Thermochemistry of free radical

J. M. Kanabus-Kaminska, B. C. Gilbert, D. Griller. Solvent Effects on the Thermochemistry of Free-Radical Reactions. J. Am. Chem. Soc. 1989, 111, 3311-3314. 

As stated above, the thermochemistry of free radicals can also be estimated by the group additivity method, if group values are available. With the exception of a few cases reported in Benson (1976), however, such information presently does not exist. Therefore, we rely on the model compound approach (for S and Cp) and bond dissociation energy (BDE) considerations and computational quantum mechanics for the determination of the heats of formation of radicals. 

Since free radicals can be viewed as being derived from a (closest) stable molecule by the removal of an atom, again only differences must be sought in establishing their thermochemistry. In addition to the symmetry considerations noted earlier, spin corrections clearly are required to establish the thermochemistry of free radicals. For example, C2H5(derived from = 18) therefore, the entropy of C2H5 can be calculated to be... 

Moreover, it can also be used for rationalizing the thermochemistry of free-radical reactions. At first, it is easy to show that the R—X bond dissociation energy of a given molecule may be written as ... 

Following Bozzelli and Ritter (Lay et al., 1995 Ritter and Bozzelli, 1991), the thermochemistry of free radicals is estimated by adding Hydrogen Bond Increments (HBI) to the energy of the corresponding stable molecule where an H has capped the radical site. The HBI groups are also stored in a functional group tree. 

For an excellent review of the methods of determining the enthalpies of formation of free radicals the reader is referred to Thermochemistry of Free Radicals by H. E. O Neal and S. W. Benson in Free Radicals, Kochi, J. K., Ed., John Wiley Sons, New York, 1973,275 and the article by J. Berkowitz, G. B. Ellison, and D. Gutman, J. Phys. Chem., 98, 2744, 1994. 

The thermochemistry values are less well known for most of the other stable species of interest in combustion, and still less well known for unstable ones. Among the unstable species, the thermochemistry of free radicals has attracted particular interest in combustion modeling because of their roles as chain centers. 

In addition to providing an alternate route to the determination of experimentally difficult rate constants, the analysis of the thermochemistry of free radical reactions can also provide help in selecting reaction mechanisms. In a recent example from... 

Quantum calculations can make some selections in this case even though thermochemistry can not. The reverse of reaction (2) involves free radicals and the activation energy of free radicals is very low, 5,000 to 10,000 calories or less. The energy of activation for decomposition of acetone by reaction (2) then can not be much greater than 75,000 or at the most 80,000 calories and it can not be much less than 70,000. 

It is now established that many chemical reactions proceed via unstable intermediates, radicals or atoms. In order to discuss whether some postulated atom or radical reaction is likely to occur it is necessary to know something of the thermochemistry of these active species. Since we can rarely have a sufficiently large concentration of free radicals to carry out thermochemical measurements on them in bulk, it is necessary to deduce their heats of formation from dissociation energies involving them. 

As described in the Introductory Chapter, attention was focused [1] prior to 1961 mainly on the morphology of the cool-flame and ignition regions, rates were followed by pressure change, and essentially chemical techniques were used for product analysis. The acceptance of free radicals, followed by the masterly and elegant Semenov theory [2], which established the principles of branched chain reactions, provided the foundation for modern interpretations of hydrocarbon oxidation. This chapter builds on these early ideas, and pioneering experiments such as those carried out by Knox and Wells [3] and Zeelenberg and Bickel [4], to provide a detailed account of the reactions, thermochemistry and detailed mechanisms involved in the gas-phase chemistry of hydrocarbon oxidation. 

While these data are limited, they can be combined with group additivity (4,31,32), to form the basis for the estimation of the thermochemistry of several classes of free radical (4,31). Some caution must be exercised, however, when this estimation procedure is applied to compounds with groups of very different polarity as here. Thus, the entropy and heat capacity of CF3CH3 is satisfactorily approximated by group additivity (9.32), but the enthalpy of formation is in error by nearly 8 kcal/mol (33). 

The classical calorimetric methods addressed in chapters 7-9, 11, and 12 were designed to study thermally activated processes involving long-lived species. As discussed in chapter 10, some of those calorimeters were modified to allow the thermochemical study of radiation-activated reactions. However, these photocalorimeters are not suitable when reactants or products are shortlived molecules, such as most free radicals. To study the thermochemistry of those species, the technique of photoacoustic calorimetry was developed (see chapter 13). It may be labeled as a nonclassical calorimetric technique because it relies on concepts that do not fit into the classification schemes just outlined. 

A number of studies of H-atom transfer from hydrogen halides to free radicals, R + HX - RH + X, have been done by FPTRMS in which R was detected by photoionization, and its decay was monitored as a function of [HX] under pseudo-first-order conditions. When the rate coefficient is combined with determinations of the rate coefficient of the reverse reaction to obtain the equilibrium constant, the enthalpy of formation of the radical can be deduced. If the kinetics are accurately measured in isolation, this is a direct kinetic method which can be used to confirm (or otherwise) thermodynamic data obtained by classical, indirect kinetic methods which depend on correct mechanistic interpretation. In a number of instances free radical enthalpies of formation by these two different approaches have not been in good agreement. It is not the purpose of this short survey to discuss the differences, but rather to briefly indicate the extent to which the FPTRMS method has contributed to the kinetics of these reactions and to free radical thermochemistry. 

Tryptophan and its derivatives such as the Hoechst compounds (Adhikary et al. 2000) have reduction potentials below that of G (tryptophan E7 = 1.0 V Jovanovic and Simic 1985) and thus are capable of repairing some of the DNA damage (for a review on indol free-radical chemistry see Candeias 1998 for the thermochemistry of N-centered radicals see Armstrong 1998). In these reactions, radical cations and N-centered radicals are formed. Similar to phenoxyl radicals, these radical react with 02- mainly by addition despite the large difference in the redox potential which would allow an ET as well (Fang et al. 1998). 

Nangia PS, Benson SW (1979) Thermochemistry of organic polyoxides and their free radicals. J Phys Chem 83 1138-1142... 

P. M. Mayer, C. J. Parkinson, D. M. Smith, and L. Radom,/. Chem. Phys., 108,604 (1998). An Assessment of Theoretical Procedures for the Calculation of Reliable Free Radical Thermochemistry A Recommended New Procedure. 

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

This review makes extensive use of ancillary thermodynamic data. The source of such data, if not specified, is the NBS tables (323). The potentials in Table A-I, in most cases, have not been measured directly, and so there is considerable uncertainty in their magnitudes. Only in one case, the C102/C102 system, has the potential been corrected for activity coefficients to obtain a standard potential. A common approach in estimating the thermochemistry of aqueous free radicals is to use gas-phase data with appropriate guesses of solvation energies an important source of data for the gas-phase species is the JANAF tables (80). 

That various forms of Sb(IV) must be considered can be inferred from the observation that Ce(IV) oxidizes Sb(III) directly and in Cl -catalyzed paths (219), that the oxidation by Fe(CN)63 is second order in [Sb(III)] (176), and that reduction of SbCl6 by Fe2+ and Fe(CN)64-occurs with Fe(III) inhibition (25). The thermochemistry of these free radicals is unknown. 

One-electron oxidation of SCN-, by coordination complexes, for example, can lead directly to SCN, although oxidation by OH gives SCNOH- first. Several equilibrium constants involving this radical have been determined, so that it is an important species in the thermochemistry of inorganic free radicals. The various reports of E° for the SCN/SCN- couple are given in Table V. 

Free radicals derived from thiourea have been proposed as intermediates in several oxidations of thiourea. However, the reactions have not yielded much information regarding the identity or thermochemistry of the species implicated. For example, oxidation by IrCl62- occurs with a second-order dependence on [thiourea], a complex pH dependence, and hints of copper catalysis (244). Oxidation by Cu-(me2-phen)2+ is suggested to be an inner-sphere mechanism (92). At this time it is difficult even to guess at the redox potential of the thiourea radical. 

I began to collect experimental and theoretical values for BDEs in 1990. Four years later. Dr. S. E. Stein of the National Institute of Standards and Technology (NIST) encouraged me to continue in this task that is essential for chemical kinetics, free radical chemistry, organic thermochemistry, and physical organic chemistry. 

The thermochemistry of the azide radical (N3) is treated in Yoffe s review article [1]. The most important quantity for the purposes of this chapter is the electron affinity A of N3. The term electron affinity will be used rather loosely to mean the minimum energy required to remove an electron from an azide ion in free space (the subscript g denotes the gaseous phase)... 

The hrst hve chapters (Part 1) present an overview of some methods that have been used in the recent hterature to calculate rate constants and the associated case studies. The main topics covered in this part include thermochemistry and kinetics, computational chemistry and kinetics, quantum instanton, kinetic calculations in liquid solutions, and new applications of density functional theory in kinetic calculations. The remaining hve chapters (Part II) are focused on apphcations even though methodologies are discussed. The topics in the second part include the kinetics of molecules relevant to combustion processes, intermolecular electron transfer reactivity of organic compounds, lignin model compounds, and coal model compounds in addition to free radical polymerization. 

Let us first examine the chemical reactions, their stoichiometry, thermochemistry, mechanism, and kinetics. The ancient name paraffins meaning alkanes are poor chemical reagents and activation of the C—H bond must first occur to generate free radicals. This can be effected with UV radiation [33] or even visible light, X- or y-rays [34,35], or peroxides. 

Quantum chemistry is particularly useful for studying complex processes such as free-radical polymerization (see Radical Polymerization). In free-radical polymerization, a variety of competing reactions occur and the observable quantities that are accessible by experiment (such as the overall reaction rate, the overall molecular weight distribution of the polymer, and the overall monomer, polymer, and radical concentrations) are a complicated function of the rates of these individual steps. In order to infer the rates of individual reactions from such measurable quantities, one has to assume both a kinetic mechanism and often some additional empirical parameters. Not surprisingly then, depending upon the assumptions, enormous discrepancies in the so-called measured values can sometimes arise. Quantum chemistry is able to address this problem by providing direct access to the rates and thermochemistry of the individual steps in the process, without recourse to such model-based assumptions. 

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