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On the stepwise change of activation energies in the hydrodechlorination of chlorobenzene over supported nickel
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Catalysis Communications 9 (2008) 333–336 www.elsevier.com/locate/catcom
On the stepwise change of activation energies in the hydrodechlorination of chlorobenzene over supported nickel Mark A. Keane a
a,*
, Ragnar Larsson
b
Chemical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, United Kingdom b Chemical Engineering II, University of Lund, P.O. Box 124, SE 22100 Lund, Sweden Received 13 April 2007; received in revised form 25 June 2007; accepted 28 June 2007 Available online 7 July 2007
Abstract Kinetics of chlorobenzene hydrodechlorination have been measured over Ni on SiO2, Al2O3, MgO, activated carbon and graphite. A stepwise variation of Ea is analysed using the selective energy transfer model where Ea is identified as the vibrational energy associated with an excitation of the chlorobenzene out-of-plane C–H bending mode. Variation of Ea with vibrational quantum number yields a vibrational frequency of 749 cm1 and a value (1.1 cm1) for the anharmonicity term, which is characteristic of bending vibrational modes. Our analysis suggests that the reacting species are weakly adsorbed on the catalyst: heat of adsorption = 0.31 kJ mol1. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Selective energy transfer model; Catalytic hydrodechlorination; Chlorobenzene; Apparent activation energy; Anharmonicity; Heat of adsorption
1. Introduction In a recent paper [1], we treated experimental kinetic data for the hydrodechlorination of chlorobenzene over a group of related supported Ni catalysts in terms of the selective energy transfer (SET) model. In this model [2], the loss of energy from an activated molecule in a condensed phase by interactions with other molecules is counteracted by energy transfer from the catalyst via vibrational resonance. The SET model as applied to heterogeneous catalysis presumes that, in the transition state, a vibrational frequency associated with the reactant (m) resonates with a vibrational frequency of the solid surface (x). We demonstrated from the application of SET that an interaction of the Ni–H stretch (x = 940 cm1) with the out-of-plane C–H bending mode (m = 740 cm1) of chlorobenzene results in a calculated hydrodechlorination isokinetic temperature (Tiso = 669 ± 2 K) that was in close agreement with the experimentally determined value. The isokinetic *
Corresponding author. E-mail address: [email protected] (M.A. Keane).
1566-7367/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.catcom.2007.06.024
temperature is defined as the temperature at which the Arrhenius lines intersect. Chlorobenzene hydrodechlorination proceeded with 100% selectivity to yield benzene and HCl as the only products where the reaction was conducted in the absence of any significant mass or heat transfer limitations with an overall raw rate measurement reproducibility better than ±7%. The catalysts (1.5–20.3% w/w Ni supported on MgO, SiO2, Al2O3, activated carbon (AC) and graphite) exhibited different Ni morphologies and particle size distributions (over the range 1–80 nm) where mean particle size was sensitive to catalyst preparation, activation and the nature of the support; the characterisation details are provided in our earlier report [1]. 2. Procedural description A basic tenet of the SET model is that values of the activation energy (Ea), or rather the enthalpy of activation (DH#), can be quantized in that a specific number of vibrational quanta have to be transferred from the catalyst to the adsorbed reactant in order to access the transition state; this has been discussed in detail elsewhere [3,4]. Broadly
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
speaking, DH# is the sum of these quanta. We should also consider the anharmonicity of reactant vibration, which implies that the vibrational quanta will decrease in size with the vibrational quantum number. Spectroscopic theory, e.g. Herzberg [5], predicts that the vibrational energy of a molecule, measured relative to the zero energy of the vibrational mode, is described (higher terms are excluded in the present treatment) by G0 ðnÞ ¼ nX0 þ X0 x0 n2
ð1Þ
where G0 represents the vibrational energy of the vibrator in excess of the zero energy vibrational level, n is the vibrational quantum number, x0 is the anharmonicity constant (characterised by a negative value) and X0, for small values of x0, is twice the vibration energy of the zero state. It should be noted that we have modified the original notation of Herzberg to suit the description of the vibration system that we are concerned with here. We can assume that all the chlorobenzene molecules, including those which undergo hydrodechlorination, are in thermal equilibrium with the catalyst surface. Following the approach of Benson [6], one can define the activation energy as ‘‘the difference between the average energy of the reacting molecules and the average energy of the molecules in the system’’. If this is so, the extra vibrational energy resulting from resonance energy transfer must be the only energy difference in the system. Consequently, it is our contention that the excess vibrational energy, G0(n), can be set equal to the activation enthalpy of the reaction, i.e. G0 ðnÞ ¼ DH #
ð2Þ
The following relation between Ea and DH# is approximately valid in a condensed phase [7] #
DH ¼ Ea RT
ð3Þ
where RT is a term that accounts for the influence of a preexponential factor that is proportional to T, e.g. kT/h in the Eyring equation. Furthermore, one has to take into consideration any energy term representing a possible adsorption equilibrium which we, for convenience, label as Q (the heat of adsorption). The contribution of the heat of adsorption in heterogeneous catalysis kinetics has been considered in detail elsewhere [8]. From our assumptions and definitions, Eq. (4) must hold DH # ¼ Ea RT þ Q
ð4Þ
and from a combination of Eqs. (1)–(4), we arrive at Ea RT ¼ Q þ nX0 þ X0 x0 n2
ð5Þ
3. Results
Table 1 Experimentally determined chlorobenzene hydrodechlorination activation energies (Ea) and subsequently derived quantities: Tmean = 533 K; RTmean = 4.43 kJ mol1 Catalyst
Ea (kJ mol1)
Ea RTmean (kJ mol1)
(Ea RTmean)/ 8.75
n
Ni/SiO2 Ni/Al2O3 Ni/MgO Ni/AC Ni/graphite
58.0 75.5 67.1 40.4 119.1
53.57 71.07 62.67 35.97 114.67
6.12 8.12 7.16 4.11 13.11
6 8 7 4 13
120
100
Ea – RTmean kJ mol-1
334
80
60
40
20
2
4
6
8
10
12
14
n Fig. 1. Dependence of Ea RTmean on the calculated n values (see Table 1): the second order fit is given in Eq. (7).
adopted a mean reaction temperature (Tmean) to test the applicability of Eq. (5) to our experimental catalytic results. It should be noted that the temperature limits were the same (1.686 K1 6 1000/T 6 2.114 K1) for each catalyst considered so that Tmean is a convenient point of comparison that applies equally to each of the catalyst systems. In order to fit the experimentally determined Ea RTmean to a suitable value of n in Eq. (5) we can, as a first trial, adopt a least common term describing the successive increase of the activation energies, i.e. 8.75 kJ mol1 determined previously [1], where we choose n according to n ¼ integer of ½ðEa RT mean Þ=8:75
ð6Þ
and the results are included in Table 1. The variation of Ea RTmean with the calculated n values was fitted to a second order polynomial and the resultant fit (see Fig. 1) can be represented by Ea RT mean ¼ 0:31 þ 8:9706n 0:013397n2
ð7Þ
with a correlation coefficient = 0.99999. The experimentally determined Ea values recorded for the hydrodechlorination of chlorobenzene are given in Table 1. The raw rate data and kinetic analysis are available elsewhere [1]; a full description of the experimental procedure is provided in a previous paper [9]. We have
3.1. Interpretation of numerical data From Eq. (7) we obtain a value for the anharmonicity term, X0x0 = 0.013397 kJ mol1, which corresponds to
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
1.1 cm1 and is characteristic of bending vibrational modes [3]. This is in accordance with our assumption [1] that the critical vibration mode is an out-of-plane C–H bending vibration. We have, unfortunately, been unable to find a X0x0 value for the m11 vibration mode (all the ring H and C atoms vibrating in-phase) of chlorobenzene, which we identified [1] as the critical vibrational mode that is excited before reaction. However, the corresponding value for benzene has been reported to equal 0.7 [10] and 0.68 [11]. These spectroscopic values are of the same order of magnitude and sign as the value (1.1 cm1) that we have derived for chlorobenzene from experimental kinetic data. Furthermore, from spectroscopic theory [5] mð1 0Þ ¼ X0 þ X0 x0
ð8Þ
where, applying Eq. (7) X0 = 8.9706 kJ mol1 = 750 cm1 and the associated wave number of the IR absorption band is given by m(1 0) = 750 1 = 749 cm1. This value is close to that quoted by Varsanyi [12] for the m11 vibration mode of chlorobenzene, i.e. 740 cm1. 4. Discussion Considering the error limits, there is good agreement between the value of the wave number for the m11 vibration mode extracted ‘‘indirectly’’ from our treatment of the stepwise nature of hydrodechlorination activation energies and the value obtained ‘‘directly’’ from spectroscopy. We can infer that the same agreement holds for the anharmonicity parameter. We have also obtained good agreement in terms of wave number from our previous SET treatment of the hydrodechlorination isokinetic temperature [1]. This level of corroboration serves to support the applicability of selective energy transfer by vibrational resonance [2]. 4.1. The meaning of Q The question remains: what is the significance of the first term of Eq. (7), i.e. 0.31 kJ mol1. We suggest that it corresponds to the term Q in Eq. (5), i.e. Q = 0.31 kJ mol1. This implies a very weak adsorption of the reacting species, i.e. adsorption that leads to catalytic transformation. This does not, however, imply that the other molecules, i.e. the non-reacting species, are not strongly adsorbed. This results in a seemingly anomalous response, albeit one that has been found in other cases [3,4,13], that the value of the heat of adsorption which emerges from an analysis of the observed activation energies as a stepwise variation, is unexpectedly low. One of the previous cases involved a study of nitrous oxide decomposition [4] and drew on a wealth of experimentally determined activation energies. In that study, it was noted that ‘‘the data are taken as experimental facts without recalculating them in relation to some assumed mechanism of adsorption’’, and Q was set at 0. A similar (but not identical) approach was taken to that employed in this study where the vibrational fre-
335
quency of the N–O stretch, the bond that should be broken for the reaction to proceed, derived from kinetic data was in good agreement with the spectroscopic value. Moreover, the anharmonicity parameter agreed well with (gas phase) spectroscopic data for N2O. A second case dealt with an analysis of activation energies for the dehydrogenation and the dehydration of formic acid over metal oxides [3] where a somewhat more sophisticated algorithm and corresponding computer program, SETOS developed by Jamroz [3], were employed. In this analysis, Q could be freely varied but was set at 0 in the first attempt which delivered vibrational frequencies and anharmonicity data that were consistent with the chemistry of the reactions: for dehydrogenation to produce CO2, a vibrational frequency = 765 cm1 and associated anharmonicity parameter = 0.5 cm1 were recorded. As the formation of CO2 most probably proceeds via a bending deformation of the O– C–O bond of the formate ion, these results can be compared with the 772 cm1 band for (solid) sodium formate [14]. Although no spectroscopic data could be found in the literature for the anharmonicity, it is generally accepted that bending vibrations are less anharmonic than stretching vibrations. Similarly, using the activation energies for the dehydration reaction (producing CO), vibrational frequency and anharmonicity values of 1505 and 9.2 cm1, respectively, were determined. As the formation of CO most probably proceeds via a stretching of one of the C– O bonds in the formate ion, the relevant reference value (1567 cm1) [14] refers to the asymmetric stretching of the O–C–O group; the participation of a stretching mode is consistent with the high anharmonicity value. Considering the relatively good agreement between experimentally derived and reference vibration/anharmonicity values, the assumption of Q = 0 kJ mol1 seems to be justified. It is worth flagging a third case involving the hydrogenation of benzene to cyclohexene over Pt(1 1 1) where the application of SET to an analysis of isokinetic behaviour has also resulted in an unexpectedly low value for Q [13]. 4.2. The reactivity of weakly interacting species From the above, it appears that in a number of cases Q = 0–2 kJ mol1. This is in striking contrast to what one, by intuition, expects from an adsorption step that results in an increase in reactivity. It does, however, concur with the work of Roberts [15] on transient species, as has been discussed previously by one of us [16]. The question remains: how can a ‘‘loosely bound’’ species initiate a chemical reaction? The surface chloro-organic species must be in close proximity to the second reacting species (Ni–H) and so reaction is facilitated once the activation barrier has been overcome. It has been shown elsewhere that chlorobenzene hydrodechlorination over supported Ni involves non-competitive adsorption of hydrogen and the chloroarene [17]. This proximity on the catalyst surface can be looked upon as an ‘‘ordering’’ or as a negative entropy term, which remains the same, whether the species in
336
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
question is strongly adsorbed or weakly adsorbed. Desorption of the surface species into the gas phase is of course accompanied by an increase in entropy. This means that as long as the entropy is constant, the adsorption equilibrium is entirely governed by the heat of adsorption. Taking the equilibrium X strongly
adsorbed
¡ X weakly
ð9Þ
adsorbed
with a corresponding heat of adsorption (Qads) for strongly adsorbed and Q for weakly adsorbed species, then the difference Qads Q determines the position of the equilibrium and ½X weakly
adsorbed
¼ eðQadsQÞ=RT ½X strongly
ment. A consequence of the close agreement of the reference (from free molecule spectral data) vibrational frequency with that obtained from experimentally determined activation energies is that the reactant species are loosely bound to the catalyst surface, i.e. heat of adsorption, Q = 0.31 kJ mol1.
adsorbed
ð10Þ
Therefore, there will always be a proportion of the molecules that are very weakly adsorbed but retaining their order relative to the surroundings. If (or rather when) these weakly bound molecules are activated up to a suitable DH# by means of selective energy transfer, they will react. 5. Conclusions We have applied the SET model to consider the stepwise variation of apparent activation energy for the gas phase hydrodechlorination of chlorobenzene over Ni supported on SiO2, Al2O3, MgO, activated carbon and graphite. SET analysis has delivered a wavenumber of 749 cm1 as representing the critical chlorobenzene vibration mode in terms of catalytic activation. This value matches the reference value (740 cm1) of the out-of-plane C–H bending mode while the magnitude and sign (1.1 cm1) of the associated anharmonicity is consistent with this assign-
References [1] M.A. Keane, R. Larsson, J. Mol. Catal. A 268 (2007) 87. [2] R. Larsson, J. Mol. Catal. 55 (1989) 70. [3] R. Larsson, M.H. Jamroz, M.A. Borowiak, J. Mol. Catal. A 129 (1988) 41. [4] R. Larsson, Catal. Today 4 (1989) 235. [5] G. Herzberg, Spectra of Diatomic Molecules, second ed., Van Nostrand, New York, 1950. [6] S.W. Benson, Thermochemical Kinetics, second ed., Wiley, New York, 1976. [7] KJ. Laidler, Chemical Kinetics, third ed., Harper & Row Publisher, New York, 1987, p. 114. [8] G.C. Bond, M.A. Keane, H. Kral, J.A. Lercher, Catal. Rev. Sci. Eng. 42 (2000) 323. [9] M.A. Keane, Appl. Catal. A 271 (2004) 109. [10] P.E. Maslen, N.C. Handy, R.D. Amos, D. Jayatilaka, J. Chem. Phys. 97 (1992) 4233. [11] E. Cane´, A. Miani, A. Trombetti, J. Mol. Spectrosc. 183 (1997) 204. [12] G. Varsanyi, Assignments for Vibrational Spectra of Seven Hundred Benzene Derivatives, Adam Hilger, London, 1974. [13] K.M. Bratlie, Y. Li, R. Larsson, G.A. Somorjai, Catal. Lett., in preparation. [14] K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordination Compounds, fourth ed., Wiley, New York, 1986. [15] M.W. Roberts, J. Mol. Catal. 74 (1982) 1. [16] R. Larsson, Catal. Lett. 36 (1996) 171. [17] M.A. Keane, D.Yu. Murzin, Chem. Eng. Sci. 56 (2001) 3185.
Catalysis Communications 9 (2008) 333–336 www.elsevier.com/locate/catcom
On the stepwise change of activation energies in the hydrodechlorination of chlorobenzene over supported nickel Mark A. Keane a
a,*
, Ragnar Larsson
b
Chemical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, United Kingdom b Chemical Engineering II, University of Lund, P.O. Box 124, SE 22100 Lund, Sweden Received 13 April 2007; received in revised form 25 June 2007; accepted 28 June 2007 Available online 7 July 2007
Abstract Kinetics of chlorobenzene hydrodechlorination have been measured over Ni on SiO2, Al2O3, MgO, activated carbon and graphite. A stepwise variation of Ea is analysed using the selective energy transfer model where Ea is identified as the vibrational energy associated with an excitation of the chlorobenzene out-of-plane C–H bending mode. Variation of Ea with vibrational quantum number yields a vibrational frequency of 749 cm1 and a value (1.1 cm1) for the anharmonicity term, which is characteristic of bending vibrational modes. Our analysis suggests that the reacting species are weakly adsorbed on the catalyst: heat of adsorption = 0.31 kJ mol1. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Selective energy transfer model; Catalytic hydrodechlorination; Chlorobenzene; Apparent activation energy; Anharmonicity; Heat of adsorption
1. Introduction In a recent paper [1], we treated experimental kinetic data for the hydrodechlorination of chlorobenzene over a group of related supported Ni catalysts in terms of the selective energy transfer (SET) model. In this model [2], the loss of energy from an activated molecule in a condensed phase by interactions with other molecules is counteracted by energy transfer from the catalyst via vibrational resonance. The SET model as applied to heterogeneous catalysis presumes that, in the transition state, a vibrational frequency associated with the reactant (m) resonates with a vibrational frequency of the solid surface (x). We demonstrated from the application of SET that an interaction of the Ni–H stretch (x = 940 cm1) with the out-of-plane C–H bending mode (m = 740 cm1) of chlorobenzene results in a calculated hydrodechlorination isokinetic temperature (Tiso = 669 ± 2 K) that was in close agreement with the experimentally determined value. The isokinetic *
Corresponding author. E-mail address: [email protected] (M.A. Keane).
1566-7367/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.catcom.2007.06.024
temperature is defined as the temperature at which the Arrhenius lines intersect. Chlorobenzene hydrodechlorination proceeded with 100% selectivity to yield benzene and HCl as the only products where the reaction was conducted in the absence of any significant mass or heat transfer limitations with an overall raw rate measurement reproducibility better than ±7%. The catalysts (1.5–20.3% w/w Ni supported on MgO, SiO2, Al2O3, activated carbon (AC) and graphite) exhibited different Ni morphologies and particle size distributions (over the range 1–80 nm) where mean particle size was sensitive to catalyst preparation, activation and the nature of the support; the characterisation details are provided in our earlier report [1]. 2. Procedural description A basic tenet of the SET model is that values of the activation energy (Ea), or rather the enthalpy of activation (DH#), can be quantized in that a specific number of vibrational quanta have to be transferred from the catalyst to the adsorbed reactant in order to access the transition state; this has been discussed in detail elsewhere [3,4]. Broadly
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
speaking, DH# is the sum of these quanta. We should also consider the anharmonicity of reactant vibration, which implies that the vibrational quanta will decrease in size with the vibrational quantum number. Spectroscopic theory, e.g. Herzberg [5], predicts that the vibrational energy of a molecule, measured relative to the zero energy of the vibrational mode, is described (higher terms are excluded in the present treatment) by G0 ðnÞ ¼ nX0 þ X0 x0 n2
ð1Þ
where G0 represents the vibrational energy of the vibrator in excess of the zero energy vibrational level, n is the vibrational quantum number, x0 is the anharmonicity constant (characterised by a negative value) and X0, for small values of x0, is twice the vibration energy of the zero state. It should be noted that we have modified the original notation of Herzberg to suit the description of the vibration system that we are concerned with here. We can assume that all the chlorobenzene molecules, including those which undergo hydrodechlorination, are in thermal equilibrium with the catalyst surface. Following the approach of Benson [6], one can define the activation energy as ‘‘the difference between the average energy of the reacting molecules and the average energy of the molecules in the system’’. If this is so, the extra vibrational energy resulting from resonance energy transfer must be the only energy difference in the system. Consequently, it is our contention that the excess vibrational energy, G0(n), can be set equal to the activation enthalpy of the reaction, i.e. G0 ðnÞ ¼ DH #
ð2Þ
The following relation between Ea and DH# is approximately valid in a condensed phase [7] #
DH ¼ Ea RT
ð3Þ
where RT is a term that accounts for the influence of a preexponential factor that is proportional to T, e.g. kT/h in the Eyring equation. Furthermore, one has to take into consideration any energy term representing a possible adsorption equilibrium which we, for convenience, label as Q (the heat of adsorption). The contribution of the heat of adsorption in heterogeneous catalysis kinetics has been considered in detail elsewhere [8]. From our assumptions and definitions, Eq. (4) must hold DH # ¼ Ea RT þ Q
ð4Þ
and from a combination of Eqs. (1)–(4), we arrive at Ea RT ¼ Q þ nX0 þ X0 x0 n2
ð5Þ
3. Results
Table 1 Experimentally determined chlorobenzene hydrodechlorination activation energies (Ea) and subsequently derived quantities: Tmean = 533 K; RTmean = 4.43 kJ mol1 Catalyst
Ea (kJ mol1)
Ea RTmean (kJ mol1)
(Ea RTmean)/ 8.75
n
Ni/SiO2 Ni/Al2O3 Ni/MgO Ni/AC Ni/graphite
58.0 75.5 67.1 40.4 119.1
53.57 71.07 62.67 35.97 114.67
6.12 8.12 7.16 4.11 13.11
6 8 7 4 13
120
100
Ea – RTmean kJ mol-1
334
80
60
40
20
2
4
6
8
10
12
14
n Fig. 1. Dependence of Ea RTmean on the calculated n values (see Table 1): the second order fit is given in Eq. (7).
adopted a mean reaction temperature (Tmean) to test the applicability of Eq. (5) to our experimental catalytic results. It should be noted that the temperature limits were the same (1.686 K1 6 1000/T 6 2.114 K1) for each catalyst considered so that Tmean is a convenient point of comparison that applies equally to each of the catalyst systems. In order to fit the experimentally determined Ea RTmean to a suitable value of n in Eq. (5) we can, as a first trial, adopt a least common term describing the successive increase of the activation energies, i.e. 8.75 kJ mol1 determined previously [1], where we choose n according to n ¼ integer of ½ðEa RT mean Þ=8:75
ð6Þ
and the results are included in Table 1. The variation of Ea RTmean with the calculated n values was fitted to a second order polynomial and the resultant fit (see Fig. 1) can be represented by Ea RT mean ¼ 0:31 þ 8:9706n 0:013397n2
ð7Þ
with a correlation coefficient = 0.99999. The experimentally determined Ea values recorded for the hydrodechlorination of chlorobenzene are given in Table 1. The raw rate data and kinetic analysis are available elsewhere [1]; a full description of the experimental procedure is provided in a previous paper [9]. We have
3.1. Interpretation of numerical data From Eq. (7) we obtain a value for the anharmonicity term, X0x0 = 0.013397 kJ mol1, which corresponds to
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
1.1 cm1 and is characteristic of bending vibrational modes [3]. This is in accordance with our assumption [1] that the critical vibration mode is an out-of-plane C–H bending vibration. We have, unfortunately, been unable to find a X0x0 value for the m11 vibration mode (all the ring H and C atoms vibrating in-phase) of chlorobenzene, which we identified [1] as the critical vibrational mode that is excited before reaction. However, the corresponding value for benzene has been reported to equal 0.7 [10] and 0.68 [11]. These spectroscopic values are of the same order of magnitude and sign as the value (1.1 cm1) that we have derived for chlorobenzene from experimental kinetic data. Furthermore, from spectroscopic theory [5] mð1 0Þ ¼ X0 þ X0 x0
ð8Þ
where, applying Eq. (7) X0 = 8.9706 kJ mol1 = 750 cm1 and the associated wave number of the IR absorption band is given by m(1 0) = 750 1 = 749 cm1. This value is close to that quoted by Varsanyi [12] for the m11 vibration mode of chlorobenzene, i.e. 740 cm1. 4. Discussion Considering the error limits, there is good agreement between the value of the wave number for the m11 vibration mode extracted ‘‘indirectly’’ from our treatment of the stepwise nature of hydrodechlorination activation energies and the value obtained ‘‘directly’’ from spectroscopy. We can infer that the same agreement holds for the anharmonicity parameter. We have also obtained good agreement in terms of wave number from our previous SET treatment of the hydrodechlorination isokinetic temperature [1]. This level of corroboration serves to support the applicability of selective energy transfer by vibrational resonance [2]. 4.1. The meaning of Q The question remains: what is the significance of the first term of Eq. (7), i.e. 0.31 kJ mol1. We suggest that it corresponds to the term Q in Eq. (5), i.e. Q = 0.31 kJ mol1. This implies a very weak adsorption of the reacting species, i.e. adsorption that leads to catalytic transformation. This does not, however, imply that the other molecules, i.e. the non-reacting species, are not strongly adsorbed. This results in a seemingly anomalous response, albeit one that has been found in other cases [3,4,13], that the value of the heat of adsorption which emerges from an analysis of the observed activation energies as a stepwise variation, is unexpectedly low. One of the previous cases involved a study of nitrous oxide decomposition [4] and drew on a wealth of experimentally determined activation energies. In that study, it was noted that ‘‘the data are taken as experimental facts without recalculating them in relation to some assumed mechanism of adsorption’’, and Q was set at 0. A similar (but not identical) approach was taken to that employed in this study where the vibrational fre-
335
quency of the N–O stretch, the bond that should be broken for the reaction to proceed, derived from kinetic data was in good agreement with the spectroscopic value. Moreover, the anharmonicity parameter agreed well with (gas phase) spectroscopic data for N2O. A second case dealt with an analysis of activation energies for the dehydrogenation and the dehydration of formic acid over metal oxides [3] where a somewhat more sophisticated algorithm and corresponding computer program, SETOS developed by Jamroz [3], were employed. In this analysis, Q could be freely varied but was set at 0 in the first attempt which delivered vibrational frequencies and anharmonicity data that were consistent with the chemistry of the reactions: for dehydrogenation to produce CO2, a vibrational frequency = 765 cm1 and associated anharmonicity parameter = 0.5 cm1 were recorded. As the formation of CO2 most probably proceeds via a bending deformation of the O– C–O bond of the formate ion, these results can be compared with the 772 cm1 band for (solid) sodium formate [14]. Although no spectroscopic data could be found in the literature for the anharmonicity, it is generally accepted that bending vibrations are less anharmonic than stretching vibrations. Similarly, using the activation energies for the dehydration reaction (producing CO), vibrational frequency and anharmonicity values of 1505 and 9.2 cm1, respectively, were determined. As the formation of CO most probably proceeds via a stretching of one of the C– O bonds in the formate ion, the relevant reference value (1567 cm1) [14] refers to the asymmetric stretching of the O–C–O group; the participation of a stretching mode is consistent with the high anharmonicity value. Considering the relatively good agreement between experimentally derived and reference vibration/anharmonicity values, the assumption of Q = 0 kJ mol1 seems to be justified. It is worth flagging a third case involving the hydrogenation of benzene to cyclohexene over Pt(1 1 1) where the application of SET to an analysis of isokinetic behaviour has also resulted in an unexpectedly low value for Q [13]. 4.2. The reactivity of weakly interacting species From the above, it appears that in a number of cases Q = 0–2 kJ mol1. This is in striking contrast to what one, by intuition, expects from an adsorption step that results in an increase in reactivity. It does, however, concur with the work of Roberts [15] on transient species, as has been discussed previously by one of us [16]. The question remains: how can a ‘‘loosely bound’’ species initiate a chemical reaction? The surface chloro-organic species must be in close proximity to the second reacting species (Ni–H) and so reaction is facilitated once the activation barrier has been overcome. It has been shown elsewhere that chlorobenzene hydrodechlorination over supported Ni involves non-competitive adsorption of hydrogen and the chloroarene [17]. This proximity on the catalyst surface can be looked upon as an ‘‘ordering’’ or as a negative entropy term, which remains the same, whether the species in
336
M.A. Keane, R. Larsson / Catalysis Communications 9 (2008) 333–336
question is strongly adsorbed or weakly adsorbed. Desorption of the surface species into the gas phase is of course accompanied by an increase in entropy. This means that as long as the entropy is constant, the adsorption equilibrium is entirely governed by the heat of adsorption. Taking the equilibrium X strongly
adsorbed
¡ X weakly
ð9Þ
adsorbed
with a corresponding heat of adsorption (Qads) for strongly adsorbed and Q for weakly adsorbed species, then the difference Qads Q determines the position of the equilibrium and ½X weakly
adsorbed
¼ eðQadsQÞ=RT ½X strongly
ment. A consequence of the close agreement of the reference (from free molecule spectral data) vibrational frequency with that obtained from experimentally determined activation energies is that the reactant species are loosely bound to the catalyst surface, i.e. heat of adsorption, Q = 0.31 kJ mol1.
adsorbed
ð10Þ
Therefore, there will always be a proportion of the molecules that are very weakly adsorbed but retaining their order relative to the surroundings. If (or rather when) these weakly bound molecules are activated up to a suitable DH# by means of selective energy transfer, they will react. 5. Conclusions We have applied the SET model to consider the stepwise variation of apparent activation energy for the gas phase hydrodechlorination of chlorobenzene over Ni supported on SiO2, Al2O3, MgO, activated carbon and graphite. SET analysis has delivered a wavenumber of 749 cm1 as representing the critical chlorobenzene vibration mode in terms of catalytic activation. This value matches the reference value (740 cm1) of the out-of-plane C–H bending mode while the magnitude and sign (1.1 cm1) of the associated anharmonicity is consistent with this assign-
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