Enthalpy estimation from

Table 4.5. Average values (kJ/mol) of the metal—metal bond enthalpies estimated from metal carbonyls (Mco) and from bulk metals (Mmet) (adapted from Mingos and Wales (1990)).

This number of enthalpies estimated from infrared frequency shifts agree with these parameters. 

Figure 2 shows similar results for ethanol(1)-n-hexane(2) at 1 atm. The liquid-phase enthalpy of mixing was again estimated from UNIQUAC using temperature-independent parameters. 

Because these various quantities are characteristics of the reactants and products but are independent of the reaction path, they cannot provide insight into mechanisms. Information about AG, AH, and AS does, however, indicate the feasibility of any specific reaction. The enthalpy change of a given reaction can be estimated from tabulated thermochemical data or from bond-energy data such as those in Table 1.3 (p. 14) The exan le below illustrates the use of bond-energy data for estimating the enthalpy of a reaction. 

It should be noted that the experimental activation enthalpy for the Diels-Alder reaction is 33 kcal/mol (estimated from the reverse reaction and the experimental reaction energy i.e. the MP2/6-31G(d) value is 14kcal/mol too low. Similarly, the calculated reaction energy of —47 kcal/mol is in rather poor agreement with the... 

It is concluded [634] that, so far, rate measurements have not been particularly successful in the elucidation of mechanisms of oxide dissociations and that the resolution of apparent outstanding difficulties requires further work. There is evidence that reactions yielding molecular oxygen only involve initial interaction of ions within the lattice of the reactant and kinetic indications are that such reactions are not readily reversed. For those reactions in which the products contain at least some atomic oxygen, magnitudes of E, estimated from the somewhat limited quantity of data available, are generally smaller than the dissociation enthalpies. Decompositions of these oxides are not, therefore, single-step processes and the mechanisms are probably more complicated than has sometimes been supposed. 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

Figure 19.3 Estimates of temperature-enthalpy profiles from existing exchanger heat duties and temperature.

The chemistry of carbenes in solution hits been extensively studied over the past few decades.1-5 Although our understanding of their chemistry is often derived from product analyses, mechanistic details are often dependent on thermodynamic and kinetic data. Kinetic data can often be obtained either directly or indirectly from time-resolved spectroscopic methods however, thermochemical data is much less readily obtained. Reaction enthalpies are most commonly estimated from calculations, Benson group additivities,6 or other indirect methods. 

Fluorobromates(V) have been isolated recently (97). Their enthalpies can be estimated from the equivalences... 

There appear to be no enthalpies of solution of rare-earth tribromides published in the available literature.2 However, Bommer and Hohmann reported a value of -230.5 kj mol-1 (at 20°C) for the enthalpy of solution of scandium tribromide in water (180). This value may be compared with -197.1 kj mol-1 for the chloride, and an estimate (from the published Lnl3 series, q.v.) of —240 to -250 kj mol-1 for the iodide. The markedly more negative values for the heavier ha-... 

Taken from NIST Chemistry Webbook. b Estimated from CH2(CN)2 adding -7 kcal/mol (exchange of a CH2 group by a CHMe group). c Enthalpy difference indicates a destabilization effect for gem-disubstitution with respect to alkanes. d Enthalpy difference shows a stabilization effect for gem-dialkoxy-disubstitution with respect to alkanes. c Enthalpy difference shows increases of enthalpic anomeric effect for tertiary acetals compared to secondary acetals. 

The pressure effect on the enthalpy of liquid ethanol can be estimated from equation 2.15, now written in terms of the coefficient of thermal expansion, a ... 

The enthalpy changes associated with proton transfer in the various 4, -substituted benzophenone contact radical ion pairs as a function of solvent have been estimated by employing a variety of thermochemical data [20]. The effect of substituents upon the stability of the radical IP were derived from the study of Arnold and co-workers [55] of the reduction potentials for a variety of 4,4 -substituted benzophenones. The effect of substituents upon the stability of the ketyl radical were estimated from the kinetic data obtained by Creary for the thermal rearrangement of 2-aryl-3,3-dimethylmethylenecyclopropanes, where the mechanism for the isomerization assumes a biradical intermediate [56]. The solvent dependence for the energetics of proton transfer were based upon the studies of Gould et al. [38]. The details of the analysis can be found in the original literature [20] and only the results are herein given in Table 2.2. 

Very few directly measured experimental enthalpies are available for methyl radical additions to substituted ethylenes. Reaction enthalpies are therefore normally estimated from other known thermochemical quantities (e.g. C-H BDEs), which often have considerable uncertainties [3], and the derivation generally involves the use of additivity approximations [42, 45], Therefore, theory may be able to provide more accurate values for these enthalpies. Tables 6.25 and 6.26 present reaction enthalpies determined at several levels of theory and compared with the experimental estimates. 

Usable equilibrium constants were obtained only for Ar = p-CHs, m-CHs (i.e. p-Tol and w -To1) and p-Ph and were reported for approach to equilibrium from both the left and right sides of the equation with equimolar concentrations of reactants. The averaged A obsd values are 0.64, 0.86 and 3.78, respectively. The corresponding values of AH, estimated from equation 13 are 1.1, 0.37 and —3.3 klmoP. From equation 11, the enthalpy of formation of p-tolyl lithium is calculated to be ca 3 klmoP where the enthalpy of formation of p-tolyl bromide is 12.1 kJmor, as suggested in Reference . The enthalpy of formation value for p-tolyl lithium derived here is nearly identical to that in Table 1. Unfortunately, there is no measured enthalpy of formation of m-tolyl bromide. However, the difference between the enthalpies of formation of phenyl bromide and phenyl lithium (9.8 kJmoU ) must be about the same as the difference between the enthalpies of formation of the m-tolyl bromide and the m-tolyl lithium when the reaction is thermoneutral for equation 12. 

Except for the direct van t Hoff method, the enthalpies of dihydrogen bonds can be estimated from the frequency shifts, Av (HX), or the integral intensity, A (XH), determined in the IR spectra for proton-donor components, HX ... 

As a general rule, it can be stated that all elements with electronegativity in the range 1.35-1.82 do not form stable hydrides [34]. Exemptions are vanadium (1.45) and chromium (1.56), which form hydrides, andmolybdenum (1.30) and technetium (1.36), where hydride formation would be expected. The adsorption enthalpy can be estimated from the local environment of the hydrogen atom on the interstitial site. 

Interestingly, the standard entropies (and in turn heat capacities) of both phases were found to be rather similar [69,70]. Considering the difference in standard entropy between F2(gas) and the mixture 02(gas) + H2(gas) taken in their standard states (which can be extracted from general thermodynamic tables), the difference between the entropy terms of the Gibbs function relative to HA and FA, around room temperature, is about 6.5 times lower than the difference between enthalpy terms (close to 125 kJ/mol as estimated from Tacker and Stormer [69]). This indicates that FA higher stability is mostly due to the lower enthalpy of formation of FA (more exothermic than for HA), and that it is not greatly affected by entropic factors. Jemal et al. [71] have studied some of the thermodynamic properties of FA and HA with varying cationic substitutions, and these authors linked the lower enthalpy of formation of FA compared to HA to the decrease in lattice volume in FA. 

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