NOTES
1521
versely dependent on the initial concentration of chloride ion in the melt, becoming negligibly small at a chloride ion concentration of 0.20 m. In all cases, analysis of the melt showed a significant increase in the concentration of chloride ion during the reaction. This observation indicates the presence of a reaction path which produces chloride ion in efficient competition with reaction 3 which consumes chloride ion. This increase in chloride ion concentration shall be referred to as additional chloride. The additional chloride can only come from chlorate. If chlorate is decomposing to chloride and oxygen C103- +C1-
+
3/202
(5)
then the ratio of chlorine gas to oxygen gas is not 1 : 1 as indicated by reaction 3. The amount of evolved oxygen was measured and found to vary depending upon the half-life of the reaction. The same dependence was found to hold true for additional chloride ion. Table I shows the relationship between oxygen evolution and additional chloride. As predicted by eq 5, 1.5 moles of oxygen are evolved for every mole of chloride formed, after correcting for the chloride consumed and oxygen produced by reaction 3. It can be argued that C1- catalyzes the decomposition of c103to C1- and 02. A similar behavior has been reported by Duke and Shute.2 They observed that the decomposition of Br03- to Br- and 0 2 is catalyzed by Br- at 350". Solutions of C103- and C1- in fused alkali nitrates a t 260" are stable for several days; therefore reaction 5 must involve a catalyst other than
the dissolved chlorine. The solution thus obtained was again indefinitely stable toward decomposition. Mechanistically the chlorine-catalyzed decomposition of chlorate can proceed by the sequence of reactions
c12
+ C1203 -+
C1203 Cl2
+
+ c1-
(6)
(7) Although Cl20s has not been prepared and isolated, it may exist as an intermediate. Attempts were made to isolate such an intermediate by sweeping the gaseous products out of the melt and allowing them to condense in a Dry Ice-acetone trap. No oxides of chlorine were found. Once the molecule C1203 is formed, it decomposes to C12and 02. In summary, the decomposition of c103- in the presence of C r 2 0 ~ ~can - proceed by two reaction paths. A trace of chloride present as an impurity is enough to start the reaction. At very low chloride ion concentrations, only the reactions shown by eq 6 and 7 which produce chloride ion are important; but as the chloride ion concentration increases, the equilibrium concentration of the postulated intermediate, CI2O3, is repressed while the rate of the competitive reaction 3 is enhanced. At high chloride ion concentration, only the reaction sequence given by eq 2 and 3 contributes significantly to the observed decomposition and can be expressed by the pseudo-first-order reaction, eq 4. (2) F. R. Duke and E. A. Shute,
3/202
J. Phys. Chem., 66, 2114
(1962).
c1-.
Anisotropy i n Physical Adsorption on Graphite
Table I: Relationship between Chloride Ion and Oxygen Produced at 260'"
by Edwin F. Meyerl and Victor R. Deitz
mmoles
Cor add1 Cl-, mmoles
02, mmoles
Cor 0 2 , mmolea
or/c1-
2.93 2.03 2.00 1.60
3.18 2.28 2.25 1.85
5.00 3.64 3.24 3.07
4.75 3.39 2.99 2.82
1.49 1.49 1.33 1.52
Add1
c1-,
Ratio
' Each run represents 0.25 mmole of K2Cr20, and 20 mmoles of Ba[NOa]z in 100 g of solvent.
A catalyst for the decomposition of chlorate was found to be Cl2. Chlorine is slightly soluble in fused alkali nitrates, imparting a pale green color to the solvent. In the presence of Cl2, ClOa- was found to undergo decomposition according to eq 5. The decomposition could be stopped by carefully sweeping out all
Chemistry Diviawn, Naval Research Labwatwy, W a s h i e n , D. C. 80990 (Received Awust 1.9, 1966)
This note examines the possibility that the strong anisotropy of graphite may be responsible for two distinct arrays of sites for physical adsorption. Dispersion attraction depends on the polarizabilities of the interacting species. Since that of graphite is high parallel to basal plane and virtually zero perpendicular to itJ2we expect that an approaching adatom will be subjected to considerably different electronic environments depending upon the direction of its approach to (1) NAB-NRC Postdoctoral Research Associate.
(2) E. R. Lippincott and J. M. Stutman, J. Phys. Chem., 6 8 , 2926 (1984).
Volume 71, Number 6 April 1967
NOTES
1522
the crystal. If it approaches the basal plane, the resulting attraction is limited by the severely attenuated electronic oscillation perpendicular to the plane; if it approaches a crystal face composed of edges of basal planes (an “edge lane"^), the maximum polarizability is presented and the interaction may lead to a higher adsorption energy.4 The factors to be considered in comparing physical adsorption on the basal with that on the edge plane are: (1) anisotropy of polarizability, (2) different density of carbon atoms, (3) different equilibrium distances of adatoms, and (4) unknown electronic states of carbon atoms in the edge plane. We have set up a computer program to perform detailed summations over both aspects of a graphite crystal, taking anisotropy into account in obtaining the expression for dispersion interaction with an adatom. Using repeated sums for a 6-12 pairwise potential with incremental distances to obtain the equilibrium separations, the first three of the above factors are considered. The possible unsaturation and/ or unusual bonding of the edge atoms have been neglected. Avgul and Kieselvsa have mentioned the anisotropy of graphite in adsorption, but give no explanation of pertinent calculations. They state only a qualitative result with which the present work does not agree. Our consideration of the anisotropy of polarizability in dispersion follows that of de Boer and Heller.5b Let the adatom be the origin of a cylindrical coordinate system (positive direction downward) perpendicular to the plane in question, located at x . The polarizability of the carbon atom is represented by two orthogonal vectors of equal length in the basal plane, the component perpendicular to the plane being zero. The dispersion interaction of the adatom with the carbon atom having coordinates r , 8, and x is basal plane
+ (3r2/R2)1 (A/Re)[2 + (3(z2 + r2 sin2 O)/R2)]
(AIR6)[2
edge plane
+
where R 2 = x 2 r2 and A = attractive constant per atom. R e have assumed that for the inert gases on graphite, A is proportional to the polarizability of the inert gas. Combining this with an inverse twelfth repulsion, it remains only to evaluate the attractive and repulsive constants per atom, A and B, and perform the summations. We use Crowell’s method6 to obtain the expression for the potential between an isotropic adatom and a semi-infinite set of basal planes from the pairwise potential. We assume (for the present) that the repulsive term is independent of anisotropic effects. The constants, evaluated from the experimental energy of The Journal of Physical Chemistry
adsorption for argon on the basal plane’ and the equilibrium distances from the surface for the inert gases are presented in Table I. Table I: Values for Attraction and Repulsive Constants B x 10-9, cal/mole
A x 10-6, cal/mole
zva Gas
A
.46
A12
Ne Ar
3.09 3.40 3.50 3.7
0.588 2.33 3.52 5.72
0.15 1.11 2.02 4.58
Kr Xe
a The sum of the radius of the atom (J. 0. Hirschfelder, C. F. Curtiss, and R. F. Bird, “Molecular Theory of Gases and Liquids,” John Wiley and Sons, Inc., New York, N. Y., 1954, p 1110) and half of the interplanar spacing in graphite.
The summations for two geometrically different locations of the adatom on each plane were set up as follows: on the basal plane, over the center of a hexagon and over a carbon atom in the plane; on the edge plane, in a gap wherein the adatom is equidistant from its three nearest carbon neighbors and over a carbon atom. The results are presented in Table 11. Table 11: Results for Potential Summed as Indicated Position
7 - N d Zoa
-AI---
695 3 . 0 980 2 . 2
2080 3 . 2 3050 2 . 3
d
-Xe-
---K*2an
d
20”
d
Zoo
Edge Plane
C atom Gap
b
2840 3 . 3 4110 2 . 4
3850 3 . 5 5450 2 . 6
2800 3 . 5 2890 3 . 5
3720 3 . 7 3790 3 . 7
Basal Plane Catom Hexagon a
700 3 . 1 765 3 . 0
2080 3 . 4 2160 3 . 4
For the edge plane, 20 is measured from the outermost set
of C atoms.
(3)There are at least two possible “edge planes” which may be considered: we have chosen the one formed by cleavage of the simple hexagonal crystal perpendicular to the basal plane and in a line which bisects opposite sides of a row of hexagons. The resulting “plane” is not strictly planar; a geometric plane on this face would have one-half of the edge atoms in the plane and one-fourth displaced slightly to each side. (4) V. R. Deitz, unpublished data. (5) (a) N. N. Avgul and A. V. Kiielev, Proc. Acad. Sci. U S S R ,Phys. Chem. Sect., 112, 63 (1957): (b) J. H. de Boer and G. Heller, Physica, 4, 1045 (1937). (6) A. D.Crowell, J . Chem. Phys., 22, 1397 (1954). (7) The value of about 2100 cal/mole at OOK was taken from the data of J. R. Sams, G. Constabaris, and G. D. Halsey, Jr., J . Phys. Chem., 64, 1689 (1960). I t is assumed that basal planes comprise the overwhelming majority of sites on the highly graphitized carbon used.
NOTES
1523
The results indicate that there is a considerable advantage from the energy point of view in adsorption above the gaps in the edge plane. The advantage increases slightly with increasing size for the inert gases. The equations indicate that, for a given interatomic spacing on the surface, the effect of anisotropy increases with the equilibrium distance of the adatom. The basal plane results may be compared with those of Crowell and Young for a detailed summation in the case of argon on graphite. They investigated the likelihood of a periodicity of energy on the basal plane by calculating an energy of adsorption for three different sites. Two of these sites are the same as ours, namely, the center of a hexagon and over a carbon atom; they calculated values of 1750 and 1710 cal/mole, respectively. (Their lower values result from the assumption of a larger repulsive constant than ours.) They concluded that there is no reason to expect localized adsorption of argon on graphite. We find that anisotropy definitely contributes to the disparity between these two sites, but not sufficiently to alter the above conclusion for argon. Based on the hexagon value, our work gives 3.7% compared to the earlier 2.3% periodicity. (For neon, however, we calculate 9.3%, neglecting the small quantum effects, and this may cause an observable localization.) It is of interest to compare the contribution of the first layer of atoms in the surface with the total interaction energy. The results for argon are presented in Table 111. The contribution of the first layer for edge adsorption comprises a much smaller fraction of the total interaction than in the case of basal plane adsorption. In the case of argon adsorbed over the gap in the edge plane, about half of the interaction arises from bulk atoms having no edge effects. This indicates that any unusual bonding in the edge atoms would have only a secondary effect on the total energy of interaction with an adatom.
Table 111: Contribution of First-Layer Atoms to Total Energy -Edge C atom
First layer Total
1410” 2080
plane--Gap
1680’
3050
-Basal C atom
1980 2080
planHexagon
1900 2160
a The layer’’ includes 811 boundary edge atoms, even though they do not lie in a single geometrical plane.
The larger attractive energy for the edge plane is in fact a ‘Onsequence Of anisotropy> since assuming the carbon atoms in graphite to be isotropic
result in a much lower energy of adsorption for the edge plane. The results for argon are typical
.
plpl..
-Edge
zo
+Catom
1098
hap
-Bass1 &atom
ZO
3 . 4 1815 2 . 5
2210
plan20
@hex
zo
3 . 4 2275 3 . 4
The results of these calculations show that anisotropy has a definite influence on the adsorptive properties of graphite. Although it is possible that unusual edge effects may cause a strong adsorption on the edge planes, we have shown that the existence of two types of sites for physical adsorption on graphite does not depend on the postulate of some particularly high-energy situation, but may result directly from the effect of anisotropy. The details of the present work will be published along with results for the adsorption of carbon dioxide on the basal and edge planes of graphite. (8) A. D. Crowell and D. M. Young, Trans. Faraday SOC.,49, 1080 (1952).
Computation of Standard Potential by a Polynomial Curve-Fitting Program
by B. Sen,l D. A. Johnson,zaand R. N. Royzb Coates Chemical La boratmies, Louiskna State University, Baton Rouge, Louisiana 70805 (Received August 16,1966)
The electromotive force of the cell Hz (1 atm)jHCl (m),organic (x),water (y>IAgCl-Ag is expressed by the equation
E
+ 2RT -1nm F
2RT
= E o - -lnyi F
...
(1)
The natural logarithm of the stoichiometric mean ionic activity coefficient for symmetrical valence type of electrolyte is given by the equation (I) To whom all correspondence should be addressed a t the Department of Chemistry, University College of London, Gower Street, W.C. I., London, England. (2) (a) Abstracted in part from a dissertation submitted by D. A. Johnson in partial fulfillment of the requirements for the ph.D. degree in Chemistry, Aug 1966; (b) abstracted in part from a dissertation submitted by R. N. Roy in partial fulfillment of the requirements for the Ph.D. degree in Chemistry, Aug 1966. (3) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing C o w , New York, N. Y., 1958,p 18. (4) T. H. Gronwall, V. K. LaMer, and K. Srtndved, z, physik, 29, 358 (1929).
Volume 71 Number 6 April 1967
