Energies and heats of formation

There is a certain sense of incongruity in speaking of heats of formation of species which are not at a temperature. Nevertheless, it is common practice to do so with gaseous ions. The tabulated heats of formation presented as values either at 0 or 298 K are intended, however, to refer to gaseous ions at these temperatures [713]. Gaseous ions characterised by temperatures are found in some ion—molecule studies [497], but, as already discussed, not in unimolecular studies. 

For the purposes of unimolecular studies, what ideally needs to be known about ions is the energy of formation at 0 K, the total vibrational energy and the rotational energy. It is important that the vibrational and rotational energies be distinguished, since their roles in unimolecular reactions are not completely equivalent (Sect. 2.3). 

Mass spectrometry is typically a flow experiment in that molecular ions are being continuously formed and are continuously reacting and it is ion currents or count rates which are measured. The molecular ions may be formed according to some sequence of pulses, but the essential situation remains the same. Generally, the molecular ions are formed at some more or less well-defined position in space and the lifetimes, t, of ions correlate with transport of the ions away from their position of formation through the analysers and towards the detector. 

Consider the simplest case of a molecular ion which is not prone to isomerisation prior to decomposition and consider an ideal instrument in which all ions are collected and detected with perfect efficiency. If JVq is the number (per time) of molecular ions formed with a discrete amount of internal energy Ej, the rate of decomposition — dN/dt is given by 

Equation (3) is valid provided internal energy is randomised. N is the number (per time) of molecular ions remaining undecomposed at time t and k(El) is the rate coefficient for decomposition of molecular ions with internal energy Uj. Equation (3) applies to the case of a single reaction. If the molecular ion undergoes n parallel reactions, the rate of disappearance of molecular ions becomes 

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Figure 2.14 Illustrating the difference between steric energy and heat of formation...

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. 

Adapted from the literature review by Sousa, Fernandes, and Ramos.5 Atomization energies, binding energies, and heats of formation are reported per molecule. 

Table 1 Resonance energies and heats of formation for compounds 27-31...

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... 

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... 

P. Politzer, P. Lane, M. E. Grice, M. C. Concha, P. C. Redfem, Comparative Computational Analysis of Some Nitramine and Difluoramine Structures, Dissociation Energies and Heats of Formation, J. Mole. Struct. (Theory), 338 (1995) 249-256. 

Diverse TB drugs and natural products 24 42 Forward feed MLR gave a cross-validated R=0.72 with dielectric energy and heats of formation contributing to activity Dwivedi et al. (39)... 

Equilibrium configuration of some Y-junctions of twig type is defined and in the frames of semi empirical method PM3 total energy and heat of formation is calculated and their electronic structure is also defined. 

To obtain the free energy and heat of formation from S, (gas), 40.9 and 90.3 kJ, respectively, must be added for each atom of sulfur in the compound. 

Figure 2.14 Illustrating the difference between steric energy and heat of formation — fitting is done to reproduce the crystal or solution phase data. Furthermore, it is possible ...

The free energies and heats of formation and the entropies of the various species are as follows (see Tables V, XV, XIX, XXIV and XL) ... 

The solubility of silver chloride in pure water is 1.314 X 10 molal, and the mean ionic activity coefficient is then 0.9985 [Neuman, J. Am. Chem. Soc., 54, 2195 (1932)]. The heat of solution of the salt is 15,740 cal. mole". Taking the entropy of solid silver chloride as 22.97 e.u. mole ", and using the results of the preceding exercise, calculate the standard free energy and heat of formation and the entropy of the Cl" ion at 25 C. 

Assuming the heats of formation to remain approximately constant in the range from 25 to 30 C, calculate the ionic product of water at theee two temperatures, using standard free energy and heat of formation data only. 

TABLE 5." STANDARD FREE ENERGIES AND HEATS OF FORMATION (iN KCAL. MOLB ) AND ENTROPIES (iN CAL. DEO. MOLE" ) AT 25 C f... 

Extensive tables of entropies, free energies, and heats of formation are to be found in Chap. 25 of the Hougen, Watson and Ragatz book. 

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)... 

Table X.—Free Energy and Heats of Formation of Some Lead Oxides.

The C-H and N-H deprotonation of pyridazine (92MI5, 92ZOB2319) and its methyl derivatives were calculated by INDO and AMI methods (92ZOB2100). The AMI method was also used to calculate the aromatiza-tion energy and heats of formation of pyridazine [89H(28)1135]. 

Thermodynamic functions for the electron in liquid ammonia (relative to H" ) have been calculated by Jolly [86]. The free energy and heat of formation at 298°K are 46.0 and 37.5 kcal mole , respectively. The entropy of formation is —13.0 cal °K mole". It is possible to calculate that the equilibrium constant for the reaction... 

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