Interaction of a Single Water Molecule with Mercury
The Journal of Physical Chemlstry, Vol. 83, No. 13, 7979
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Theoretlcal Approach to the Interaction of a Single Water Molecule with Mercury J. R. Gonzllez Marofo, D. Posadas, and A. J. Arda Instltuto de Investlgaclones Flslcoqdmlcas Tee6rlcas y Apllcadas, Dlvlsl6n Electroqdmlca, Sucursal 4, Casllla de Correo 16, 1000 La Plate, Argentlna (Recelved February 6, 1078; Revised Manuscript Recelved February 28, 1070) Publlcatlon costs asslsted by Consejo Naclonal de Investlgaclones Clentlflcas y TBcnlcas, Argentlna
The interaction energy of a water molecule with a mercury surface is calculated on the basis of a relatively simple model. The interaction energy of an isolated molecule and the metal surface is evaluated in terms of the water-metal surface distance and of the degree of dipole orientation. The most probable equilibrium orientation of the water dipole corresponds to the Oo angle at an operational equilibrium distance of 1.85 X cm. The calculated total energy coincides with the most reliable experimental value.
Introduction The evaluation of the potential energy of a water molecule with a mercury surface as a function of the separation distance and orientation of the molecule is of importance to develop different models in order to explain the physicochemical behavior of the Hg-water vapor,1-6 Hg-liquid water, and Hg-aqueous electrolyte solution interfacesa7-l2These calculations are relevant to problems related to the dielectric behavior of the so1vent,13J4to the specific adsorption of ions,12J6J6 the adsorption of organic compounds>17and to the thermodynamic entropy excesses at the mercury-solution interface."J* The present paper deals with the evaluation of the potential energy between an isolated molecule and the metal surface in terms of the water-metal surface distance and of the degree of orientation of the water molecule. The potential energy was evaluated as the sum of three independent contributions. In the attractive energy term two contributions are considered, namely, the classical electrostatic interaction energy, corrected for quantum effects between the water molecule and the metal surface, and the dispersion energy. The latter is evaluated by conventional procedures used for nonpolar molecules, with the polar effect included in the electrostatic term. The third term corresponds to the repulsive energy contribution. Electrostatic Interaction Energy. The water molecule is considered as in the model of Rernal and F0w1er.l~The oxygen atom bears a charge of -0.98e where e denotes the electron charge, and each hydrogen atom bears a charge of +0.49e. The charge distribution is such that it reproduces the experimental dipole moment of the water molecule. In this model the center of the molecule differs from the center of the electrical charges. With this model the electrostatic interaction energy can be calculated by application of the electrical image method to each charge in the atom of the molecule. This allows for the interaction of each charge with its own image as well as with the image charge induced by the rest of the charges in the molecule. On admitting that the metal behaves as a perfect conductor, we can write the image energy for a system of three charges interacting with their images as20
where the surface charge density, charge qi is
induced by the
0022-3654/79/2083-1733$0 1.OO/O
V;.(s)is the electrostatic potential at the element of surface area ds due to the charge q j (3) and re,iand rs,idenote the distance of the i charge to the metal plane and the distance to the element of area, respectively. At short distances the correction according to Sachs and Dexterz2and Cuttler and Gibbonsz3is applied. By taking the correction term into account, we can express the image energy for a single charge as
where re is the distance to the metal plane, W ais the work function plus the energy of the first Fermi level, and U,& = - q2/(4r,).Taking into account the latter equation, we introduce the correction term in eq 1 rendering
where k and 1 are the ordinal numbers of the polynomial terms resulting after integration and 8k,l is the Kronecker delta function. Equation 4 allows one to calculate the image energy between a system of charges and any surface of the infinite metal plane. A screening effect correction6 is introduced in order to proceed with the electrostatic calculation at different distances in terms of the charge distribution of the water molecule interacting with the image charges on the metal. The influence of water molecule orientation with respect to the metal surface plane is also included. To take this effect into account one considers that, whenever an atom of the water molecule lies between the interacting charge and the surface, it behaves as a perfect screening sphere making V,(s) in the screened region on the surface equal to zero (Figure 1). The radii of the screening spheres are taken as those of the oxygen and hydrogen atoms. The image energy is then calculated after integration of eq 4 to the metal plane excluding the screened zones. (Tables including orientations between 0 and 180", at 10" intervals, for distances between 1 and 4 A, are given in the literaturez4.) Dispersion Energy. Various equations were used to calculate the dispersion energy term. They are the Kirkwood-Muller e q u a t i ~ nafter ~ ~ *integration ~~ to the whole surface (KM), the equation of Mareenau and Pollard 0 1979 American Chemical Society
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The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
Figure 1. Model of the water molecule used for the screening effect calculation. re is the distance from the center of charge (center of the water molecule) to the metal plane; rc, the distance from the center of the oxygen atom to the metal plane; ro, the radius of the oxygen atom (1.33 A); q = 0.49e;6 = 105".
(MP),25the Bardeen's equation (B),26and the LennardJones equation (LJ).2' The KM equation was applied to the force centers resulting from the following different molecular models: (i) the center of the water molecule as in the BF model; (ii) the water molecule conceived of as two spheres centered at the 0-H bonds, whose diameters are the 0-H bond distance; (iii) the water molecule considered as two spheres whose diameters are twice the 0-H bond distance; (iv) taking U&pas the sum of the atom interactions at the metal plane. The main purpose of using different locations for the force center of the molecule is to maintain the coherence between the U, expression and the repulsive energy, Urep,which is considered later on, taking the influence of the molecule orientation into account at the same time. For case i the water molecule polarizability is the corresponding average experimental value. Case ii corresponds to an extension of Mdler's criterium employed for calculating the lattice energy in paraffin crystals.20 The bond is represented by an ellipsoid (isotropic approximation) and the mean bond polarizability, &OH, is &OH = &H20/2. Analogously, for jioH the mean diamagnetic susceptibility of the OH bond is xoH= XH 012. In case iii the ellipsoid, which is approached by a spkere, comprises both the complete hydrogen and oxygen atoms and its center is located on the 0-H bond at 0.3 X cm from the oxygen atom center. The polarizability and susceptibility considered for case iv are those of the free atoms, which are estimated by the variational method,16applying Slater's electronic wave functions.2s For the 0" orientation the different U&pvalues are quite alike and those resulting from case iv are the lowest. The largest energy difference,which is about 3 kcal/mol, results for r = 1.7 x cm. Other orientations exhibit a larger dependence of Udispon the chosen position for the force cm the largest differences center. Thus, a t r = 1.7 X are found for the 90" orientation. The MP equation is applied using p , and a r, value implying two electrons per mercury atom25p29 and the force center is located at the oxygen atom. The B equation is used with the same assumptions as with the MP equation; the force center is located again at the oxygen atom and (r:) = (5.1 f 0.7) X cm2. Finally, the LJ expression is employed considering the center of force at the oxygen atom.
J. R. Gonzglez Maroto, D. Posadas, and A. J. A d a
The lowest values are those derived from the LJ equation, which can be considered as suitable to evaluate the water-metal interaction.26 Repulsion Energy Term. The repulsion energy term, Urep,is obtained from Pollard's equation.30 It is admitted that the four electrons of the 0-H bonds behave as highly repulsive ones, involving a relatively large radius for the maximum electronic charge probability and consequently a relatively high 0-H polarizability. The four electrons of the remaining hybrid orbitals also contribute to repulsion and the latter effect increases as they are located closer to the metal surface. Their interaction decreases as the radius for the maximum electronic charge probability diminishes. The orbitals are then assumed to involve a certain s orbital character and the overall charge distribution in the molecule corresponds to a bonding orbital formed by a hybrid sp orbital, overlapping two s functions. The repulsion of the eight valence electrons of the water molecule can be represented by the four electrons of the two 0-H bonds involving a suitable position for the force center and taking the radius of the maximum electronic charge probability to embrace the total effect. For this purpose, the water molecule is decomposed into two spheroids, one for each 0-H bond, and a, the distance of maximum electronic charge density, is increased to take into account those electrons which do not participate in the bond. This is made by increasing the value of the bond polarization, for example, by attributing the total polarizability of the molecule or any other property related to ( r 2 ) to the 0-H bonds. The net effect is to substitute the former distribution by equivalent two 1s orbitals involving two electrons each. The force centers are taken on each bond as in cases ii, iii, and iv for the calculation of Udisp with the KM equation. The electron polarizability, ae,for a 1s atom, according to the variational method, is
a. is the radius of the first Bohr orbit. Thus, the distance
corresponding to the maximum electronic charge density is 114
(7)
The polarizability aHzois exclusively attributed to the four electrons participating in the two OH bonds. Then, the polarizability of each electron ae is a, = aoH/2 = B H ~ o / ~ . Therefore, taking aHzO= 1.444 X cm3, eq 6 and 7 yield a = 4.67 X cm, which is a reasonable value. The value of a can also be deduced either from x,, the magnetic susceptibility per electron
a=
(8)
or from geometric considerations. It should be remarked here that Pollard's equation implies Wigner's modeP1 which is acceptable for monovalent metals, but its extension to a liquid metal such as mercury should be considered a rather crude approxicm is obtained from mation. Otherwise, r, = 1.43 X the Hg(I1) atomic volume while r, = 1.80 X cm derives from the Hg(1) atomic volume. The number of free electrons for this metal is fractional between 1 and 2.32 According to Margenau and Pollard25and Kemba1129the former value of r, is chosen in the calculation because it corresponds to the largest electronic density in the metal, a fact which makes the approximations involved in Pol-
The Journal of Physlcal Chemlstry, Vol. 83,No. 13, 1979
Interaction of a Single Water Molecule with Mercury
1735
TABLE I: Total Interaction Energy (in kcal/mol) at Different Distances and Dipole Orientations re x
0
1.0
58.8 -9.72 -15.86 -11.39 -8.48 -6.35
1.5 2.0 2.5 3.0 3.5 a
deg
8,
lo8/
cm
20
40
60
80
100
140
160
69.9
84.6 -4.15 -14.86 -11.51 -8.36 -6.34
108 2.43 -12.85 -10.52 -7.84 -6.28
105 3.64 -13.97 -11.44 -8.53 -6.52
23.5 3.51 -15.06 -12.33 -8.89 - 6.68
53.2 -4.44 -14.52 -10.54 -7.55 - 5.49
108 -0.87 -12.73 -9.67 - 6.69 -4.83
- 7.47 -14.86 -11.15 -8.05 - 6.07
180 122
0.81 -11.85 -9.11 -6.34 -4.57
The center of forces corresponds to case iii.
TABLE 11: Total Interaction Energy (in kcal/mol) at Different Distances and Dipole Orientations re x l o s / cm 1.0
1.5 2.0 2.5 3.0 3.5 a
8,
0 73.50 -11.92 -15.04 -11.09 -8.06 -6.11
20 95.42 -8.15 -13.44 -10.44 - 7.64 -5.82
40 171.13 -0.55 -13.94 -10.91 -8.71 - 6.09
60 310.64 19.05 -10.31 -9.93 -7.63 - 5.90
deg 80
100
140
160
180
499.47 69.47 - 9.68 - 10.93 -8.35 - 6.45
590.24 45.85 - 9.74 - 11.53 - 8.94 -6.76
495.71 35.99 -9.66 - 10.06 -7.65 -5.61
406.36 29.02 -9.24 -9.45 -6.84 -4.97
352.22 24.87 -9.05 -9.01 -6.44 -4.69
The center of forces corresponds to case ii. I
lard's equation more acceptable at short distances. The calculated repulsion energy per electron is one-half the energy per spheroid and equal to one fourth the total repulsion energy for the 0 and 180' orientations.
Discussion Equilibrium Distance for t h e Dipole a t 0'. By combining the image, dispersion, and repulsion energies obtained from the various equations under different assumptions, we can derive values of U, the potential energy. The following combinations of Vi, with U,, and Udisp are particularly interesting: (i) u d i s p from the KM equation with Urep,with the force center at the middle of the bond; (ii) U&, from the KM equation with Urep, placing the force center 0.3 X cm from the oxygen atom centers; (iii) u d i s p from the B equation applied to the center of the oxygen atom with Urepreferred to the center of the spheroid; (iv) Udisp from the LJ equation centered in the molecule with Urepcentered in the spheroid, taking only the unscreened part of Vi,, since the polarization effects are included in LJ equation (in this case both centers are practically coincident); (v) finally, u d i s p from the MP equation applied at the center of the oxygen atom with U,, considering the center of the spheroid. The five combinations for the 0' orientation yield rather similar energy/distance profiles (Figure 2). The minimum energy is considered between -15 and -17 kcal/mol (case iii) and U = 0 in the 1.15 X I r I 1.35 X cm range. The minimum energy occurs at 1.85 X cm with respect to the water molecule center and at 1.70 X cm with respect to the center of the oxygen atom. These equilibrium distances are practically independent of the Udisp and Uh equations as a consequence of the type of equation used for Urep. The value U = -17 kcal/mol compares satisfactorily, in principle, with (AH),,, the experimental enthalpy at zero coverage determined by Kemball, (AH), = -17.6 kcal/mol.' Influence of Dipole Orientation. The potential energy for different distances and orientations of the molecule on the metal surface are reported in Tables I and I1 for the centers of force for cases iii and ii, respectively. (Data from 0 to 180' in 10" steps are available in ref 21.) These are the two cases where the dispersive and repulsive energies become angular dependent. According to molecular orientation the minimum energy range is between -17 and
l i 10
I
20
,
I
I
I
40
30
Distance
x
1od/(crn)
Flgure 2. Total energy/distance profile with the dipole orientation at .'0 (---) KM, case iii; (.-.-e) B, case i; (.e.) W, case i; (--.e-) MP, case i; (-) summing over the atoms of the water molecule. The center of forces situated on each atom. The repulsion energy is considered with the center of forces as in case iii.
-12 kcal/mol. The lowest energy value corresponds to the
0" orientation, the water molecule directing the oxygen atom toward the metal. Contrarily, the 180" orientation comprises the largest energy value. The latter is more reasonable because this position, involving two hydrogen atoms very close to the metal, leads to an appreciable relative increase in the repulsion energy term at short distances. The deviation from the trend of the monotonic change of U with 6 at 90" is probably due to the accumulation of errors for this particular orientation.21 It is interesting to note that the equilibrium distance, 1.7 X cm with respect to the oxygen atom, is slightly smaller than the sum of the water molecule and mercury atom radii as one should expect.33 Regarding the equilibrium distance, its value contains the uncertainties implied in the location of the metal plane.34,35
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The Journal of Physical Chemistry, Vol. 83,
No. 13, 1979
J. R. Gonzllez Maroto, D. Posadas, and A. J. Arda
0
1
1
2 " 0
2
I n [(roxx 10*)/(cm 11
1
I
I
2
3
Figure 5. Logarithmic plot of Udlsp vs. the metal-oxygen equilibrium distance for two different water dipole orientations. The center of forces corresponds to case iii.
Flgure 3. Semilogarithmic plot of U, vs. the metal-oxygen equilibrium distance for two different water dipole orientations. The center of forces corresponds to case iii.
dipole corresponds to positions perpendicular to the metal surface. The dispersion energy fits a similar linear-type relationship (Figure 5) as it should if the expression
Udisp= D(0)/roxm(B)
I
I
I
II
0
1
2
'I
I
I
I
0
1
2
I n [ ( r o x x loe) /(cm)I Figure 4. Logarithmic plot of U,, vs. the metal-oxygen equilibrium distance for two different water dipole orientations.
Functional Relationships among the Different Energy Contributions and the Water-Molecule-Metal Surface Distance. The expressions for the different energy contributions can be linearized as a function of the structural parameters of the interface. Thus, for molecular model iii a linear relationship is obtained between In [ Urep]as a function of rm, the metal to oxygen atom distance (Figure 3). This means that the approximation already made in the evaluation of the repulsion energy term can be substituted by the following expression: Urep
= b(0) exp[-(3.95rOx)l
(9)
(11)
is valid. Both D(t9) and m(t9)depend on the dipole orientation although to a lesser extent than the constants appearing in eq 10. m(0)is close to 3, the deviation from the rounded value due to the contribution of the second and third terms of the Udisp equation. The above mentioned linear relationships allow an immediate interpolation of the energy values and, eventually, they can be used to adjust calculated magnitudes where errors of different weight are included as is the case for Vi,. In conclusion, the electrostatic approach for water adsorption on mercury gives an acceptable explanation of the phenomena at the molecular level. Under conditions of zero charge on the metal, the most probable equilibrium orientation of the water dipole correspondsto the 0" angle and the corresponding operational equilibrium distance is 1.85 X cm. Finally it is interesting to compare the present results with other calculations for the adsorption of water on mercury, based upon electrostatic interactions assuming water structural model^.^*^' The re value given by Bod@ is 2.09 X cm which corresponds to Vi, = -15.1 kcal/mol for the dipole at Oo as compared to -9.1 kcal/mol reported here. The dispersion energy, which was calculated with the directional water polarizabilities taken from Le F e ~ r eis, -7.22 ~ ~ kcal/mol for the equilibrium distance for the Oo orientation.
(10)
Acknowledgment. The Institute (INIFTA) is patronized by the following institutions: Universidad Naciond de La Plata, Consejo Nacional de Investigaciones Cientificas y TBcnicas, the Comisidn de Investigaciones Cientificas (Provincia de Buenos Aires). This work was partially supported by the Regional Program for the Scientific and Technological Development of the Organization of the American States. Dr. J.R.G.M. thanks the Organization of American States for the fellowship granted (1974-1976) and the Universidad de Costa Rica for the leave of absence (1974-1977).
where C(0) and n(0)are functions of the dipole orientation and 1 5 n(0) I 3. Equation 10 involves the limiting classical interaction between two ideal dipoles [n(0)= 31 and two point charges [n(0)= 11. The largest induced
Supplementary Material Available: Calculation procedures followed to obtain the image, dispersive, and repulsive energy terms, as well as tables and graphs of these data (14 pages). Ordering information is given on
rox is given in A. An equation, such as eq 9, is already
known both from atom-atom and water-water repulsive interaction potential^.^^ The exponent is practically independent of the dipole orientation, contrary to the constant b(0), which is not. A linear relationship is also obtained by plotting In [ U b ] vs. In [rox](Figure 4), as it corresponds to an equation such as
Vi, = C(0)/roxn(o)
Absorption Study of Iron Oxide Surface
any current masthead page.
References and Notes (1) C. Kemball, Proc. R . SOC. London, Ser. A , 190, 117 (1947). (2) J. T. Law, Ph.D. Thesis, Royal College of Science, London, 1951. (3) S. V. Karpachev, M. V. Smirnov, and 2. J. Volchenkova, Zb. Fir. Kbim., 27, 1228 (1953). (4) C. Kemball, Trans. Faraday Soc., 42, 526 (1946). (5) J. R. Gonzllez Maroto and D. Posadas, submltted for publication. (6) D. D. Bod& Adv. Cbem. Pbys., 21, 362 (1971). (7) R. J. Watts-Tobin, Phil. Mag., 6, 133 (1961). (8) J. O’M. Bockris, M. A. V. Devanathan, and K. Muller, Proc. R . SOC. London, Ser. A , 274, 55 (1963). (9) J. O’M. Bockris and M. A. Habib, Electrochim. Acta, 22, 41 (1977). (10) S.Trasatti, J . Electroanal. Cbem., 33, 351 (1971). (11) J. O’M. Bockris and M. A. Habib, J . Electroanal. Cbem., 65, 473 (1975). (12) J. O’M. Bockris and T. N. Anderson, E k t m b i m . Acta, 9, 347 (1964). (13) J. R. Macdonald and C. A. Barlow, J. Cbem. Phys., 36, 3062 (1962). (14) K. Muller, “Eiectrosorption”, E. Glleadl, Ed., Plenum Press, New York, 1967. (15) D. D. Bod& J . Pbys. Chem., 76, 2915 (1972). (16) J. R. Gonzllez Maroto, D. Posadas, and A. J. Ada, An. Acad. Nac. Cienc. Exactas, Fis. Nat. Buenos Aires, 29, 115 (1977). (17) B. J. Piersma, “Electrosorption”, E. Gileadi, Ed., Plenum Press, New York, 1967.
The Journal of Physical Chemistry, Vol. 83, No. 13, 1979
(18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38)
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I. L. Cooper and J. A. Harrison, J. Electrmnai. Cbem., 66, 85 (1975). J. D. Bernal and R. H. Fowler, J. Cbem. Phys., 1, 515 (1933). J. D. Jackson, “Electrodinlmica Clsica”, Ed. Alhambra, Madrkl, 1966. J. R. Gonfilez Maroto, Doctoral Thesis, Facultad de Clenclas Exactas, Universidad Nacional de La Piata, La Plata, Argentina, 1976. R. G. Sachs and D. L. Dexter, J. Appl. Pbys., 21, 1314 (1950). P. H. Cuttler and J. J. Gibbons, Pbys. Rev., 111, 394 (1958). J. C. Sbter and J. A. Kirkwood. Pbys. Rev., 37,682 (1931); A. Muller, Proc. R. Soc., London, Ser. A , 154, 624 (1936). H. Margenau and W. G. Pollard, Pbys. Rev., 60, 128 (1941). J. Bardeen, Pbys. Rev., 58, 727 (1940). J. E. Lennard-Jones, Trans. Faraday SOC.,28, 333 (1932). J. C. Slater, Pbys. Rev., 36, 51 (1930). C. Kemball, Proc. R . SOC. London, Ser. A , 187, 73 (1946). W. G. Pollard, Pbys. Rev., 60, 578 (1941). E. Wigner and F. Seitz, Pbys. Rev., 46, 509 (1934). J. C. Slater, “Introduction to Chemical Physics”, McGraw-Hill, New York, 1963. H. Eisemberg, I. M. Pochan, and W. H. Flygare, J . Cbem. Pbys., 43, 4531 (1965). N. D. Lang and W. Khon, Pbys. Rev., B3, 1215 (1971). N. D. Lang and W. Khon, Pbys. Rev., B7, 3541 (1973). J. 0. Hlrshfelder, C. F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids”, Wiiey, New York, 1954. D. D. Eley and M. G. Evans, Trans. Faraday Soc., 34, 1093 (1938). C. G. Le Fevre, R. J. W. Le Fevre, 8 . Purchandra Rao, and A. J. Williams, J . Chem. Soc., 123 (1960).
Study of Iron Oxide Surface by Adsorption and Temperature-Programmed Desorptiont M. C. Kung, W. H. Cheng, and H. H. Kung” Department of Chemical Engineerlng and The Materials Research Center, Northwestern University, Evanston, Illinois 6020 1 (Received September 5, 1978; Revised Manuscript Received January 22, 1979) Publication costs assisted by the Department of Energy
Catalytic sites on an iron oxide surface, active in the selective oxidation of butene to butadiene, were studied by adsorption and temperature-programmed desorption of cis-Bbutene, butadiene, and carbon dioxide. Three distinct types of sites were identified: isomerization site, selective oxidation site, and combustion site. Results indicate that the three sites are independent of each other. Interaction of hydrocarbons was the weakest with the isomerization site, and strongest with the combustion site. Desorption from the oxidation sites can be identified. By quantitatively determining the desorption products in the adsorption of cis-2-buteneand butadiene, concentrations of the selective oxidation and the combustion sites were estimated.
Introduction The activity of a catalyst is known to depend on two parameters, the concentration of active sites per unit weight or area of catalyst, and the activity per site. The latter quantity is useful for fundamental understanding of the physics and chemistry of catalysis, and can be extracted from kinetic measurements once the site concentration is known. Thus research and progress have continued to be made in methods to determine site concentrations. For this, specific adsorption is perhaps the most common method and has been applied to metallic, and acidic and basic oxide catalysts. For oxidation catalyst, however, methods for site density measurement have not been reported. The difficulty here is perhaps the presence of different types of sites on the surface and the inability of the common adsorption methods to discriminate among the different sites. We report here our results on a-iron oxide which demonstrate that quantitative adsorption coupled with temperature-programmed desorption can provide vital information for the butene oxidative dehydrogenation reaction. The information ‘This work was initiated by a grant from the Research Corporation. 0022-365417912083-1737$01 ,0010
includes the types and concentrations of sites involved in the reaction and the strength of interaction of these sites with the adsorbates as measured by the activation energy of desorption of the reactants and products. The reactant and product molecules (cis-2-butene, butadiene, and COz) of the reaction were used as probe molecules. Specifically we showed that there are three distinct types of sites on an a-Fe203surface: combustion site for the combustion of butene and butadiene to carbon dioxide, selective oxidation site for the oxidative dehydrogenation of butene to butadiene, and isomerization site. Furthermore, the concentrations of the combustion and selective oxidation sites are estimated. It has been shown that among the first period transition metal binary oxides, iron oxide shows the highest activity for selective oxidative dehydrogenation of butene.’ Subsequently, other reports appeared which showed that butene can be converted to butadiene and carbon dioxide in the presence and absence of gaseous 0xygen.~8 This behavior is similar to those observed on other ferrite and bismuth molybdate catalyst^.^^ In the absence of gaseous oxygen, the formation of the oxidized products must be accompanied by reduction of the oxide, and the depletion 0 1979 American Chemical Society
