Bond dissociation energies equation

Bond dissociation energies have also been obtained (Table 3.3) from calorimetric measurements of the heat of protonation of neutral complexes with CF3SO3H in dichlo-roethane. These heats correlate linearly with differences in pK (even differences in pK in another solvent, CH3CN) and thus can be used along with measured electrochemical potentials to estimate bond dissociation energies (Equation 3.127). 

A variety of new reaction pathways are made possible by the ability of the aromatic ring to reduce bond-dissociation energies (Equations 4.41 and 8.81), stabilize the ion and radical sites, and provide an unsaturated site for rearrangement, displacement, and elimination reactions (Equations 4.36, 8.110, 8.122, 8.123). As an example of Equation 4.36, (M — CHjCO)" " is a peak characteristic of aryl acetate spectra (CgHgO" is the base peak in the spectrum of CgHsOCOCHa). 

The same conclusion is reached using bond dis sociation energies The following equation shows the bond dissociation energies of the reactants and prod ucts taken from Table 4 3... 

Compare chlorination of methane with lodina tion The relevant bond dissociation energies are given in the equation... 

This seems reasonable when we think only in terms of normal vibrations, but intuition suggests that, since the dissociation in Equation (6.90) would require something like six times the C—H bond dissociation energy ca 6 x 412 kJ mol ), the process... 

The latter equation contains constants with well-known values and can therefore be used to predict the fracture stress of most polymers. For example, the bond dissociation energy Do, is about 80 kcal/mol for a C-C bond. For polystyrene, the modulus E 2 GPa, A. 4, p = 1.2 g/cm, = 18,000, and we obtain the fracture stress, o A1 MPa, which compares well with reported values. Polycarbonate, with similar modulus but a lower M. = 2,400 is expected to have a fracture stress of about 100 MPa. In general, letting E 1 GPa, p = 1.0 g/cm, and Do — 335 kJ/mol, the tensile strength is well approximated by... 

As with the Marcus-Hush model of outer-sphere electron transfers, the activation free energy, AG, is a quadratic function of the free energy of the reaction, AG°, as depicted by equation (7), where the intrinsic barrier free energy (equation 8) is the sum of two contributions. One involves the solvent reorganization free energy, 2q, as in the Marcus-Hush model of outer-sphere electron transfer. The other, which represents the contribution of bond breaking, is one-fourth of the bond dissociation energy (BDE). This approach is... 

The validity of equation (12) has been checked for several families of alkyl halides for which D and E /x- are known (Ref. 32, see particularly figure 6 therein). It was thus found that for v = 0.1 V s the constant is equal to 0.3 eV at 20°C (expressing D in eV and the potentials in V). Equation (12) was then applied to the approximate determination of unknown BDEs in several series of compounds undergoing dissociative electron transfer, namely, TV-halosultams,32 sulfonium cations,33 vicinal dihalides,34 1,3-dihaloadamantes, 1,4-dihalo-bicyclo[2.2.2]octanes, and l,3-dihalobicyclo[l.l.l]pentanes.35 In the latter case, the mutual influence of the two halogens could be rationalized thanks to the conversion of the peak potential data to bond dissociation energies. 

The empirical correlation equation for re as a function of the bond dissociation energy Z>xy. difference in electronegativity AEAxy f°r the radical reaction abstraction of the type... 

The coordinate pertaining to solvent reorganization, z, is the same fictitious charge number as already considered in the Hush-Marcus model of outer-sphere electron transfer (Section 1.4.2), and so is the definition of 2q [equation (1.27)] and the difference between the Hush and Marcus estimation of this parameter. The coordinated describing the cleavage of the bond is the bond length, y, referred to its equilibrium value in the reactant, yRX. Db is the bond dissociation energy and the shape factor ft is defined as... 

The reaction enthalpy and thus the RSE will be negative for all radicals, which are more stable than the methyl radical. Equation 1 describes nothing else but the difference in the bond dissociation energies (BDE) of CH3 - H and R - H, but avoids most of the technical complications involved in the determination of absolute BDEs. It can thus be expected that even moderately accurate theoretical methods give reasonable RSE values, while this is not so for the prediction of absolute BDEs. In principle, the isodesmic reaction described in Eq. 1 lends itself to all types of carbon-centered radicals. However, the error compensation responsible for the success of isodesmic equations becomes less effective with increasingly different electronic characteristics of the C - H bond in methane and the R - H bond. As a consequence the stability of a-radicals located at sp2 hybridized carbon atoms may best be described relative to the vinyl radical 3 and ethylene 4 ... 

---