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Heats of formation of HNO and some related species
Heats of Formation of HNO and Some Related Species WILLIAM R. ANDERSON
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5066, USA A critical review of the heat of formation of HNO is presented. This molecule and its thermodynamics parameters play crucial roles in the chemical mechanisms of propellant combustion and NOx pollutant chemistry. It was found that predissociation experiments, which have gone largely unnoticed for about 15 years, 10.6 lead to a significant revision in the recommended value. The new value, 25.620.1 kcal/mol (298 K; 26.3 kcal/mol at 0 K), is 1 to 2 kcal/mol higher than previous recommendations and has much narrower error limits. Heats of formation of NO, NH2OH, HNO1, and HNO2 are also briefly examined, and recommendations are made. © 1999 by The Combustion Institute
INTRODUCTION The1 HNO molecule plays crucial roles in the formation of NOx pollutants during combustion [1], in mechanisms describing the effects of additives used for removal of NOx from combustion exhaust gases [1], in the conversion of H2/NO mixtures to final products H2O and N2 [2, 3], in the so-called dark zone of solid rocket and gun propellants [3, 4], and in the primary flame zones of such propellants. Under many conditions of interest, several key reactions involving HNO are significantly reversed or even partially equilibrated. Since reverse rate coefficients are typically calculated using thermodynamics, modeling results involving the detailed chemistry can be very sensitive to input thermodynamic parameters. In particular, the heat of formation of HNO is therefore a sensitive input parameter in such calculations. This paper reports a critical review that was recently performed on the heat of formation of HNO. In spite of the highly reactive trace nature of this species, it is possible to specify its heat of formation within narrow error limits. Furthermore, the recommendation is about 1 to 2 kcal/mol larger than values in the commonly used Joint Army–Navy–Air Force (JANAF) [5, 6] and Russian [7] databases. Previous recommendations for the heat of formation of HNO [5–7] are based heavily on predissociation results from about 35 years ago [8, 9]. However, a brief inspection of a more recent result [10] for the predissociation limit revealed a much better theoretical analysis than E-mail: [email protected] 0010-2180/99/$–see front matter PII S0010-2180(98)00077-7
the earlier works. Also, the resulting heat of formation was significantly larger than that in the earlier works. Consequently, a thorough review of the literature on this heat of formation was in order. As shown in the next section, further spectroscopic studies on HNO and DNO isotopic effects, on kinetics of the recombination reaction H 1 NO 1 M 3 HNO 1 M, and ab initio calculations strongly support the conclusion that there is no barrier to the reverse reaction. The predissociation results therefore yield an exact equality for the HNO heat of formation rather than a lower limit as usually obtained from such experiments. This fact, in combination with the low error limits of the result, is presented as strong evidence that it is the best value currently available. The recommended heat of formation for HNO may be combined with photoionization mass spectrometric data on NH2OH to yield a new value for the heat of formation of NH2OH(g). This and other values are reviewed, and a new recommendation made. In addition, the heats of formation of the species HNO1 and HNO2 are discussed. Most of the information given in the present work first appeared as part of an unrefereed report [3]. Since the publication of Anderson [3], a note pointing out the significance of the predissociation experiments [10] with regard to the HNO heat of formation has appeared [11]. However, Dixon [11] focuses only on the predissociation results as they relate to the HNO heat of formation. The present report covers all literature relevant to this important quantity; in addition, a careful assessment of the error limits was performed, yielding more conservative reCOMBUSTION AND FLAME 117:394 – 403 (1999) © 1999 by The Combustion Institute Published by Elsevier Science Inc.
HEAT OF FORMATION OF HNO
395 TABLE 1
Results for the Heat of Formation of HNO Reference Experimental Cashion and Polanyi, 1959 [13] Clement and Ramsay, 1961 [8] Bancroft et al. 1962 [9] Clyne and Thrush, 1962 [14] Holmes, 1969 [15] Dixon et al., 1981 [10] Kutina et al., 1982 [16] Adams et al., 1989 [17] Recent theoretical Bruna and Marian, 1979 [18] Nomura and Iwata, 1979 [19] Adams et al., 1981 [20] Walch and Rohlfing, 1989 [21] Pauzat et al., 1993 [22] Diau et al., 1995 [2] Lee and Dateo, 1995 [23] Guadagnini et al., 1995 [24] Lee and Dateo, 1998 [25] Recommendations JANAF, 1977 [5] Gurvich et al., 1978 [7] This work a b
Method Threshold of A-X Emission Predissociation of HNO Kinetics of H 1 NO 1 M Kinetics of HI 1 NO 3 HNO 1 I Predissociation of HNO AP (NH2OH 3 HNO1 1 H2 1 e2) Proton affinity of NO MRD/CI SCF/CI 4 MBPT methods CASSCF/CCI 8e2, 10e2 CASSCF/CI BAC/MP4 CCSD(T) CASSCF/ICCI CCSD(T)
DH°f,298 (kcal/mol)a ;26.4 $23.8 (61.4) 523.8 (61.4) 25.3 6 0.4 (#24.6 6 ;3) 25.6 6 0.03 (21.4 6 2.8) (25.8 6 1.0) 26.1 26.3 26.4–28.0 26.8, 28.2 32.3 23.4 26.0 6 0.8 28.0 25.4 6 0.4 23.8b (62.5) 24.4 6 0.7 (62.5) 10.6 25.620.1
Quantities indicated in parentheses were derived in the present work. More recent updates to the JANAF database (prior to Anderson [3]) also recommend this older result [6].
sults. Dixon [11] points out that a better value for the NO heat of formation than recommended in Chase et al. [5] is available. This recommendation is accepted and discussed briefly. The change accounts for the slight increase in HNO heat of formation recommended in this work, as opposed to that in Anderson [3]. A few other pertinent studies that have appeared since Anderson [3] are also discussed. After presentation of the reviews on the heats of formation of the various species and a short summary section, fits of the results for the neutral species to a functional form commonly used in chemical modeling are given in the Appendix. The fits should readily enable usage of the new recommendations in future calculations. Also, a U.S. Army Research Laboratory (ARL) internal report on the present work has recently appeared [12]; it is more detailed than the present paper and contains recommendations for future work and a review of procedures for making HNO for study. The fits of thermodynamic data in the appendix of the present paper supersede those in the prior one.
REVIEW OF EXPERIMENTAL AND THEORETICAL RESULTS PERTAINING TO THE HEAT OF FORMATION OF HNO All of the results found in which the heat of formation of HNO was given or from which it could be derived are shown in Table 1. Quantities in parentheses, including error limits in some cases, are new results derived in the present work. The new results were either derived using results of the work cited or the old results were reevaluated. The earliest source of the heat of formation of HNO is from measurement by Cashion and Polanyi [13] of the threshold of A1A0-X1A9 system emission from the reaction of H with NO. Although that result agrees well with the present recommendation, it must be recognized that this determination was much more approximate. Cashion and Polanyi did not establish the cutoff of emission. They thought that with increased sensitivity, higher energy transitions might be observed, yielding a larger dissociation
396 energy than the approximate one they recommended. Shortly after Cashion and Polanyi’s work, Ramsay and coworkers [8, 9] performed further A-X emission and absorption studies on HNO. The studies yielded a more precise determination of D0 than provided in Cashion and Polanyi [13] based upon proof that the excited state was predissociating to H 1 NO along the groundstate asymptote. An upper limit to the value of D0 was established by observation of the breakoff points within the coarse rotational K9 structure of the molecule. The breakoff points were noted by presence or absence of entire K9 subbands within two upper state vibrational levels for HNO and one upper state vibrational level for DNO. From examination of spacing between the K9 rotational sublevels involved, one can infer that error limits in the D0 determined for HNO must be about 500 cm21, or 1.4 kcal/mol. Shortly after Clement and Ramsay’s [8] publication, Clyne and Thrush [14] pointed out that their kinetic studies on H 1 NO 1 M 3 HNO 1 M indicated this reaction has a small, negative activation energy. This means the H 1 NO recombination has little or no barrier, as one would expect, since the combining species are open-shell. Thus, the predissociation experiments establish an equality, rather than lower limit, for the heat of formation. There is much more information establishing lack of any barrier to the recombination reaction, but further discussion of this issue is deferred until later. Over 15 years ago, Dixon et al. [10] presented an important reexamination of the A state predissociation, studied via laser-induced fluorescence (LIF) experiments. Prior to the present work, the Dixon study had gone largely unnoticed in the kinetics and thermodynamics communities. This and later related works on both HNO and DNO by Dixon and coworkers [26 –28] and Petersen [29] include measurement and assignment of the breakoff points of fluorescence vs the rotational J9 quantum number (finer rotational structure) for a large number of the more coarsely spaced vibrational-K9 subbands of the molecule. Dixon et al. [10] contains an innovative theoretical analysis of the variation of the centrifugal barrier for rotational quanta K9, J9 and the vibrational levels involved
W. R. ANDERSON for a triatomic molecule. Such a theory was not applied in the early study by Ramsay and coworkers [8, 9]. The application of a correction for centrifugal barrier and associated extrapolation to the rotationless condition by Dixon et al. [10] must, in principle, yield much higher accuracy for the dissociation energy than in the earlier work. The correction for centrifugal barrier explains the somewhat smaller D0 reported by Dixon et al. [10] corresponding to the increased heat of formation vs Ramsay and coworkers [8, 9] (see Table 1). The result of Dixon et al. also has a much higher precision than the earlier work for two reasons. First, a much larger number of excited state vibrational-K9 levels was available in the later work. Second, and more important, the later work utilized breakoff points in the J9 fine structure whose energies are much more closely spaced than those of the K9 structure used in the earlier work. It is the present recommendation that the heat of formation derived from results of Dixon et al. [10] is therefore clearly the most accurate and precise value currently available. The assignment of error limits is discussed later. As stated earlier, Dixon [11] has recently independently pointed out the long-overlooked significance of his group’s predissociation studies on HNO. Dixon cites information on the heat of formation of NO from spectroscopic studies [30 –33], missed in Chase et al. [5], claiming it is more accurate than the data upon which the recommendation [5] is based. Gurvich et al. [7] are in agreement with Dixon. In Chase et al., the heat of formation is given as 21.6 6 0.04 kcal/mol (298 K), based upon calorimetry data. The spectroscopic studies, based upon an NO predissociation, strongly corroborate one another. The D0 corresponds to a heat of formation (298 K) of 21.82 6 0.04 kcal/mol (utilizing data on N and O atoms and H° 2 H°(Tr) functions from Chase et al. [5]). These predissociation experiments yield a firm lower limit to the heat of formation and thus strong evidence that the slightly smaller calorimetry result is too low. The recommendation by Gurvich et al. [7] and Dixon [11] for NO is therefore accepted. This new ancillary datum has been used in the present work, accounting for minor changes in results for HNO and related species vs Anderson [3].
HEAT OF FORMATION OF HNO It is found that most of the other works cited in Table 1 agree with the recommendation. These are discussed in the following paragraphs. The result of Holmes [15] was based upon measurements of the activation energy for the endothermic reaction HI 1 NO 3 HNO 1 I and an assumption that the reverse reaction is barrierless. Because the reverse reaction actually could have a barrier, the resulting heat of formation must be regarded as an upper limit. The present reevaluation of the heat of formation, result given in Table 1, took into account more recent values of the heats of formation of the other species [5]. The error limit in the activation energy given by Holmes is only 0.4 kcal/mol, implying fairly narrow error limits in the heat of formation. This result would therefore appear not to support the recommended value. However, Holmes’ paper is extremely short and sketchy, the experiments were only performed over a modest range in 1/T, and there is no corroborative kinetics evidence on this reaction from other laboratories. Consequently, this result is not at all convincing that the predissociation results are in error. Estimated error limits of ;3 kcal/mol are assigned for the resulting heat of formation. Results of either Kutina et al. [16] or of Adams et al. [17] can be combined with other data to yield the heat of formation of the HNO1 ion (see later). These results were combined with the ionization potential of HNO, 10.18 6 0.01 eV, to yield the resulting HNO heats of formation given in Table 1. This ionization potential was first obtained by Baker et al. [34]. A strongly supportive result, identical in both magnitude and error limits after rounding to the same number of significant digits, was obtained by a different method in the recent work of Kuo et al. [35].1 As added support, one notes 2
In support of their result, Kuo et al. [35] derived two values for the heat of formation of HNO1 utilizing data on the exothermicities of two ion-molecule reactions, which they claim were measured by Burt et al. [36]. They then compared these to results obtained utilizing their measured ionization potential as one input datum. However, the energies of those reactions were apparently not measured by Burt et al. as Kuo et al. thought. Instead, the rate coefficients of the two pertinent reactions were obtained by a flow technique. In fact, the energetics of such exothermic reactions probably cannot be determined via kinetics experi-
397 Baker et al. also measured the ionization potential of DNO, obtaining 10.20 6 0.01 eV. A much earlier measurement of this quantity, 10.29 6 0.14 eV which agrees well with Baker et al., was obtained by Kohout and Lampe [37]. Adams et al. [17] presented a measurement of the proton affinity of NO, 127 6 1 kcal/mol at 300 K. In the present work, the heat of formation of HNO1 was obtained from this proton affinity using the heat of formation of NO discussed previously and the heat of formation of H1 from Chase et al. [5]. Conversion of the result to 0 K was accomplished using H° 2 H°(Tr) functions for the reference elements from the JANAF tables [5] and equations from the introductory material for H° 2 H°(Tr) in Chase et al. [5] to determine this function for HNO1. Ab initio calculations of the vibrational frequencies of HNO1 from Bruna and Marian [38] were used in the latter calculation. These frequencies were first multiplied by 0.9, an average correction found necessary [39] to get good agreement between such ab initio results and experiments in cases in which, unlike this one, measurements exist. Note the thermodynamic results are not very sensitive to this correction. The resulting HNO1 heat of formation, combined with the aforementioned ionization potential [34, 35], yields the heat of formation for HNO given in Table 1. The result is in excellent agreement with the present recommendation. The heat of formation given for HNO1 by Kutina et al. [16], 256.8 6 1.4 kcal/mol (0 K), leads to an HNO heat of formation much lower than that recommended (see Table 1). Kutina et al. obtained the ion’s heat of formation by combining their measurement of the appearance potential for the reaction NH2OH 3 HNO1 1 H2 1 e2, 11.56 6 0.06 eV, with the heat of formation of NH2OH, 2 9.738 kcal/mol (0 K), derived by the authors from calorimetry data in a manner analogous to that used in Gurvich et al. [7]. Now, it immediately occurs that the products could be internally excited, thus leading to a systematic error. However, this ments. The reaction energies quoted in Kuo et al. were given in Table 1 of Burt et al. with no comment regarding their source, and with no error limits. Consequently, little meaning can be assigned to those comparisons.
398 would lead to an erroneously large appearance potential, hence, too large a value for the heat of formation of HNO. In contrast, the result of Ref. 16 is much too low. As discussed previously, the analysis of Dixon et al. [10] is very convincing. It is in reasonable agreement with most of the other results. This type of predissociation experiment yields a firm lower limit to the heat of formation. The result given in Table 1 derived from this appearance potential is therefore clearly incorrect. However, the measurement and analysis of the appearance potential seems straightforward and convincing, especially since there are no apparent spectral interferences. The ionization potential from Baker et al. [34] and Kuo et al. [35] is also convincing, particularly since, as mentioned previously, its use in combination with the NO proton affinity leads to an HNO heat of formation in good agreement with most of the other results (see Table 1). The currently accepted heat of formation of NH2OH(g), the other datum used in this approach to calculate the HNO heat of formation, is thus suspect. A brief review has shown that all prior measured or calculated values of this quantity have fairly large error limits. It is probably best, therefore, to regard the heat of formation of NH2OH, rather than HNO, as the quantity to be determined in combining these appearance and ionization potential data. This subject is discussed later. The recommended value of the HNO heat of formation is, reassuringly, in reasonable agreement with most of the recent theoretical results (see Table 1). It is believed the most accurate methods were used by Adams et al. [20], Walch and Rohlfing [21], Guadagnini et al. [24], and Lee and Dateo [23, 25]. Results from such methods have generally been within about 2–3 kcal/mol of good experimental results for 15 years. The results from these sources are thus in reasonable agreement with the recommendation. Lee and Dateo claim smaller error limits for their results than usual for ab initio work, particularly in their most recent effort [25]. They utilized a new extrapolation technique which promises to provide very high precision enthalpies. It is felt that the method is too new to warrant averaging their result into the recommendation at this time. However, it is obvi-
W. R. ANDERSON ous that their result is in excellent agreement with the present recommendation. Turning now to the prior recommendations, both are significantly smaller than the present recommendation. The JANAF recommendation [5, 6], which is used in the Sandia thermodynamics database [40], is based upon the older predissociation result [8, 9] combined with the kinetic observations of Clyne and Thrush [14], which indicate that there is no barrier to the recombination. As should now be clear, this should be replaced with the newer result of Dixon et al. [10]. The recommendation from Gurvich et al. [7] was obtained by averaging the old predissociation result [8, 9, 14] with the result of Holmes [15]. It should be noted that the error limits suggested by Gurvich et al. [7] seem altogether too optimistic. It would seem that reasonable error limits for both of the values being averaged should be about 1.4 –3 kcal/mol. Thus, the small error limit is likely the result of a coincidental close agreement in the two results being averaged; a more reasonable error limit for their recommendation would be about 2–3 kcal/mol. When consideration is given to the sources of the earlier recommendations and the appropriate associated error limits, they are seen to be in reasonable agreement with the present, more precise, recommendation. As mentioned earlier, a discussion of work supporting the notion that the recombination reaction H 1 NO 1 M 3 HNO 1 M is barrierless is now given. This discussion leads naturally into a defense of the error limits given for the recommended HNO heat of formation. There are several facts from different types of studies leading to this important conclusion: (1) kinetics experiments on the recombination reaction; (2) results from some of the ab initio studies, and (3) isotopic substitution effects on the predissociation results. These and the recommended error limits are now considered. There are kinetics studies by two groups, Clyne and Thrush [14] and Cvetanovic and coworkers [41, 42], wherein the temperature dependence of the recombination reaction H 1 NO 1 M 3 HNO 1 M has been studied so that an effective activation energy can be inferred. For the Cvetanovic group, the more recent study [42] is taken as the final result. The two
HEAT OF FORMATION OF HNO sets of experiments cover the region from 231 , T , 704 K for M 5 H2. The agreement between results in the region of overlap, 298 K , T , 477 K, is excellent. Furthermore, when data of either study is fitted to the form k 5 A exp(2Ea/ RT), the resulting activation energy is about 20.65 kcal/mol [42]. Now, in a case where a reaction exhibits a negative activation energy, the corresponding rotationless reaction barrier must be nearly zero. However, though it seems improbable, a slight recombination barrier cannot be entirely ruled out on the basis of these experiments because, as is well-known, the fitted activation energy arises from the difference between average energy of reacting complexes at the transition state minus average energy of reactants [see, e.g., 43]. An energy difference within internal modes thus could conceal a small barrier. The theoretical results of Adams et al. [20] indicate a barrier of about 0.6 kcal/mol exists at 4.0 Å H2N distance in the H2NO dissociation channel. Calculations of Walch and coworkers [21, 24], which in principle should be more accurate, indicate there is no barrier at all. In addition, those workers feel intuitively there should be no such long-range interactions in the potential. However, their actual calculations, unfortunately, extended only to 2.6 Å. Therefore, it is deemed prudent to consider that the 0.6-kcal/mol barrier may actually exist and use this notion in determination of error limits. As pointed out by Dixon and Rosser [26], the observed difference in dissociation energies of HNO and DNO determined from the breakoff points in the rotational branch structure is, within error limits, identically equal to the difference in HNO and DNO zero-point energies. This would not be possible if there is a very significant barrier in the dissociation channel because the difference in H or D atom vibrational motion would contribute an additional difference to the respective dissociation energies. Using simple harmonic oscillator calculations and equations in Dixon et al. [10], one can show, however, that a barrier of only a few tenths of a kcal/mol still cannot be ruled out, particularly if the exit channel is very broad. The preceding ideas lead to a discussion of the error limits in the recommended heat of formation. A notion of how much the predisso-
399 ciation model of Dixon et al. [10] affects the extrapolation to zero rotation can be obtained by comparing the results for DNO [26] with the similar results of Petersen [29]. Petersen performed the extrapolation, as is often done, by simply fitting a straight line to the typical plot of rotational energies at the breakoff points vs J(J 1 1) for the various upper state vibronic sublevels and extending it to J 5 0. This procedure leads to a dissociation energy that is ;0.1 kcal/mol smaller than that of Dixon and Rosser [26], whose more theoretically correct approach exhibits upwards curvature. This difference is considered a conservative estimate of the systematic error that could be induced by an error in the model of centrifugal barrier effects; it is used as the lower error limit of the present heat of formation recommendation. If the aforementioned concern about a possible slight barrier in the H-NO dissociation channel can eventually be alleviated, then the upper error limit would also become 0.1 kcal/mol. This upper error limit would result because it is just conceivable that the predissociation is taking place, albeit slowly, at the last observed emitting J9 level in each vibrational-K9 subband. In fact, lifetime measurements performed on the (1,0,0) K9 5 4 vibronic sublevel show that for the last observed emission, at J9 5 11, the fluorescence lifetime is significantly shorter than for lower levels [28], evidently due to predissociation. However, a more conservative estimate is recommended for the upper error limit for the present. This is obtained using the calculated barrier of Adams et al. [20] in the ground-state exit channel for the predissociation. This 0.6-kcal/mol barrier is large enough that it completely overshadows the possible error due to uncertainty in threshold J level. The final recommended value is thus 25.610.6 20.1 kcal/mole (298 K). It is to be emphasized that these error limits seem conservative. In regard to two other species closely related to HNO, the positive and negative HNO ion heats may be easily derived from the HNO heat of formation and ancillary data. As previously mentioned, for the positive ion, the heat of formation was obtained using the NO proton affinity from Adams et al. [17] (just prior to determination of the heat of formation of HNO). The result thus obtained for the ion was 261.2 6 1.0 kcal/mol (0 K). Alternatively, one
400 may obtain results with higher precision by using the heat of formation of HNO recommended herein as an input parameter. This value, when combined with the ionization potential [34, 35], yields 261.1 6 0.6 kcal/mol (0 K), in excellent agreement with the previous result obtained using the proton affinity measurement. The weighted average [44] of these two experimental results, 261.1 6 0.5 kcal/mol (0 K), is the final recommendation of this study. The recommendation is in excellent agreement with the MRD-CI ab initio result, 260.7 6 2 kcal/mol, from Bruna and Marian [38]. Turning to the negative ion, one obtains its heat of formation by combining the heat of formation of the neutral molecule with the electron affinity, 0.338 6 0.015 eV, measured by Ellis and Ellison [45]. The result is 18.5 6 0.7 kcal/mol (0 K). A brief review of the heat of formation of NH2OH(g) was also performed. As discussed by Gurvich et al. [7], and later similarly by Kutina et al. [16], this quantity can be derived from calorimetry measurements on the heat of solution of hydroxylamine and the enthalpy of its reactions with a number of species in solution (see Gurvich et al. [7] regarding these works), coupled with sublimation data on hydroxylamine from Back and Betts [46]. Using these data, Gurvich et al. [7] recommend 29.6 6 2.4 kcal/mol for the heat of formation of NH2OH(g) (0 K; 212.0 6 2.4 kcal/mol at 298 K). Alternatively, combining the appearance potential for NH2OH 3 HNO1 1 H2 1 e2 [16] together with the heat of formation of HNO recommended in the present work and the HNO ionization potential [34, 35], yields 25.5 6 1.5 kcal/mol for this quantity at 0 K (27.9 6 1.5 kcal/mol at 298 K). Two theoretical calculations were found [47,48 –51]. Wiberg’s study [47] included a calculation of the bond energy D0(NH22OH) using the Pople G1 method. This energy may be combined with heats of formation of NH2 [52] and OH [5] to yield the heat of formation of NH2OH. The result is 28.2 kcal/mol at 0 K (210.6 kcal/mol at 298 K). Sana and coworkers [48 –51] used four similar MP4 methods to calculate the heat of formation of NH2OH and a number of other compounds, all yielding comparable results. The value from the most recent of these works
W. R. ANDERSON TABLE 2 Recommended Heats of Formation From the Present Study Species HNO NO NH2OH HNO1 HNO2
DH°f,0 (kcal/mol)
DH°f,298 (kcal/mol)
10.6 26.320.1 21.70 6 0.04 27.2 6 2.2 261.1 6 0.5 18.5 6 0.7
10.6 25.620.1 21.82 6 0.04 29.6 6 2.2 260.4 6 0.5 —
[51], 211.7 kcal/mol (298 K), is taken as the final result of that group. The ab initio calculations seem to better support the calorimetric than the spectroscopic measurement. However, error limits for the ab initio results are estimated to be about 3 kcal/mol; thus, error limits in the ab initio results overlap both the spectroscopic and the calorimetric results. No apparent reason could be found to favor any of these four techniques. Therefore, the weighted average [44], 29.6 6 2.2 kcal/mol at 298 K, is the recommendation of the present study. Clearly further work on this quantity is warranted. SUMMARY A critical review of the heats of formation of several species has been completed. A synopsis of the recommendations is given in Table 2. For HNO, the new recommendation is significantly larger than previous recommendations and the error limits are much smaller. This outcome is primarily due to the discovery of the most recent results from predissociation experiments and ancillary works on the molecule, which indicate that the back reaction has nearly zero barrier. Heats of formation of NO, NH2OH, HNO1, and HNO2 were also briefly examined, and recommendations were made. To facilitate usage of these new results in future calculations, fitted constants to the functional form recommended in the NASA-Lewis studies [53–54], a form frequently used in detailed chemistry codes, are given for the neutral species in the Appendix. The author is grateful to Professor R. N. Dixon, Dr. J. Berkowitz, Dr. C. F. Chabalowski, Professor
HEAT OF FORMATION OF HNO C. Wittig, Professor J. W. Bozzelli, and Dr. A. J. Kotlar for enlightening discussions; to Dr. A. J. Kotlar for a critical reading of the manuscript; and to Professor J. W. Bozzelli for his encouragement during the course of the research.
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401 20. Adams., G. F., Bent, G. D., Bartlett, R. J., and Purvis, G. D. in Potential Energy Surfaces and Dynamics Calculations (D. G. Truhlar, Ed.), Plenum Press, New York, 1981, p. 133. 21. Walch, S. P., and Rohlfing, C. M., J. Chem. Phys. 91:2939 (1989). 22. Pauzat, F., Ellinger, Y., Berthier, G., Ge´rin, M., and Viala, Y., Chem. Phys. 174:71 (1993). 23. Lee, T. J., and Dateo, C. E., J. Chem. Phys. 103:9110 (1995). 24. Guadagnini, R., Schatz, G. C., and Walch, S. P., J. Chem. Phys. 102:774 (1995). 25. (a) Lee, T. J., and Dateo, C. E., to be published. (b) Lee, T. J., Private communication. 26. Dixon, R. N., and Rosser, C. A., Chem. Phys. Lett. 108:323 (1984). 27. Dixon, R. N., and Rosser, C. A., J. Mol. Spectrosc. 110:262 (1985). 28. Dixon, R. N., Noble, M., Taylor, C. A., and Delhoume, M., Faraday Discuss. Chem. Soc. I 71:125 (1981). 29. Petersen, J. C., J. Mol. Spectrosc. 110:277 (1985). 30. Dingle, T. W., Freedman, P. A., Gelernt, B., Jones, W. J., and Smith, I. W. M., Chem. Phys. 8:171 (1975). 31. Callear, A. B., and Pilling, M. J., Trans. Faraday Soc. 66:1886 (1970). 32. Callear, A. B., and Pilling, M. J., Trans. Faraday Soc. 66:1618 (1970). 33. Kley, D. (1973). Habilitationsschrift, University of Bonn, as quoted in Dingle et al. [30]. 34. Baker, J., Butcher, V., Dyke, J. M., and Morris, A., J. Chem. Soc. Faraday Trans. 86:3843 (1990). 35. Kuo, S. C., Zhang, Z., Ross, S. K., Klemm, R. B., Johnson, R. D., III, Monks, P. S., Thorn, R. P., Jr., and Stief, L. J., J. Phys. Chem. A 101:4035 (1997). 36. Burt, J. A., Dunn, J. L., McEwan, M. H., Sutton, M. M., Roche, A. E., and Schiff, H. I., J. Chem. Phys. 52:6062 (1970). 37. Kohout, F. C., and Lampe, F. W., J. Chem. Phys. 45:1074 (1966). 38. Bruna, P. J., and Marian, C. M., Chem. Phys. 37:425 (1979). 39. Hehre, W. J., Random, L., Schleyer, P. V. R., and Pople, J. A. Ab Initio Molecular Orbital Theory. John Wiley, New York, 1986, p. 236. 40. Kee, R. J., Rupley, F. M., and Miller, J. A. (1987). The CHEMKIN Thermodynamic Database. Sandia National Laboratories Report No. SAND87-8215. 41. Atkinson, A., and Cvetanovic, R. J., Can. J. Chem. 51:370 (1973). 42. Oka, K., Singleton, D. L., and Cvetanovic, R. J., J. Chem. Phys. 67:4681 (1977). 43. Benson, S. W. Thermochemical Kinetics. John Wiley, New York, 1968, p. 14. 44. Meyer, S. L. Data Analysis for Scientists and Engineers. John Wiley, New York, 1975, p. 146. 45. Ellis, H. B., Jr., and Ellison, G. B., J. Chem. Phys. 78:6541 (1983). 46. Back, R. A., and Betts, J., Can. J. Chem. 43:2157 (1965). 47. Wiberg, K. B., J. Phys. Chem. 96:5800 (1992). 48. Sana, M., Leroy, G., Peeters, D., and Younang, E., J. Mol. Struct. (Theochem.) 151:325 (1987).
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49. Sana, M., Leroy, G., Peeters, D., and Wilante, C., J. Mol. Struct. (Theochem.) 164:249 (1988). 50. Leroy, G., Sana, M., and Wilante, C., J. Mol. Struct. (Theochem.) 207:85 (1990). 51. Sana, M., and Leroy, G., J. Mol. Struct. (Theochem.) 226:307 (1991). 52. Anderson, W. R., J. Phys. Chem. 93:530 (1989). 53. Gordon, S., and McBride, B. J. (1994). Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. I. Analysis. NASA Lewis Research Center Ref. Pub. No. 1311. 54. Gordon, S., and McBride, B. J. (1996). Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. II. Users Manual and Program Description. NASA Lewis Research Center Ref. Pub. No. 1311. 55. McBride, B. J., Gordon, S., and Reno, M. A. (1993). Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, NASA Lewis Research Center Technical Memorandum No. 4513. 56. Jacox, M. E., J. Phys. Chem. Ref. Data 17:269 (1988). 57. McBride, B.J., Private communication. 58. Program THMFIT is included in the CHEMKIN package of chemistry related computer codes. See Kee, R. J., Rupley, F. M., and Miller, J. A. (1989). Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics. Sandia National Laboratories Report No. SAND89-8009. Received 13 November 1997; accepted 5 May 1998
APPENDIX: FITS TO NASA-LEWIS FORMAT To facilitate usage of the current recommendations, fits to thermodynamic data are provided for the neutral species. The fits utilized the NASA-Lewis form [53, 54]. The results are given in Table A1. The older, 14-parameter
form was used. For explanation of the various constants and their arrangement, see [53]. Note an ARL internal report [12] on this work included fits which are superseded by the present results. A reviewer has pointed out the fitting method used earlier [12] incorporates an extrapolation of fitted data from 1500 K to higher temperature. However, where data are available, as in the present case, a better approach should be used. It was also pointed out that McBride et al. [55], a reference missed in the earlier report [12], have provided useful fits for some of the species. For HNO, in Ref. 55, thermodynamic data from 200 to 6000 K were recomputed taking into account the recent updates to spectroscopic data given by Jacox [56] and fitted. The McBride et al. fit, therefore, should provide the best current representation of Cp(T), S(T), and H°-H°(Tr). However, the heat of formation was taken from Gurvich et al. It was pointed out [57] that one may utilize the McBride et al. fit simply by adjusting the enthalpy integration constants a6 and a13 to reflect the present recommendation. The result is given in the table. For NO, McBride et al. were aware of the recommendations of Gurvich et al. [7] for the heat of formation and fitted this and their other data from 200 – 6000 K. The data for Cp(T), S(T), and H°-H°(Tr) of NO from [7] are apparently based upon the best spectroscopic data currently available and are in excellent agreement with other results, e.g. [5]. In addition, the reader is reminded of the present acceptance of recommendations of [7] and [11]
TABLE A1 NASA-Lewis Fitted Parameters for Thermodynamic Data of HNO, NO, and NH2OHa
a
Data are in an 80-column format, suitable for input to user computer codes formatted for NASA-Lewis fits [53].
HEAT OF FORMATION OF HNO concerning the best heat of formation to use for NO. Consequently, no adjustment to the fit of McBride et al. is warranted for NO. McBride et al.’s coefficients are repeated in the table for the reader’s convenience. For NH2OH, data for S(T), Cp(T), and H°-H°(Tr) have been provided by Gurvich et al. [7]. These data on intervals of 100 K in the range 200 – 6000 K were fitted, along with the present recommendation for the heat of formation, using the program THMFIT [58]. The result is given in the table. The fit reproduces the Cp(T) function to within 0.05 cal/K-mole to 5900 K and 0.09 cal/K-mole at 6000 K. For HNO and NH2OH, the constants a6 and a13 have been adjusted to match the current recommendations at 298.15
403 K exactly. For NH2OH, the entropy integration constants a7 and a14 have similarly been adjusted to match the Gurvich et al. value at 298.15 K exactly. It should be pointed out that McBride and coworkers now prefer a functional form which utilizes more terms [53, 57]. This form can provide better fits for condensed-phase species than the 14-parameter form [57]. Additionally, many of the fits are now performed to 20,000 K. Perhaps the flexibility of the new form is needed for such a wide temperature range. However, the older, 14-parameter form is used in many readily available computer codes. It should continue to be quite reliable for gas-phase species at combustion temperatures.
U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5066, USA A critical review of the heat of formation of HNO is presented. This molecule and its thermodynamics parameters play crucial roles in the chemical mechanisms of propellant combustion and NOx pollutant chemistry. It was found that predissociation experiments, which have gone largely unnoticed for about 15 years, 10.6 lead to a significant revision in the recommended value. The new value, 25.620.1 kcal/mol (298 K; 26.3 kcal/mol at 0 K), is 1 to 2 kcal/mol higher than previous recommendations and has much narrower error limits. Heats of formation of NO, NH2OH, HNO1, and HNO2 are also briefly examined, and recommendations are made. © 1999 by The Combustion Institute
INTRODUCTION The1 HNO molecule plays crucial roles in the formation of NOx pollutants during combustion [1], in mechanisms describing the effects of additives used for removal of NOx from combustion exhaust gases [1], in the conversion of H2/NO mixtures to final products H2O and N2 [2, 3], in the so-called dark zone of solid rocket and gun propellants [3, 4], and in the primary flame zones of such propellants. Under many conditions of interest, several key reactions involving HNO are significantly reversed or even partially equilibrated. Since reverse rate coefficients are typically calculated using thermodynamics, modeling results involving the detailed chemistry can be very sensitive to input thermodynamic parameters. In particular, the heat of formation of HNO is therefore a sensitive input parameter in such calculations. This paper reports a critical review that was recently performed on the heat of formation of HNO. In spite of the highly reactive trace nature of this species, it is possible to specify its heat of formation within narrow error limits. Furthermore, the recommendation is about 1 to 2 kcal/mol larger than values in the commonly used Joint Army–Navy–Air Force (JANAF) [5, 6] and Russian [7] databases. Previous recommendations for the heat of formation of HNO [5–7] are based heavily on predissociation results from about 35 years ago [8, 9]. However, a brief inspection of a more recent result [10] for the predissociation limit revealed a much better theoretical analysis than E-mail: [email protected] 0010-2180/99/$–see front matter PII S0010-2180(98)00077-7
the earlier works. Also, the resulting heat of formation was significantly larger than that in the earlier works. Consequently, a thorough review of the literature on this heat of formation was in order. As shown in the next section, further spectroscopic studies on HNO and DNO isotopic effects, on kinetics of the recombination reaction H 1 NO 1 M 3 HNO 1 M, and ab initio calculations strongly support the conclusion that there is no barrier to the reverse reaction. The predissociation results therefore yield an exact equality for the HNO heat of formation rather than a lower limit as usually obtained from such experiments. This fact, in combination with the low error limits of the result, is presented as strong evidence that it is the best value currently available. The recommended heat of formation for HNO may be combined with photoionization mass spectrometric data on NH2OH to yield a new value for the heat of formation of NH2OH(g). This and other values are reviewed, and a new recommendation made. In addition, the heats of formation of the species HNO1 and HNO2 are discussed. Most of the information given in the present work first appeared as part of an unrefereed report [3]. Since the publication of Anderson [3], a note pointing out the significance of the predissociation experiments [10] with regard to the HNO heat of formation has appeared [11]. However, Dixon [11] focuses only on the predissociation results as they relate to the HNO heat of formation. The present report covers all literature relevant to this important quantity; in addition, a careful assessment of the error limits was performed, yielding more conservative reCOMBUSTION AND FLAME 117:394 – 403 (1999) © 1999 by The Combustion Institute Published by Elsevier Science Inc.
HEAT OF FORMATION OF HNO
395 TABLE 1
Results for the Heat of Formation of HNO Reference Experimental Cashion and Polanyi, 1959 [13] Clement and Ramsay, 1961 [8] Bancroft et al. 1962 [9] Clyne and Thrush, 1962 [14] Holmes, 1969 [15] Dixon et al., 1981 [10] Kutina et al., 1982 [16] Adams et al., 1989 [17] Recent theoretical Bruna and Marian, 1979 [18] Nomura and Iwata, 1979 [19] Adams et al., 1981 [20] Walch and Rohlfing, 1989 [21] Pauzat et al., 1993 [22] Diau et al., 1995 [2] Lee and Dateo, 1995 [23] Guadagnini et al., 1995 [24] Lee and Dateo, 1998 [25] Recommendations JANAF, 1977 [5] Gurvich et al., 1978 [7] This work a b
Method Threshold of A-X Emission Predissociation of HNO Kinetics of H 1 NO 1 M Kinetics of HI 1 NO 3 HNO 1 I Predissociation of HNO AP (NH2OH 3 HNO1 1 H2 1 e2) Proton affinity of NO MRD/CI SCF/CI 4 MBPT methods CASSCF/CCI 8e2, 10e2 CASSCF/CI BAC/MP4 CCSD(T) CASSCF/ICCI CCSD(T)
DH°f,298 (kcal/mol)a ;26.4 $23.8 (61.4) 523.8 (61.4) 25.3 6 0.4 (#24.6 6 ;3) 25.6 6 0.03 (21.4 6 2.8) (25.8 6 1.0) 26.1 26.3 26.4–28.0 26.8, 28.2 32.3 23.4 26.0 6 0.8 28.0 25.4 6 0.4 23.8b (62.5) 24.4 6 0.7 (62.5) 10.6 25.620.1
Quantities indicated in parentheses were derived in the present work. More recent updates to the JANAF database (prior to Anderson [3]) also recommend this older result [6].
sults. Dixon [11] points out that a better value for the NO heat of formation than recommended in Chase et al. [5] is available. This recommendation is accepted and discussed briefly. The change accounts for the slight increase in HNO heat of formation recommended in this work, as opposed to that in Anderson [3]. A few other pertinent studies that have appeared since Anderson [3] are also discussed. After presentation of the reviews on the heats of formation of the various species and a short summary section, fits of the results for the neutral species to a functional form commonly used in chemical modeling are given in the Appendix. The fits should readily enable usage of the new recommendations in future calculations. Also, a U.S. Army Research Laboratory (ARL) internal report on the present work has recently appeared [12]; it is more detailed than the present paper and contains recommendations for future work and a review of procedures for making HNO for study. The fits of thermodynamic data in the appendix of the present paper supersede those in the prior one.
REVIEW OF EXPERIMENTAL AND THEORETICAL RESULTS PERTAINING TO THE HEAT OF FORMATION OF HNO All of the results found in which the heat of formation of HNO was given or from which it could be derived are shown in Table 1. Quantities in parentheses, including error limits in some cases, are new results derived in the present work. The new results were either derived using results of the work cited or the old results were reevaluated. The earliest source of the heat of formation of HNO is from measurement by Cashion and Polanyi [13] of the threshold of A1A0-X1A9 system emission from the reaction of H with NO. Although that result agrees well with the present recommendation, it must be recognized that this determination was much more approximate. Cashion and Polanyi did not establish the cutoff of emission. They thought that with increased sensitivity, higher energy transitions might be observed, yielding a larger dissociation
396 energy than the approximate one they recommended. Shortly after Cashion and Polanyi’s work, Ramsay and coworkers [8, 9] performed further A-X emission and absorption studies on HNO. The studies yielded a more precise determination of D0 than provided in Cashion and Polanyi [13] based upon proof that the excited state was predissociating to H 1 NO along the groundstate asymptote. An upper limit to the value of D0 was established by observation of the breakoff points within the coarse rotational K9 structure of the molecule. The breakoff points were noted by presence or absence of entire K9 subbands within two upper state vibrational levels for HNO and one upper state vibrational level for DNO. From examination of spacing between the K9 rotational sublevels involved, one can infer that error limits in the D0 determined for HNO must be about 500 cm21, or 1.4 kcal/mol. Shortly after Clement and Ramsay’s [8] publication, Clyne and Thrush [14] pointed out that their kinetic studies on H 1 NO 1 M 3 HNO 1 M indicated this reaction has a small, negative activation energy. This means the H 1 NO recombination has little or no barrier, as one would expect, since the combining species are open-shell. Thus, the predissociation experiments establish an equality, rather than lower limit, for the heat of formation. There is much more information establishing lack of any barrier to the recombination reaction, but further discussion of this issue is deferred until later. Over 15 years ago, Dixon et al. [10] presented an important reexamination of the A state predissociation, studied via laser-induced fluorescence (LIF) experiments. Prior to the present work, the Dixon study had gone largely unnoticed in the kinetics and thermodynamics communities. This and later related works on both HNO and DNO by Dixon and coworkers [26 –28] and Petersen [29] include measurement and assignment of the breakoff points of fluorescence vs the rotational J9 quantum number (finer rotational structure) for a large number of the more coarsely spaced vibrational-K9 subbands of the molecule. Dixon et al. [10] contains an innovative theoretical analysis of the variation of the centrifugal barrier for rotational quanta K9, J9 and the vibrational levels involved
W. R. ANDERSON for a triatomic molecule. Such a theory was not applied in the early study by Ramsay and coworkers [8, 9]. The application of a correction for centrifugal barrier and associated extrapolation to the rotationless condition by Dixon et al. [10] must, in principle, yield much higher accuracy for the dissociation energy than in the earlier work. The correction for centrifugal barrier explains the somewhat smaller D0 reported by Dixon et al. [10] corresponding to the increased heat of formation vs Ramsay and coworkers [8, 9] (see Table 1). The result of Dixon et al. also has a much higher precision than the earlier work for two reasons. First, a much larger number of excited state vibrational-K9 levels was available in the later work. Second, and more important, the later work utilized breakoff points in the J9 fine structure whose energies are much more closely spaced than those of the K9 structure used in the earlier work. It is the present recommendation that the heat of formation derived from results of Dixon et al. [10] is therefore clearly the most accurate and precise value currently available. The assignment of error limits is discussed later. As stated earlier, Dixon [11] has recently independently pointed out the long-overlooked significance of his group’s predissociation studies on HNO. Dixon cites information on the heat of formation of NO from spectroscopic studies [30 –33], missed in Chase et al. [5], claiming it is more accurate than the data upon which the recommendation [5] is based. Gurvich et al. [7] are in agreement with Dixon. In Chase et al., the heat of formation is given as 21.6 6 0.04 kcal/mol (298 K), based upon calorimetry data. The spectroscopic studies, based upon an NO predissociation, strongly corroborate one another. The D0 corresponds to a heat of formation (298 K) of 21.82 6 0.04 kcal/mol (utilizing data on N and O atoms and H° 2 H°(Tr) functions from Chase et al. [5]). These predissociation experiments yield a firm lower limit to the heat of formation and thus strong evidence that the slightly smaller calorimetry result is too low. The recommendation by Gurvich et al. [7] and Dixon [11] for NO is therefore accepted. This new ancillary datum has been used in the present work, accounting for minor changes in results for HNO and related species vs Anderson [3].
HEAT OF FORMATION OF HNO It is found that most of the other works cited in Table 1 agree with the recommendation. These are discussed in the following paragraphs. The result of Holmes [15] was based upon measurements of the activation energy for the endothermic reaction HI 1 NO 3 HNO 1 I and an assumption that the reverse reaction is barrierless. Because the reverse reaction actually could have a barrier, the resulting heat of formation must be regarded as an upper limit. The present reevaluation of the heat of formation, result given in Table 1, took into account more recent values of the heats of formation of the other species [5]. The error limit in the activation energy given by Holmes is only 0.4 kcal/mol, implying fairly narrow error limits in the heat of formation. This result would therefore appear not to support the recommended value. However, Holmes’ paper is extremely short and sketchy, the experiments were only performed over a modest range in 1/T, and there is no corroborative kinetics evidence on this reaction from other laboratories. Consequently, this result is not at all convincing that the predissociation results are in error. Estimated error limits of ;3 kcal/mol are assigned for the resulting heat of formation. Results of either Kutina et al. [16] or of Adams et al. [17] can be combined with other data to yield the heat of formation of the HNO1 ion (see later). These results were combined with the ionization potential of HNO, 10.18 6 0.01 eV, to yield the resulting HNO heats of formation given in Table 1. This ionization potential was first obtained by Baker et al. [34]. A strongly supportive result, identical in both magnitude and error limits after rounding to the same number of significant digits, was obtained by a different method in the recent work of Kuo et al. [35].1 As added support, one notes 2
In support of their result, Kuo et al. [35] derived two values for the heat of formation of HNO1 utilizing data on the exothermicities of two ion-molecule reactions, which they claim were measured by Burt et al. [36]. They then compared these to results obtained utilizing their measured ionization potential as one input datum. However, the energies of those reactions were apparently not measured by Burt et al. as Kuo et al. thought. Instead, the rate coefficients of the two pertinent reactions were obtained by a flow technique. In fact, the energetics of such exothermic reactions probably cannot be determined via kinetics experi-
397 Baker et al. also measured the ionization potential of DNO, obtaining 10.20 6 0.01 eV. A much earlier measurement of this quantity, 10.29 6 0.14 eV which agrees well with Baker et al., was obtained by Kohout and Lampe [37]. Adams et al. [17] presented a measurement of the proton affinity of NO, 127 6 1 kcal/mol at 300 K. In the present work, the heat of formation of HNO1 was obtained from this proton affinity using the heat of formation of NO discussed previously and the heat of formation of H1 from Chase et al. [5]. Conversion of the result to 0 K was accomplished using H° 2 H°(Tr) functions for the reference elements from the JANAF tables [5] and equations from the introductory material for H° 2 H°(Tr) in Chase et al. [5] to determine this function for HNO1. Ab initio calculations of the vibrational frequencies of HNO1 from Bruna and Marian [38] were used in the latter calculation. These frequencies were first multiplied by 0.9, an average correction found necessary [39] to get good agreement between such ab initio results and experiments in cases in which, unlike this one, measurements exist. Note the thermodynamic results are not very sensitive to this correction. The resulting HNO1 heat of formation, combined with the aforementioned ionization potential [34, 35], yields the heat of formation for HNO given in Table 1. The result is in excellent agreement with the present recommendation. The heat of formation given for HNO1 by Kutina et al. [16], 256.8 6 1.4 kcal/mol (0 K), leads to an HNO heat of formation much lower than that recommended (see Table 1). Kutina et al. obtained the ion’s heat of formation by combining their measurement of the appearance potential for the reaction NH2OH 3 HNO1 1 H2 1 e2, 11.56 6 0.06 eV, with the heat of formation of NH2OH, 2 9.738 kcal/mol (0 K), derived by the authors from calorimetry data in a manner analogous to that used in Gurvich et al. [7]. Now, it immediately occurs that the products could be internally excited, thus leading to a systematic error. However, this ments. The reaction energies quoted in Kuo et al. were given in Table 1 of Burt et al. with no comment regarding their source, and with no error limits. Consequently, little meaning can be assigned to those comparisons.
398 would lead to an erroneously large appearance potential, hence, too large a value for the heat of formation of HNO. In contrast, the result of Ref. 16 is much too low. As discussed previously, the analysis of Dixon et al. [10] is very convincing. It is in reasonable agreement with most of the other results. This type of predissociation experiment yields a firm lower limit to the heat of formation. The result given in Table 1 derived from this appearance potential is therefore clearly incorrect. However, the measurement and analysis of the appearance potential seems straightforward and convincing, especially since there are no apparent spectral interferences. The ionization potential from Baker et al. [34] and Kuo et al. [35] is also convincing, particularly since, as mentioned previously, its use in combination with the NO proton affinity leads to an HNO heat of formation in good agreement with most of the other results (see Table 1). The currently accepted heat of formation of NH2OH(g), the other datum used in this approach to calculate the HNO heat of formation, is thus suspect. A brief review has shown that all prior measured or calculated values of this quantity have fairly large error limits. It is probably best, therefore, to regard the heat of formation of NH2OH, rather than HNO, as the quantity to be determined in combining these appearance and ionization potential data. This subject is discussed later. The recommended value of the HNO heat of formation is, reassuringly, in reasonable agreement with most of the recent theoretical results (see Table 1). It is believed the most accurate methods were used by Adams et al. [20], Walch and Rohlfing [21], Guadagnini et al. [24], and Lee and Dateo [23, 25]. Results from such methods have generally been within about 2–3 kcal/mol of good experimental results for 15 years. The results from these sources are thus in reasonable agreement with the recommendation. Lee and Dateo claim smaller error limits for their results than usual for ab initio work, particularly in their most recent effort [25]. They utilized a new extrapolation technique which promises to provide very high precision enthalpies. It is felt that the method is too new to warrant averaging their result into the recommendation at this time. However, it is obvi-
W. R. ANDERSON ous that their result is in excellent agreement with the present recommendation. Turning now to the prior recommendations, both are significantly smaller than the present recommendation. The JANAF recommendation [5, 6], which is used in the Sandia thermodynamics database [40], is based upon the older predissociation result [8, 9] combined with the kinetic observations of Clyne and Thrush [14], which indicate that there is no barrier to the recombination. As should now be clear, this should be replaced with the newer result of Dixon et al. [10]. The recommendation from Gurvich et al. [7] was obtained by averaging the old predissociation result [8, 9, 14] with the result of Holmes [15]. It should be noted that the error limits suggested by Gurvich et al. [7] seem altogether too optimistic. It would seem that reasonable error limits for both of the values being averaged should be about 1.4 –3 kcal/mol. Thus, the small error limit is likely the result of a coincidental close agreement in the two results being averaged; a more reasonable error limit for their recommendation would be about 2–3 kcal/mol. When consideration is given to the sources of the earlier recommendations and the appropriate associated error limits, they are seen to be in reasonable agreement with the present, more precise, recommendation. As mentioned earlier, a discussion of work supporting the notion that the recombination reaction H 1 NO 1 M 3 HNO 1 M is barrierless is now given. This discussion leads naturally into a defense of the error limits given for the recommended HNO heat of formation. There are several facts from different types of studies leading to this important conclusion: (1) kinetics experiments on the recombination reaction; (2) results from some of the ab initio studies, and (3) isotopic substitution effects on the predissociation results. These and the recommended error limits are now considered. There are kinetics studies by two groups, Clyne and Thrush [14] and Cvetanovic and coworkers [41, 42], wherein the temperature dependence of the recombination reaction H 1 NO 1 M 3 HNO 1 M has been studied so that an effective activation energy can be inferred. For the Cvetanovic group, the more recent study [42] is taken as the final result. The two
HEAT OF FORMATION OF HNO sets of experiments cover the region from 231 , T , 704 K for M 5 H2. The agreement between results in the region of overlap, 298 K , T , 477 K, is excellent. Furthermore, when data of either study is fitted to the form k 5 A exp(2Ea/ RT), the resulting activation energy is about 20.65 kcal/mol [42]. Now, in a case where a reaction exhibits a negative activation energy, the corresponding rotationless reaction barrier must be nearly zero. However, though it seems improbable, a slight recombination barrier cannot be entirely ruled out on the basis of these experiments because, as is well-known, the fitted activation energy arises from the difference between average energy of reacting complexes at the transition state minus average energy of reactants [see, e.g., 43]. An energy difference within internal modes thus could conceal a small barrier. The theoretical results of Adams et al. [20] indicate a barrier of about 0.6 kcal/mol exists at 4.0 Å H2N distance in the H2NO dissociation channel. Calculations of Walch and coworkers [21, 24], which in principle should be more accurate, indicate there is no barrier at all. In addition, those workers feel intuitively there should be no such long-range interactions in the potential. However, their actual calculations, unfortunately, extended only to 2.6 Å. Therefore, it is deemed prudent to consider that the 0.6-kcal/mol barrier may actually exist and use this notion in determination of error limits. As pointed out by Dixon and Rosser [26], the observed difference in dissociation energies of HNO and DNO determined from the breakoff points in the rotational branch structure is, within error limits, identically equal to the difference in HNO and DNO zero-point energies. This would not be possible if there is a very significant barrier in the dissociation channel because the difference in H or D atom vibrational motion would contribute an additional difference to the respective dissociation energies. Using simple harmonic oscillator calculations and equations in Dixon et al. [10], one can show, however, that a barrier of only a few tenths of a kcal/mol still cannot be ruled out, particularly if the exit channel is very broad. The preceding ideas lead to a discussion of the error limits in the recommended heat of formation. A notion of how much the predisso-
399 ciation model of Dixon et al. [10] affects the extrapolation to zero rotation can be obtained by comparing the results for DNO [26] with the similar results of Petersen [29]. Petersen performed the extrapolation, as is often done, by simply fitting a straight line to the typical plot of rotational energies at the breakoff points vs J(J 1 1) for the various upper state vibronic sublevels and extending it to J 5 0. This procedure leads to a dissociation energy that is ;0.1 kcal/mol smaller than that of Dixon and Rosser [26], whose more theoretically correct approach exhibits upwards curvature. This difference is considered a conservative estimate of the systematic error that could be induced by an error in the model of centrifugal barrier effects; it is used as the lower error limit of the present heat of formation recommendation. If the aforementioned concern about a possible slight barrier in the H-NO dissociation channel can eventually be alleviated, then the upper error limit would also become 0.1 kcal/mol. This upper error limit would result because it is just conceivable that the predissociation is taking place, albeit slowly, at the last observed emitting J9 level in each vibrational-K9 subband. In fact, lifetime measurements performed on the (1,0,0) K9 5 4 vibronic sublevel show that for the last observed emission, at J9 5 11, the fluorescence lifetime is significantly shorter than for lower levels [28], evidently due to predissociation. However, a more conservative estimate is recommended for the upper error limit for the present. This is obtained using the calculated barrier of Adams et al. [20] in the ground-state exit channel for the predissociation. This 0.6-kcal/mol barrier is large enough that it completely overshadows the possible error due to uncertainty in threshold J level. The final recommended value is thus 25.610.6 20.1 kcal/mole (298 K). It is to be emphasized that these error limits seem conservative. In regard to two other species closely related to HNO, the positive and negative HNO ion heats may be easily derived from the HNO heat of formation and ancillary data. As previously mentioned, for the positive ion, the heat of formation was obtained using the NO proton affinity from Adams et al. [17] (just prior to determination of the heat of formation of HNO). The result thus obtained for the ion was 261.2 6 1.0 kcal/mol (0 K). Alternatively, one
400 may obtain results with higher precision by using the heat of formation of HNO recommended herein as an input parameter. This value, when combined with the ionization potential [34, 35], yields 261.1 6 0.6 kcal/mol (0 K), in excellent agreement with the previous result obtained using the proton affinity measurement. The weighted average [44] of these two experimental results, 261.1 6 0.5 kcal/mol (0 K), is the final recommendation of this study. The recommendation is in excellent agreement with the MRD-CI ab initio result, 260.7 6 2 kcal/mol, from Bruna and Marian [38]. Turning to the negative ion, one obtains its heat of formation by combining the heat of formation of the neutral molecule with the electron affinity, 0.338 6 0.015 eV, measured by Ellis and Ellison [45]. The result is 18.5 6 0.7 kcal/mol (0 K). A brief review of the heat of formation of NH2OH(g) was also performed. As discussed by Gurvich et al. [7], and later similarly by Kutina et al. [16], this quantity can be derived from calorimetry measurements on the heat of solution of hydroxylamine and the enthalpy of its reactions with a number of species in solution (see Gurvich et al. [7] regarding these works), coupled with sublimation data on hydroxylamine from Back and Betts [46]. Using these data, Gurvich et al. [7] recommend 29.6 6 2.4 kcal/mol for the heat of formation of NH2OH(g) (0 K; 212.0 6 2.4 kcal/mol at 298 K). Alternatively, combining the appearance potential for NH2OH 3 HNO1 1 H2 1 e2 [16] together with the heat of formation of HNO recommended in the present work and the HNO ionization potential [34, 35], yields 25.5 6 1.5 kcal/mol for this quantity at 0 K (27.9 6 1.5 kcal/mol at 298 K). Two theoretical calculations were found [47,48 –51]. Wiberg’s study [47] included a calculation of the bond energy D0(NH22OH) using the Pople G1 method. This energy may be combined with heats of formation of NH2 [52] and OH [5] to yield the heat of formation of NH2OH. The result is 28.2 kcal/mol at 0 K (210.6 kcal/mol at 298 K). Sana and coworkers [48 –51] used four similar MP4 methods to calculate the heat of formation of NH2OH and a number of other compounds, all yielding comparable results. The value from the most recent of these works
W. R. ANDERSON TABLE 2 Recommended Heats of Formation From the Present Study Species HNO NO NH2OH HNO1 HNO2
DH°f,0 (kcal/mol)
DH°f,298 (kcal/mol)
10.6 26.320.1 21.70 6 0.04 27.2 6 2.2 261.1 6 0.5 18.5 6 0.7
10.6 25.620.1 21.82 6 0.04 29.6 6 2.2 260.4 6 0.5 —
[51], 211.7 kcal/mol (298 K), is taken as the final result of that group. The ab initio calculations seem to better support the calorimetric than the spectroscopic measurement. However, error limits for the ab initio results are estimated to be about 3 kcal/mol; thus, error limits in the ab initio results overlap both the spectroscopic and the calorimetric results. No apparent reason could be found to favor any of these four techniques. Therefore, the weighted average [44], 29.6 6 2.2 kcal/mol at 298 K, is the recommendation of the present study. Clearly further work on this quantity is warranted. SUMMARY A critical review of the heats of formation of several species has been completed. A synopsis of the recommendations is given in Table 2. For HNO, the new recommendation is significantly larger than previous recommendations and the error limits are much smaller. This outcome is primarily due to the discovery of the most recent results from predissociation experiments and ancillary works on the molecule, which indicate that the back reaction has nearly zero barrier. Heats of formation of NO, NH2OH, HNO1, and HNO2 were also briefly examined, and recommendations were made. To facilitate usage of these new results in future calculations, fitted constants to the functional form recommended in the NASA-Lewis studies [53–54], a form frequently used in detailed chemistry codes, are given for the neutral species in the Appendix. The author is grateful to Professor R. N. Dixon, Dr. J. Berkowitz, Dr. C. F. Chabalowski, Professor
HEAT OF FORMATION OF HNO C. Wittig, Professor J. W. Bozzelli, and Dr. A. J. Kotlar for enlightening discussions; to Dr. A. J. Kotlar for a critical reading of the manuscript; and to Professor J. W. Bozzelli for his encouragement during the course of the research.
REFERENCES 1. Miller, J. A., and Bowman, C. T., Prog. Energy Combust. Sci. 15:287 (1989). 2. Diau, E. W. G., Lin, M. C., He Y., and Melius, C. F., Prog. Energy Combust. Sci. 21:1 (1995). 3. Anderson, W. R., 30th JANNAF Combustion Subcommittee Meeting, CPIA Publication No. 606, Vol. II, 1993, p. 205. 4. Vanderhoff, J. A., Anderson, W. R., and Kotlar, A. J., 29th JANNAF Combustion Subcommittee Meeting, CPIA Publication 593, Vol. II, 1992, p. 225. 5. Chase, M. W., Jr., Davies, C.A., Downey, J. R., Jr., Frurip, D. J., McDonald, R. A., and Syverud, A. N., J. Phys. Chem. Ref. Data 14 Suppl. 1 (1985). 6. Abramowitz, S., National Institute of Standards and Technology. Private communication concerning recent updates to the last published JANAF thermodynamic database, Ref. 5. 7. Gurvich, L. V., Veyts, I. V., Medvedev, V. A., Khachkuruzov, G. A., Yungman, V. S., Bergman, G. A., Iorish, V. S., Yurkov, G. N., Gorbov, S. I., Kuratova, L. F., Trishcheva, N. P., Przheval’skiy, I. N., Leonidov, V. Y., Ezhov, Y. S., Tomberg, S. E., Nazarenko, I. I., Rogatskiy, A. L., Dorofeyeva, O. V., and Demidova, M. S. Thermodynamic Properties of Individual Substances, 4th ed. Hemisphere, New York, 1989, Vol. 1, parts 1 and 2. 8. Clement, M. J. Y., and Ramsay, D. A., Can. J. Physics 39:205 (1961). 9. Bancroft, J. L., Hollas, J. M., and Ramsay, D. A., Can. J. Physics 40:322 (1962). 10. Dixon, R. N., Jones, K. B., Noble, M., and Carter, S., Mol. Phys. 42:455 (1981). 11. Dixon, R. N., J. Chem. Phys. 104:6905 (1996). 12. Anderson, W. R. (1997). Critical Review of the Heats of Formation of HNO and Some Related Species, U.S. Army Research Laboratory Technical Report No. ARL-TR-1557. 13. Cashion, J. K., and Polanyi, J. C., J. Chem. Phys. 30:317 (1959). 14. Clyne, M. A. A., and Thrush, B. A., Discussions of the Faraday Society 139 (1962). 15. Holmes, J. L., Proc. Chem. Soc. London 75 (1969). 16. Kutina, R. E., Goodman, G. L., and Berkowitz, J., J. Chem. Phys. 77:1664 (1982). 17. Adams, N. G., Smith, D., Tichy, M., Javahery, G., Twiddy, N. D., and Ferguson, E. E., J. Chem. Phys. 91:4037 (1989). 18. Bruna, P. J., and Marian, C. M., Chem. Phys. Lett. 67:109 (1979). 19. Nomura, O., and Iwata, S., Chem. Phys. Lett. 66:523 (1979).
401 20. Adams., G. F., Bent, G. D., Bartlett, R. J., and Purvis, G. D. in Potential Energy Surfaces and Dynamics Calculations (D. G. Truhlar, Ed.), Plenum Press, New York, 1981, p. 133. 21. Walch, S. P., and Rohlfing, C. M., J. Chem. Phys. 91:2939 (1989). 22. Pauzat, F., Ellinger, Y., Berthier, G., Ge´rin, M., and Viala, Y., Chem. Phys. 174:71 (1993). 23. Lee, T. J., and Dateo, C. E., J. Chem. Phys. 103:9110 (1995). 24. Guadagnini, R., Schatz, G. C., and Walch, S. P., J. Chem. Phys. 102:774 (1995). 25. (a) Lee, T. J., and Dateo, C. E., to be published. (b) Lee, T. J., Private communication. 26. Dixon, R. N., and Rosser, C. A., Chem. Phys. Lett. 108:323 (1984). 27. Dixon, R. N., and Rosser, C. A., J. Mol. Spectrosc. 110:262 (1985). 28. Dixon, R. N., Noble, M., Taylor, C. A., and Delhoume, M., Faraday Discuss. Chem. Soc. I 71:125 (1981). 29. Petersen, J. C., J. Mol. Spectrosc. 110:277 (1985). 30. Dingle, T. W., Freedman, P. A., Gelernt, B., Jones, W. J., and Smith, I. W. M., Chem. Phys. 8:171 (1975). 31. Callear, A. B., and Pilling, M. J., Trans. Faraday Soc. 66:1886 (1970). 32. Callear, A. B., and Pilling, M. J., Trans. Faraday Soc. 66:1618 (1970). 33. Kley, D. (1973). Habilitationsschrift, University of Bonn, as quoted in Dingle et al. [30]. 34. Baker, J., Butcher, V., Dyke, J. M., and Morris, A., J. Chem. Soc. Faraday Trans. 86:3843 (1990). 35. Kuo, S. C., Zhang, Z., Ross, S. K., Klemm, R. B., Johnson, R. D., III, Monks, P. S., Thorn, R. P., Jr., and Stief, L. J., J. Phys. Chem. A 101:4035 (1997). 36. Burt, J. A., Dunn, J. L., McEwan, M. H., Sutton, M. M., Roche, A. E., and Schiff, H. I., J. Chem. Phys. 52:6062 (1970). 37. Kohout, F. C., and Lampe, F. W., J. Chem. Phys. 45:1074 (1966). 38. Bruna, P. J., and Marian, C. M., Chem. Phys. 37:425 (1979). 39. Hehre, W. J., Random, L., Schleyer, P. V. R., and Pople, J. A. Ab Initio Molecular Orbital Theory. John Wiley, New York, 1986, p. 236. 40. Kee, R. J., Rupley, F. M., and Miller, J. A. (1987). The CHEMKIN Thermodynamic Database. Sandia National Laboratories Report No. SAND87-8215. 41. Atkinson, A., and Cvetanovic, R. J., Can. J. Chem. 51:370 (1973). 42. Oka, K., Singleton, D. L., and Cvetanovic, R. J., J. Chem. Phys. 67:4681 (1977). 43. Benson, S. W. Thermochemical Kinetics. John Wiley, New York, 1968, p. 14. 44. Meyer, S. L. Data Analysis for Scientists and Engineers. John Wiley, New York, 1975, p. 146. 45. Ellis, H. B., Jr., and Ellison, G. B., J. Chem. Phys. 78:6541 (1983). 46. Back, R. A., and Betts, J., Can. J. Chem. 43:2157 (1965). 47. Wiberg, K. B., J. Phys. Chem. 96:5800 (1992). 48. Sana, M., Leroy, G., Peeters, D., and Younang, E., J. Mol. Struct. (Theochem.) 151:325 (1987).
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49. Sana, M., Leroy, G., Peeters, D., and Wilante, C., J. Mol. Struct. (Theochem.) 164:249 (1988). 50. Leroy, G., Sana, M., and Wilante, C., J. Mol. Struct. (Theochem.) 207:85 (1990). 51. Sana, M., and Leroy, G., J. Mol. Struct. (Theochem.) 226:307 (1991). 52. Anderson, W. R., J. Phys. Chem. 93:530 (1989). 53. Gordon, S., and McBride, B. J. (1994). Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. I. Analysis. NASA Lewis Research Center Ref. Pub. No. 1311. 54. Gordon, S., and McBride, B. J. (1996). Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications. II. Users Manual and Program Description. NASA Lewis Research Center Ref. Pub. No. 1311. 55. McBride, B. J., Gordon, S., and Reno, M. A. (1993). Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, NASA Lewis Research Center Technical Memorandum No. 4513. 56. Jacox, M. E., J. Phys. Chem. Ref. Data 17:269 (1988). 57. McBride, B.J., Private communication. 58. Program THMFIT is included in the CHEMKIN package of chemistry related computer codes. See Kee, R. J., Rupley, F. M., and Miller, J. A. (1989). Chemkin-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics. Sandia National Laboratories Report No. SAND89-8009. Received 13 November 1997; accepted 5 May 1998
APPENDIX: FITS TO NASA-LEWIS FORMAT To facilitate usage of the current recommendations, fits to thermodynamic data are provided for the neutral species. The fits utilized the NASA-Lewis form [53, 54]. The results are given in Table A1. The older, 14-parameter
form was used. For explanation of the various constants and their arrangement, see [53]. Note an ARL internal report [12] on this work included fits which are superseded by the present results. A reviewer has pointed out the fitting method used earlier [12] incorporates an extrapolation of fitted data from 1500 K to higher temperature. However, where data are available, as in the present case, a better approach should be used. It was also pointed out that McBride et al. [55], a reference missed in the earlier report [12], have provided useful fits for some of the species. For HNO, in Ref. 55, thermodynamic data from 200 to 6000 K were recomputed taking into account the recent updates to spectroscopic data given by Jacox [56] and fitted. The McBride et al. fit, therefore, should provide the best current representation of Cp(T), S(T), and H°-H°(Tr). However, the heat of formation was taken from Gurvich et al. It was pointed out [57] that one may utilize the McBride et al. fit simply by adjusting the enthalpy integration constants a6 and a13 to reflect the present recommendation. The result is given in the table. For NO, McBride et al. were aware of the recommendations of Gurvich et al. [7] for the heat of formation and fitted this and their other data from 200 – 6000 K. The data for Cp(T), S(T), and H°-H°(Tr) of NO from [7] are apparently based upon the best spectroscopic data currently available and are in excellent agreement with other results, e.g. [5]. In addition, the reader is reminded of the present acceptance of recommendations of [7] and [11]
TABLE A1 NASA-Lewis Fitted Parameters for Thermodynamic Data of HNO, NO, and NH2OHa
a
Data are in an 80-column format, suitable for input to user computer codes formatted for NASA-Lewis fits [53].
HEAT OF FORMATION OF HNO concerning the best heat of formation to use for NO. Consequently, no adjustment to the fit of McBride et al. is warranted for NO. McBride et al.’s coefficients are repeated in the table for the reader’s convenience. For NH2OH, data for S(T), Cp(T), and H°-H°(Tr) have been provided by Gurvich et al. [7]. These data on intervals of 100 K in the range 200 – 6000 K were fitted, along with the present recommendation for the heat of formation, using the program THMFIT [58]. The result is given in the table. The fit reproduces the Cp(T) function to within 0.05 cal/K-mole to 5900 K and 0.09 cal/K-mole at 6000 K. For HNO and NH2OH, the constants a6 and a13 have been adjusted to match the current recommendations at 298.15
403 K exactly. For NH2OH, the entropy integration constants a7 and a14 have similarly been adjusted to match the Gurvich et al. value at 298.15 K exactly. It should be pointed out that McBride and coworkers now prefer a functional form which utilizes more terms [53, 57]. This form can provide better fits for condensed-phase species than the 14-parameter form [57]. Additionally, many of the fits are now performed to 20,000 K. Perhaps the flexibility of the new form is needed for such a wide temperature range. However, the older, 14-parameter form is used in many readily available computer codes. It should continue to be quite reliable for gas-phase species at combustion temperatures.