Bond Dissociation Energies and Heats of Formation

Great efforts have been made to generate accurate and reliable ion thermochemistry data (Chap. 1.2.8). Once such data is available, it can be employed to elucidate fragmentation mechanisms and in addition, it is useful for obtaining some background on the energetic dimensions in mass spectrometry. 

Heats of formation of neutral molecules, AHf(RH), can be obtained from combustion data with high accuracy. Bond dissociation energies can either be derived for homolytic bond dissociation 

The value of 169.9 kJ mol (1.75 eV) corresponds to AE(ch3+) = 14.35 eV which is in good agreement with published values of about 14.3 eV. [28,39] In addition, this is only 40 % of the homolytic C-H bond dissociation enthalpy of the neutral methane molecule, thereby indicating the weaker bonding in the molecular ion. 

The heat of formation of organic radicals and positive ions decreases with their size and even more important with their degree of branching at the radical or ionic site. A lower heat of formation is equivalent to a higher thermodynamic stability 

Example The effects of isomerization upon thermal stability of butyl ions, C4H9 are impressing. This carbenium ion can exist in four isomers with heats of formation that range from 837 kJ mol in case of -butyl over 828 kJ mol for wu-butyl (also primary) to 766 kJ mol for 5cc-butyl to 699 kJ mol in case of t-butyl, meaning an overall increase in thermodynamic stability of 138 kJ mol (Chap. 6.6.2) [36]. 

Heats of formation of neutral molecules, can be obtained from combus- 

Example The minimum energy needed to form a CHs ion and a hydrogen radical from the methane molecular ion can be estimated from the heat of reaction, AH, of this process. According to Fig. 2.6, AHr = A (ch3+) -/ (ch4)- hi order to calculate the missing A (ch3+) we use the tabulated values of A//f(H.) = 218.0 kJ 

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APPEARANCE POTENTIALS, BOND DISSOCIATION ENERGIES, AND HEATS OF FORMATION... 

The appearance potentials for molecular ions (ionization potentials) and for fragment ions formed in the mass spectra of metallocenes and related compounds are listed in Table XIII. These appearance potentials have been used to calculate bond dissociation energies and heats of formation of organometallic compounds, but the results obtained must be treated cautiously because the appearance potentials of fragment ions include excess energy due to excited species. The values obtained for the heats of formation are best considered as upper limits, rather than precise determinations. The extent to which energy due to excited states can contribute... 

Egger K.W. and Cocks A.T., Homopolar and heterpolor bond dissociation energy and heat of formation of radicals and ions in the gas phase. I. Data on organic molecules . Helvetica Chimica Acta, 56,5, Nr. 148-149, 1516-1536. (1973)... 

From ion-efficiency curves, the ionization potential of M and the splitting potentials of the fragments can be obtained and in turn, bond-dissociation energies and heats of formation of gas-phase ions can be obtained from the ionization potentials [13]. 

BOND DISSOCIATION ENERGIES AND HEATS OF FORMATION OF FREE RADICALS... 

Egger, K.W. Cocks, A.T. Homopolar-and Heteropolar Bond Dissociation Energies and Heats of Formation of Radicals and Ions in the Gas Phase I. Data on Orgarric Molecules. Helv. Chim. Acta 1973,56, 1516-1536. 

Compounds with Elements of Group V. An effusion-mass spectrometric study has afforded values of 380 + 20 and 450 + 20 kJ mol - respectively, for the dissociation energy and heat of formation at 298 K of CrN(g).59 X-Ray crystallographic data have been determined for TiCrAs and the metal-metal bonding in this and other NiAs-related structures has been discussed.60 The thermodynamic properties of... 

The bond dissociation energies that follow are taken from the review of McMillan and Golden [Ann. Rev. Phys. Chem. 33, 493 (1982)]. The reader should refer to this publication for the methods of determining the values presented, their uncertainty, and the original sources. In the tables presented, all bond energies and heats of formation are in kJ/mol. The values listed in the first column are the heats of formation at 298 K for the reference radical and those above the column heading for the associated radical. Thus, the tables presented are not only a source of bond energies, but also of heats of formation of radicals. 

The mass spectrum of FClOs was measured (82, 138, 234). The vertical ionization potential ahd the F—ClOg bond dissociation energy were found to be 13.6 0.2 eV and 60 kcal mole , respectively. The average CIO bond dissociation energy and the heat of formation were estimated (82) to be 60 and —5.3 kcal mole", respectively. 

Of fundamental importance to free-radical chemistry are bond dissociation energies and radical heats and entropies of formation. Bond dissociation energy is defined as the energy required to break a particular bond to form two radicals. More precisely, bond dissociation energy of the R—X bond, D(R—X), is the enthalpy change of Reaction 9.7.37... 

Radical heats of formation are defined in the usual way, that is, as enthalpy of formation of the radical in question from the elements in their standard states. The heats of formation and the bond dissociation energies are derivable from each other and are based on the same data. Thus, in Reaction 9.7, the heat of formation of R- is readily found from the bond dissociation energy by means of the enthalpy cycle shown in Scheme 3 if heats of formation of R—X and X are known conversely, D( R—X) may be found once heats of formation of RX, R-,... 

Table 9.3 Selected Bond Dissociation Energies and Radical Heats of Formation at 25°C (kcal mole-1)0...

Tables 9.3 and 9.4 list selected bond dissociation energies and radical heats of formation. Note particularly that the decrease in energy required to remove hydrogen in the series methane, primary, secondary, tertiary, parallels increasing radical stability, and that aldehydic, allylic, and benzylic hydrogens have bond dissociation energies substantially lower than do alkyl hydrogens.

Calculate ArxnH° for the reaction 2CO + 02 —> 2C02 from generic bond dissociation energies and compare with the value obtained from heats of formation in Problem 4. 

To convert the steric energy to heat of formation, terms can be added depending on the number and types of bond present in the molecule. This again rests on the assumption of transferability, e.g. all C-H bonds have a dissociation energy close to lOOkcal/mol. A heat of formation parameter can be assigned to each bond type, and the numerical... 

The free radical formation and propagation process usually occur with the dissociation of the weaker bonds. Besides the weaker bonds, other bonds also can be dissociated, which happens mainly when there are small differences between the bond dissociation energies. The strength of the bond being broken is not always known, and in some cases can be derived from tabulated heats of formation as shown in Section 2.2. 

We also examined the energy dependence of the cross sections for CID of SF+ (n = 1 to 5) with Xe (Fisher et al., 1992). Analysis of these cross sections yielded the 0-K bond-dissociation energies (BDEs) listed in Table VI. Experimental values in the literature (Chase et al., 1985 Lias et al., 1988) prior to our study had large error bars, but subsequent photoionization studies by Ng and coworkers (Cheung et al., 1995) probably provide the most accmate heats of formation for SFj, SFj, and SF4 that are presently available. The heat of formation for SF has been measured by the same group using a sophisticated photoelectron-photoion coincidence experiment (Evans et al., 1997). BDEs calculated using these values and heats of formation for S+ and SF " from... 

Much of the available thermodynamic data, snch as bond dissociation energies, gas-phase acidities and basicities, and heats of formation for ions and neutral target species, has been determined nsing TCID [37, 38]. These data inclnde a variety of metals (alkalis, magnesitrm, altrmintrm, and first and second row transition metals), and many types of target molectrles. For instance, Armentront [39] stndied an abso-Inte cation affinity scale, thermochemistry of alkali-metal cation interactions with histidine,and host-gnest interactions of crown ethers with alkali ions nsing TCID. 

The result from a HF-SCF-LCAO computation includes information on the equilibrium geometry of the molecule in addition to thermodynamic information such as total energy of the molecule, heats of formation, and bond dissociation energy. The results of some HF-SCF-LCAO computations are shown in Tables 9-i and 9-5. 

The heats of formation of the gaseous atoms, 4, are not very different clearly, it is the change in the bond dissociation energy of HX, which falls steadily from HF to HI, which is mainly res ponsible for the changes in the heats of formation. 6. We shall see later that it is the very high H—F bond energy and thus the less easy dissoeiation of H—F into ions in water which makes HF in water a weak aeid in comparison to other hydrogen halides. 

Emphasis was put on providing a sound physicochemical basis for the modeling of the effects determining a reaction mechanism. Thus, methods were developed for the estimation of pXj-vahies, bond dissociation energies, heats of formation, frontier molecular orbital energies and coefficients, and stcric hindrance. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

You have seen that measurements of heats of reaction such as heats of combustion can pro vide quantitative information concerning the relative stability of constitutional isomers (Section 2 18) and stereoisomers (Section 3 11) The box in Section 2 18 described how heats of reaction can be manipulated arithmetically to generate heats of formation (AH ) for many molecules The following material shows how two different sources of thermo chemical information heats of formation and bond dissociation energies (see Table 4 3) can reveal whether a particular reaction is exothermic or en dothermic and by how much... 

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