induction, 100; and orientation, 1140. If r is but half again as large - for orientation as for the other two, the orientation contribution is reduced by an order of magnitude, and the resulting relative values reflect qualitatively those obtained by our method. It is interesting to note that the measured and calculated ratios of dispersion to induction are the same.
Critiaue of AssumDtions The value Sor induction energy depends on the estimated dispersion equivalence between the polar group
3167
method. The dependence is not strong, however; increasing the equivalence from 2.5 to 3.0 reduces the induction contribution by 0.2 kcal/mole. The value for orientation is clearly independent of the equivalence concept. It is, however, based on the assumption of constant dipole moment for the series. This is quite sound, the only possible exception being acetone, with six a hydrogens vs. five for the other members of the series. The literature values” are 2.86 D. for acetone and about 2.6 D. for the remaining ketones. The effect of acetone’s slightly higher moment is to raise the estimate of its orientation energy a t the expense of its induction energy; but the difference is insignificant in the present approach. We have assumed that any specific interaction between dipoles is lessened by the introduction of a CH2 group; i.e., the entropy factor introduced is sufficient to oppose the orientation energy to a noticeable extent. Evidence that this is the case lies in the entropy of vaporization of the ketones relative to that of the paraffins. Trouton’s rule constants available from our data can be compared with those for the paraffins as shown in Table V. The higher values for the ketones indicate a small degree of association. However, if these values are plotted us. nz, the difference between the ketones and paraffins (a measure of the association of the dipoles) is seen to decrease rapidly, and extrapolation indicates that it becomes negligible a t about 2undecanone, in agreement with the findings of our method. ~~
~
Table V Paraffins
AS
Ketones
AS
CS C8
20.6 21.1 21.7 22.0 22.3 2 3 . 8 (?) 23.3
CI
22.5 22.4 22.6 22.8
C? C8
c9 ClO C,?
c 4
c5 C?
The most arbitrary feature of the method is the location of the asymptote to the ketone curve. Justification for the procedure used lies in the rapid decay of orientation energy with distance between dipoles. The apparent increase in orientation energy with temperature in Table IV is surely an artifacd. I n order to study the effect of temperature on these energies, more precise values for E , are necessary.
Volume 70,Number 10 October 1966’
J. B. PERI
3168
Conclusion
-4method for quantitative estimation of the contributions of dispersion, induction, and orientation energies to cohesion in polar organic liquids has been proposed and illustrated with the methyl n-alkyl ketones. Dispersion always predominates, with induction in a minor, but constant, role. Orientation rapidly loses significance as the hydrocarbon side chain is increased.
Induction energy is more important than is generally appreciated, contributing 5-10% to the total cohesion of the higher, “mostly nonpolar” 2-ketones.
Acknowledgment. We acknowledge many stimulating discussions with Dr. Myer Rosenfeld and thank the Director of the U. S. Army Coating & Chemical Laboratory for permission to publish this work.
Infrared Study of Adsorption of Carbon Dioxide, Hydrogen Chloride, and Other Molecules on “Acid” Sites on Dry Silica-Alumina and y-rilumina’
by J. B. Peri Research and Development Department, American Oil Company, Whiting, Indiana
(Received M a y 3, 1866)
The adsorption of various molecules on specially prepared transparent plates of dry, higharea silica-alumina and y-alumina was studied by infrared and gravimetric techniques. Carbon dioxide was selectively and reversibly adsorbed on a few so-called “acid” sites on both silica-alumina and y-alumina, producing an infrared band near 2375 em-‘ for the former and near 2370 cm-l for the latter. Use of adsorbed CO2 as an indicator allowed titration of these sites, tentatively named “CY sites,” with other adsorbates which displaced carbon dioxide. The CY sites on silica-alumina selectiveIy adsorbed carbon dioxide, acetylene, butene, benzene, and hydrogen chloride. They also strongly adsorbed ammonia and water, but these adsorbates were also held by many other sites. Their reaction with hydrogen chloride produced hydroxyl groups. Their surface concentration fell in the range 3-9 X 1012/cm2. Similar sites on y-alumina predried at 800’ had a surface concentration of about 5 X 1012/cm2. The CY sites are apparently formed by condensation of AI-OH groups during dehydration of the surface. They contain a reactive oxide ion (or ions) in close proximity to an exposed aluminum ion. Their role in catalysis is not yet clear.
Introduction Although the important “acidic oxide” catalysts have been studied intensively for many years, little is known about the surface sites responsible for their activity.2sa Active sites are usually thought to be acidic, but the exact nature of the acidity remains controversial. 3,4 Numerous attempts have been made to measure and characterize the acidity by adsorption of NH,, butylThe Journal of Physical Chemistry
amine, or other bases, often using organic indicators. While such methods show wide variations among sites on a given catalyst and among distributions of sites on (1) Presented in part at 145th National Meeting of the American Chemical Society, New York, N. Y., Sept 1963. (2) L. B. Ryland, M. W. Tamele, and J. N. Wilson, “Catalysis,” Vol. 7, P. H. Emmett, Ed., Reinhold Publishing Corp., New York, N. Y.. 1960.
