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CBS-QB3 determination of enthalpy and free energy changes at normal and elevated temperatures
Journal of Molecular Structure (Theochem) 529 (2000) 41–45 www.elsevier.nl/locate/theochem
CBS-QB3 determination of enthalpy and free energy changes at normal and elevated temperatures P. Politzer*, M.C. Concha, P. Lane Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA Received 3 December 1999; accepted 19 January 2000
Abstract The CBS-QB3 procedure has been used to compute DH and DG at 298 and 2000 K for a group of reactions representative of those involved in the combustion of boron in oxygen/fluorine environments. Good agreement is found between the calculated and experimental values of DH(298 K), DH(2000 K) and DG(298 K). Whereas DH changes very little between 298 and 2000 K, DG can vary quite considerably over this temperature range. At 2000 K, the computed and the experimental DG are sometimes in serious disagreement; this is particularly likely when DG has a high temperature dependence. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Boron combustion; Enthalpy changes; Free energy changes; Temperature dependence; CBS-QB3 procedure
1. Introduction The oxidation of boron to either B2O3 or BF3 is highly exothermic; the heats of formation are about ⫺15 kcal per gram of boron for both liquid and solid B2O3, and about ⫺27 for gaseous BF3 [1,2]. The combustion of boron in oxygen/fluorine environments is accordingly of considerable interest as a source of energy for propellants [3–7]. We have recently computed the enthalpies and free energies at 298 K of 66 atoms and molecules that have been implicated in the ignition/combustion of boron, and used these to find their heats of formation as well as DH (and sometimes DG) for a variety of reactions that are likely to be involved in these processes [8]. * Corresponding author. Tel.: ⫹1-504-280-6850; fax: ⫹1-504280-6860. E-mail address: [email protected] (P. Politzer).
We have subsequently also determined some of the transition states and activation barriers [9]. Our primary objective is to provide data relevant to modelling studies of the combustion of boron-containing propellants [4–6]. In the present work, we have addressed the important issues of how the thermochemical quantities change in going to the elevated temperatures actually associated with boron combustion [4–6], and how well these changes are reproduced computationally. Earlier, we made a preliminary inquiry into the first of these questions [8], but with no comparison to experimental data. We have now gone into the matter more thoroughly and at a higher computational level. We have calculated DH and DG at 298 and at 2000 K for 14 reactions representative of boron combustion in oxygen/fluorine environments, and compared the results to experimental values. The significance of a change in DH is of course related to the exothermicity
0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(00)00529-7
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P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
2. Methods
Table 1 Reactions for which DH and DG were computed 1.
2CO ⫹ H2 ! 2HCO
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
2BF ⫹ H2 ! 2BH ⫹ F2 2BH ⫹ 3F2 ! 2BF3 ⫹ H2 BO ⫹ F ! FBO BO2 ⫹ F ! FBO ⫹ O 2CO ⫹ O2 ! 2CO2 F ⫹ H2 ! HF ⫹ H Cl ⫹ H2 ! HCl ⫹ H BF ⫹ OH ! FBO ⫹ H BO ⫹ OH ! BO2 ⫹ H BO ⫹ CO2 ! BO2 ⫹ CO HCO ⫹ O2 ! CO2 ⫹ OH H2 ⫹ 2CO2 ! 2CO ⫹ 2OH HCO ⫹ Cl ! HCl ⫹ CO
or endothermicity of a reaction, while in the case of DG it is the possibility that an equilibrium may be markedly affected or even reversed. (For some examples and a related study, see the recent paper by Bohr and Henon [10], who compared the effectiveness of various computational procedures in calculating equilibrium constants at different temperatures. They did not include the CBS-QB3 method that is used in the present work.)
The reactions upon which we have focused are listed in Table 1. They contain 19 different atoms and molecules, for which we optimized geometries and computed energy minima and enthalpies and free energies at both 298 and 2000 K with the CBSQB3 procedure [11] and the Gaussian 98 code [12]. CBS-QB3 is a very recent extension of the “complete basis set” extrapolation technique and represents an improvement over CBS-Q, which we used in our earlier work [8]. With our computed enthalpies and free energies, we determined DH and DG at 298 and 2000 K for reactions 1–14. Experimental DH(298 K) and DG(298 K) were found from heats of formation and entropies at 298 K given in Refs. [1,2]. These sources also contain enthalpies and entropies as functions of temperature, from which were obtained the experimental DH(2000 K) and DG(2000 K).
3. Results The computed atomic and molecular energy minima and enthalpies and free energies at 298 and 2000 K are in Table 2. The resulting DH and DG for
Table 2 Computed (CBS-QB3) energy minima, and enthalpies and free energies at 298 and 2000 K, in hartrees Atom or molecule
Emin
H(298 K)
G(298 K)
H(2000 K)
G(2000 K)
H O F Cl H2 O2 F2 BH OH HF HCl BO BO2 BF BF3 CO CO2 HCO FBO
⫺0.49982 ⫺74.98763 ⫺99.64311 ⫺459.68358 ⫺1.17605 ⫺150.16816 ⫺199.34854 ⫺25.23753 ⫺75.65805 ⫺100.36917 ⫺460.35480 ⫺99.89743 ⫺175.09381 ⫺124.53493 ⫺324.27980 ⫺113.18697 ⫺188.38354 ⫺113.71754 ⫺199.80227
⫺0.49746 ⫺74.98527 ⫺99.64075 ⫺459.68122 ⫺1.16277 ⫺150.16115 ⫺199.34298 ⫺25.22897 ⫺75.64639 ⫺100.35658 ⫺460.34488 ⫺99.88978 ⫺175.08298 ⫺124.52850 ⫺324.26317 ⫺113.17866 ⫺188.36946 ⫺113.70094 ⫺199.78995
⫺0.51047 ⫺75.00259 ⫺99.65793 ⫺459.69926 ⫺1.17757 ⫺150.18442 ⫺199.36596 ⫺25.24848 ⫺75.66662 ⫺100.37629 ⫺460.36607 ⫺99.91288 ⫺175.10492 ⫺124.55127 ⫺324.29380 ⫺113.20109 ⫺188.39026 ⫺113.72641 ⫺199.81102
⫺0.48398 ⫺74.97180 ⫺99.62728 ⫺459.66775 ⫺1.14302 ⫺150.13895 ⫺199.31978 ⫺25.20764 ⫺75.62624 ⫺100.33667 ⫺460.32415 ⫺99.86797 ⫺175.04855 ⫺124.50593 ⫺324.21492 ⫺113.15720 ⫺188.33704 ⫺113.67016 ⫺199.75640
⫺0.60142 ⫺75.11807 ⫺99.77262 ⫺459.81888 ⫺1.28563 ⫺150.34293 ⫺199.52451 ⫺25.38451 ⫺75.80590 ⫺100.51245 ⫺460.51118 ⫺100.06993 ⫺175.26918 ⫺124.70748 ⫺324.52198 ⫺113.35388 ⫺188.54492 ⫺113.90498 ⫺199.96914
P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
43
Table 3 Calculated and experimental DH(298 K) and DH(2000 K), in kcal/mol (experimental data are from Refs. [1,2]) Reaction
DH(298 K), calc.
DH(298 K), exp.
DH(2000 K), calc.
DH(2000 K), exp.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
74.2 262.8 ⫺754.4 ⫺162.8 ⫺32.3 ⫺138.3 ⫺31.7 1.0 ⫺70.6 ⫺27.8 ⫺1.5 ⫺96.5 157.9 ⫺88.7
73.6 267.0 ⫺754.4 ⫺163. ⫺35. ⫺135.3 ⫺32.0 1.0 ⫺74. ⫺25. 0. ⫺95.1 153.9 ⫺87.9
73.5 263.4 ⫺751.9 ⫺163.9 ⫺32.9 ⫺138.5 ⫺31.6 1.7 ⫺67.9 ⫺24.0 ⫺0.5 ⫺96.7 157.0 ⫺90.0
72.8 268.1 ⫺753.8 ⫺162.8 ⫺36.2 ⫺132.8 ⫺32.3 1.0 ⫺69.5 ⫺20.1 0.9 ⫺94.0 150.4 ⫺89.6
reactions 1–14, at both temperatures, are presented in Tables 3 and 4, along with the experimental values.
4. Discussion
not reflected in the heats of reaction, evidently due to cancellations. The average absolute change in DH over this temperature range is predicted to be only 1.2 kcal/mol, which agrees very well with the observed 1.6 kcal/mol. This confirms earlier computational findings [8,13].
4.1. Enthalpy changes The calculated and experimental DH are in good agreement at both 298 and 2000 K (Table 3), the average absolute differences being 1.8 and 2.5 kcal/mol, respectively. Although Table 2 shows the enthalpies of the individual atoms and molecules to increase significantly in going from 298 to 2000 K, this is
4.2. Free energy changes At 298 K, the calculated and the experimental DG differ by an average of only 1.8 kcal/mol (Table 4). At 2000 K, however, the situation becomes more complicated. The first point to note is that the agreement between
Table 4 Calculated and experimental DG(298 K) and DG(2000 K), in kcal/mol (experimental data are from Refs. [1,2]) Reaction
DG(298 K), calc.
DG(298 K), exp.
DG(2000 K), calc.
DG(2000 K), exp.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
79.6 261.8 ⫺734.4 ⫺150.7 ⫺31.9 ⫺121.7 ⫺32.2 0.2 ⫺65.0 ⫺22.5 ⫺1.8 ⫺91.6 139.7 ⫺88.8
79.1 265.9 ⫺732.1 ⫺153. ⫺35. ⫺123.0 ⫺31.9 0.6 ⫺71. ⫺22. ⫺1. ⫺92.8 139.3 ⫺87.5
115.1 255.4 ⫺619.4 ⫺79.4 ⫺28.5 ⫺24.6 ⫺34.9 ⫺5.1 ⫺35.9 3.3 ⫺5.2 ⫺64.6 35.1 ⫺88.6
114.4 259.1 ⫺602.4 ⫺95.8 ⫺32.7 ⫺52.7 ⫺31.0 ⫺1.2 ⫺56.3 ⫺10.7 ⫺7.6 ⫺81.4 57.1 ⫺83.9
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P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
Table 5 Experimental DS at 298 and 2000 K, in cal/K-mol (experimental data are from Refs. [1,2]) Reaction
DS(298 K)
DS(2000 K)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
⫺18.33 3.55 ⫺74.74 ⫺32.85 ⫺0.66 ⫺41.30 ⫺0.23 1.38 ⫺10.68 ⫺10.20 2.44 ⫺7.70 48.87 ⫺1.26
⫺20.80 4.51 ⫺75.69 ⫺33.52 ⫺1.76 ⫺40.04 ⫺0.64 1.10 ⫺6.61 ⫺4.71 4.25 ⫺6.33 46.62 ⫺2.86
the computed and experimental DG(2000 K) is not nearly as good as it was for DH(298 K), DH(2000 K) and DG(298 K). The absolute difference averages 11.3 kcal/mol, and reaches 28.1 for reaction 6. A second important point, and perhaps they are related, is that DG, unlike DH, may change very considerably between 298 and 2000 K. This can be seen from either the calculated or the experimental data in Table 4. The change, D(DG), is 10 kcal/mol or more in 8 of the 14 reactions, and can be greater than 100 kcal/mol. This cannot be attributed to large temperature variations in DS, since the average absolute difference between the experimental DS at 298 and 2000 K is only 1.8 cal/K-mol (Table 5), and there is no clear correlation between D(DG) and D(DS). The reactions for which there is the greatest disagreement between the computed and the experimental DG(2000 K) are 3,4,6,9,10,12 and 13. We believe it to be significant that all of these also show a large change in DG between 298 and 2000 K. Since this cannot be explained in terms of the contribution of DH to DG, because the temperature variation of the former is so small, one must focus upon the contribution of TDS to DG. Even though DS itself changes very little between 298 and 2000 K, as mentioned above, this is not true for the product TDS; at 2000 K, DS is being multiplied by a factor 6.7 times greater than at 298 K. Thus, a large value for DS will
result in DG(2000 K) differing considerably from DG(298 K). A second consequence is that the effect of any error in DS is substantially magnified in the subsequent DG(2000 K). 5. Conclusions For the group of 14 reactions examined in this work, we find that (a) there is good agreement between the CBS-QB3 calculated and the experimental DH(298 K), DH(2000 K) and DG(298 K); (b) DH changes very little between 298 and 2000 K, whereas DG can vary considerably over the same temperature range; and (c) there is sometimes serious disagreement between the computed and the experimental DG(2000 K). This appears to be particularly likely when DG shows a high temperature dependence, and may reflect the role of a large value of T in magnifying the error associated with DS(T ).
Acknowledgements We greatly appreciate the financial support provided by the Ballistic Missile Defense Organization and the Office of Naval Research through contract N00014-95-1-1339, Program Officers Dr Leonard H. Caveny (BMDO) and Dr Judah Goldwasser (ONR). References [1] M.W. Chase Jr., NIST-JANNAF Thermochemica Tables, J. Phys. Chem. Ref. Data, Monograph 9, 4 ed. 1998. [2] W.G. Mallard, P.J. Linstom, Eds., NIST Chemistry Webbook, NIST Standard Reference Database No. 69, November 1998, NIST, Gaithersburg, MD, 20899 (http://webbook.nist.gov). [3] R.C. Brown, C.E. Kolb, R.A. Yetter, F.L. Dryer, H. Rabitz, Combust. Flame 101 (1995) 221. [4] C.L. Yeh, K.K. Kuo, Prog. Energy Combust. Sci. 22 (1996) 511. [5] R.A. Yetter, F.L. Dryer, H. Rabitz, R.C. Brown, C.E. Kolb, Combust. Flame 112 (1998) 387. [6] W. Zhou, R.A. Yetter, F.L. Dryer, H. Rabitz, R.C. Brown, C.E. Kolb, Combust. Flame 112 (1998) 507. [7] D.P. Belyung, G.T. Dalakos, J.-D.R. Rocha, A. Fontijn, submitted for publication.
P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45 [8] P. Politzer, P. Lane, M.C. Concha, J. Phys. Chem. A 103 (1999) 1419. [9] P. Politzer, P. Lane, M.C. Concha, Proceedings of the 35th JANNAF Combust. Mtg., October 1999, in press. [10] F. Bohr, E. Henon, J. Phys. Chem. A 102 (1998) 4857. [11] J.A. Montgomery Jr., M.J. Frisch, J.W. Ochterski, G.A. Petersson, J. Chem. Phys. 110 (1999) 2822. [12] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrezewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dappich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.
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Adamo, S. Clifford, J. Ochterski, G. Petersson, P.Y. Aayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rubuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M. A.Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, M. Head-Gordon, E.S. Replogle and J.A. Pople, Gaussian 98, Revision A.5; Gaussian, Inc.: Pittsburgh, PA, 1998. [13] P. Politzer, P. Lane, J. Mol. Struct. (Theochem) 454 (1998) 229.
CBS-QB3 determination of enthalpy and free energy changes at normal and elevated temperatures P. Politzer*, M.C. Concha, P. Lane Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA Received 3 December 1999; accepted 19 January 2000
Abstract The CBS-QB3 procedure has been used to compute DH and DG at 298 and 2000 K for a group of reactions representative of those involved in the combustion of boron in oxygen/fluorine environments. Good agreement is found between the calculated and experimental values of DH(298 K), DH(2000 K) and DG(298 K). Whereas DH changes very little between 298 and 2000 K, DG can vary quite considerably over this temperature range. At 2000 K, the computed and the experimental DG are sometimes in serious disagreement; this is particularly likely when DG has a high temperature dependence. 䉷 2000 Elsevier Science B.V. All rights reserved. Keywords: Boron combustion; Enthalpy changes; Free energy changes; Temperature dependence; CBS-QB3 procedure
1. Introduction The oxidation of boron to either B2O3 or BF3 is highly exothermic; the heats of formation are about ⫺15 kcal per gram of boron for both liquid and solid B2O3, and about ⫺27 for gaseous BF3 [1,2]. The combustion of boron in oxygen/fluorine environments is accordingly of considerable interest as a source of energy for propellants [3–7]. We have recently computed the enthalpies and free energies at 298 K of 66 atoms and molecules that have been implicated in the ignition/combustion of boron, and used these to find their heats of formation as well as DH (and sometimes DG) for a variety of reactions that are likely to be involved in these processes [8]. * Corresponding author. Tel.: ⫹1-504-280-6850; fax: ⫹1-504280-6860. E-mail address: [email protected] (P. Politzer).
We have subsequently also determined some of the transition states and activation barriers [9]. Our primary objective is to provide data relevant to modelling studies of the combustion of boron-containing propellants [4–6]. In the present work, we have addressed the important issues of how the thermochemical quantities change in going to the elevated temperatures actually associated with boron combustion [4–6], and how well these changes are reproduced computationally. Earlier, we made a preliminary inquiry into the first of these questions [8], but with no comparison to experimental data. We have now gone into the matter more thoroughly and at a higher computational level. We have calculated DH and DG at 298 and at 2000 K for 14 reactions representative of boron combustion in oxygen/fluorine environments, and compared the results to experimental values. The significance of a change in DH is of course related to the exothermicity
0166-1280/00/$ - see front matter 䉷 2000 Elsevier Science B.V. All rights reserved. PII: S0166-128 0(00)00529-7
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P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
2. Methods
Table 1 Reactions for which DH and DG were computed 1.
2CO ⫹ H2 ! 2HCO
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
2BF ⫹ H2 ! 2BH ⫹ F2 2BH ⫹ 3F2 ! 2BF3 ⫹ H2 BO ⫹ F ! FBO BO2 ⫹ F ! FBO ⫹ O 2CO ⫹ O2 ! 2CO2 F ⫹ H2 ! HF ⫹ H Cl ⫹ H2 ! HCl ⫹ H BF ⫹ OH ! FBO ⫹ H BO ⫹ OH ! BO2 ⫹ H BO ⫹ CO2 ! BO2 ⫹ CO HCO ⫹ O2 ! CO2 ⫹ OH H2 ⫹ 2CO2 ! 2CO ⫹ 2OH HCO ⫹ Cl ! HCl ⫹ CO
or endothermicity of a reaction, while in the case of DG it is the possibility that an equilibrium may be markedly affected or even reversed. (For some examples and a related study, see the recent paper by Bohr and Henon [10], who compared the effectiveness of various computational procedures in calculating equilibrium constants at different temperatures. They did not include the CBS-QB3 method that is used in the present work.)
The reactions upon which we have focused are listed in Table 1. They contain 19 different atoms and molecules, for which we optimized geometries and computed energy minima and enthalpies and free energies at both 298 and 2000 K with the CBSQB3 procedure [11] and the Gaussian 98 code [12]. CBS-QB3 is a very recent extension of the “complete basis set” extrapolation technique and represents an improvement over CBS-Q, which we used in our earlier work [8]. With our computed enthalpies and free energies, we determined DH and DG at 298 and 2000 K for reactions 1–14. Experimental DH(298 K) and DG(298 K) were found from heats of formation and entropies at 298 K given in Refs. [1,2]. These sources also contain enthalpies and entropies as functions of temperature, from which were obtained the experimental DH(2000 K) and DG(2000 K).
3. Results The computed atomic and molecular energy minima and enthalpies and free energies at 298 and 2000 K are in Table 2. The resulting DH and DG for
Table 2 Computed (CBS-QB3) energy minima, and enthalpies and free energies at 298 and 2000 K, in hartrees Atom or molecule
Emin
H(298 K)
G(298 K)
H(2000 K)
G(2000 K)
H O F Cl H2 O2 F2 BH OH HF HCl BO BO2 BF BF3 CO CO2 HCO FBO
⫺0.49982 ⫺74.98763 ⫺99.64311 ⫺459.68358 ⫺1.17605 ⫺150.16816 ⫺199.34854 ⫺25.23753 ⫺75.65805 ⫺100.36917 ⫺460.35480 ⫺99.89743 ⫺175.09381 ⫺124.53493 ⫺324.27980 ⫺113.18697 ⫺188.38354 ⫺113.71754 ⫺199.80227
⫺0.49746 ⫺74.98527 ⫺99.64075 ⫺459.68122 ⫺1.16277 ⫺150.16115 ⫺199.34298 ⫺25.22897 ⫺75.64639 ⫺100.35658 ⫺460.34488 ⫺99.88978 ⫺175.08298 ⫺124.52850 ⫺324.26317 ⫺113.17866 ⫺188.36946 ⫺113.70094 ⫺199.78995
⫺0.51047 ⫺75.00259 ⫺99.65793 ⫺459.69926 ⫺1.17757 ⫺150.18442 ⫺199.36596 ⫺25.24848 ⫺75.66662 ⫺100.37629 ⫺460.36607 ⫺99.91288 ⫺175.10492 ⫺124.55127 ⫺324.29380 ⫺113.20109 ⫺188.39026 ⫺113.72641 ⫺199.81102
⫺0.48398 ⫺74.97180 ⫺99.62728 ⫺459.66775 ⫺1.14302 ⫺150.13895 ⫺199.31978 ⫺25.20764 ⫺75.62624 ⫺100.33667 ⫺460.32415 ⫺99.86797 ⫺175.04855 ⫺124.50593 ⫺324.21492 ⫺113.15720 ⫺188.33704 ⫺113.67016 ⫺199.75640
⫺0.60142 ⫺75.11807 ⫺99.77262 ⫺459.81888 ⫺1.28563 ⫺150.34293 ⫺199.52451 ⫺25.38451 ⫺75.80590 ⫺100.51245 ⫺460.51118 ⫺100.06993 ⫺175.26918 ⫺124.70748 ⫺324.52198 ⫺113.35388 ⫺188.54492 ⫺113.90498 ⫺199.96914
P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
43
Table 3 Calculated and experimental DH(298 K) and DH(2000 K), in kcal/mol (experimental data are from Refs. [1,2]) Reaction
DH(298 K), calc.
DH(298 K), exp.
DH(2000 K), calc.
DH(2000 K), exp.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
74.2 262.8 ⫺754.4 ⫺162.8 ⫺32.3 ⫺138.3 ⫺31.7 1.0 ⫺70.6 ⫺27.8 ⫺1.5 ⫺96.5 157.9 ⫺88.7
73.6 267.0 ⫺754.4 ⫺163. ⫺35. ⫺135.3 ⫺32.0 1.0 ⫺74. ⫺25. 0. ⫺95.1 153.9 ⫺87.9
73.5 263.4 ⫺751.9 ⫺163.9 ⫺32.9 ⫺138.5 ⫺31.6 1.7 ⫺67.9 ⫺24.0 ⫺0.5 ⫺96.7 157.0 ⫺90.0
72.8 268.1 ⫺753.8 ⫺162.8 ⫺36.2 ⫺132.8 ⫺32.3 1.0 ⫺69.5 ⫺20.1 0.9 ⫺94.0 150.4 ⫺89.6
reactions 1–14, at both temperatures, are presented in Tables 3 and 4, along with the experimental values.
4. Discussion
not reflected in the heats of reaction, evidently due to cancellations. The average absolute change in DH over this temperature range is predicted to be only 1.2 kcal/mol, which agrees very well with the observed 1.6 kcal/mol. This confirms earlier computational findings [8,13].
4.1. Enthalpy changes The calculated and experimental DH are in good agreement at both 298 and 2000 K (Table 3), the average absolute differences being 1.8 and 2.5 kcal/mol, respectively. Although Table 2 shows the enthalpies of the individual atoms and molecules to increase significantly in going from 298 to 2000 K, this is
4.2. Free energy changes At 298 K, the calculated and the experimental DG differ by an average of only 1.8 kcal/mol (Table 4). At 2000 K, however, the situation becomes more complicated. The first point to note is that the agreement between
Table 4 Calculated and experimental DG(298 K) and DG(2000 K), in kcal/mol (experimental data are from Refs. [1,2]) Reaction
DG(298 K), calc.
DG(298 K), exp.
DG(2000 K), calc.
DG(2000 K), exp.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
79.6 261.8 ⫺734.4 ⫺150.7 ⫺31.9 ⫺121.7 ⫺32.2 0.2 ⫺65.0 ⫺22.5 ⫺1.8 ⫺91.6 139.7 ⫺88.8
79.1 265.9 ⫺732.1 ⫺153. ⫺35. ⫺123.0 ⫺31.9 0.6 ⫺71. ⫺22. ⫺1. ⫺92.8 139.3 ⫺87.5
115.1 255.4 ⫺619.4 ⫺79.4 ⫺28.5 ⫺24.6 ⫺34.9 ⫺5.1 ⫺35.9 3.3 ⫺5.2 ⫺64.6 35.1 ⫺88.6
114.4 259.1 ⫺602.4 ⫺95.8 ⫺32.7 ⫺52.7 ⫺31.0 ⫺1.2 ⫺56.3 ⫺10.7 ⫺7.6 ⫺81.4 57.1 ⫺83.9
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P. Politzer et al. / Journal of Molecular Structure (Theochem) 529 (2000) 41–45
Table 5 Experimental DS at 298 and 2000 K, in cal/K-mol (experimental data are from Refs. [1,2]) Reaction
DS(298 K)
DS(2000 K)
1 2 3 4 5 6 7 8 9 10 11 12 13 14
⫺18.33 3.55 ⫺74.74 ⫺32.85 ⫺0.66 ⫺41.30 ⫺0.23 1.38 ⫺10.68 ⫺10.20 2.44 ⫺7.70 48.87 ⫺1.26
⫺20.80 4.51 ⫺75.69 ⫺33.52 ⫺1.76 ⫺40.04 ⫺0.64 1.10 ⫺6.61 ⫺4.71 4.25 ⫺6.33 46.62 ⫺2.86
the computed and experimental DG(2000 K) is not nearly as good as it was for DH(298 K), DH(2000 K) and DG(298 K). The absolute difference averages 11.3 kcal/mol, and reaches 28.1 for reaction 6. A second important point, and perhaps they are related, is that DG, unlike DH, may change very considerably between 298 and 2000 K. This can be seen from either the calculated or the experimental data in Table 4. The change, D(DG), is 10 kcal/mol or more in 8 of the 14 reactions, and can be greater than 100 kcal/mol. This cannot be attributed to large temperature variations in DS, since the average absolute difference between the experimental DS at 298 and 2000 K is only 1.8 cal/K-mol (Table 5), and there is no clear correlation between D(DG) and D(DS). The reactions for which there is the greatest disagreement between the computed and the experimental DG(2000 K) are 3,4,6,9,10,12 and 13. We believe it to be significant that all of these also show a large change in DG between 298 and 2000 K. Since this cannot be explained in terms of the contribution of DH to DG, because the temperature variation of the former is so small, one must focus upon the contribution of TDS to DG. Even though DS itself changes very little between 298 and 2000 K, as mentioned above, this is not true for the product TDS; at 2000 K, DS is being multiplied by a factor 6.7 times greater than at 298 K. Thus, a large value for DS will
result in DG(2000 K) differing considerably from DG(298 K). A second consequence is that the effect of any error in DS is substantially magnified in the subsequent DG(2000 K). 5. Conclusions For the group of 14 reactions examined in this work, we find that (a) there is good agreement between the CBS-QB3 calculated and the experimental DH(298 K), DH(2000 K) and DG(298 K); (b) DH changes very little between 298 and 2000 K, whereas DG can vary considerably over the same temperature range; and (c) there is sometimes serious disagreement between the computed and the experimental DG(2000 K). This appears to be particularly likely when DG shows a high temperature dependence, and may reflect the role of a large value of T in magnifying the error associated with DS(T ).
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