Energy formation enthalpy

A variant on this procedure produces a first approximation to the molecular mechanics (MM) heat paiameters (Chapters 4 and 5) for C—C and C—H. Instead of atomization energies, the enthalpies of formation of propane and butane (—25.02 and —30.02 kcal mol ) are put directly into the b vector. The results (2.51 kcal mol and —3.76 kcal mol ) are not very good approximations to the heat parameters actually used (2.45 kcal mol and —4.59 kcal mol ) because of other factors to be taken up later, but the calculation illustrates the method and there is rough agreement. 

By systematically applying a series of corrections to approximate solutions of the Schroedinger equation the Pople group has anived at a family of computational protocols that include an early method Gl, more recent methods, G2 and G3, and their variants by which one can anive at themiochemical energies and enthalpies of formation, Af and that rival exper imental accuracy. The important thing... 

First, we would like to ehange the reference state from the isolated nuelei and eleetions to the elements in their standard states, C(graphite) and H2(g) at 298 K. This leads to the energy of formation at 0 K AfEo, whieh is identieal to the enthalpy of formation AfHo at 0 K. The energy and enthalpy are identieal only at 0 K. Next we would like to know the enthalpy ehange on heating propene from 0 to 298 K so as to obtain the enthalpy of formation from the isolated nuelei and eleetions elements This we will eonvert to from the elements in their standard... 

The stmcture of DPXN was determined in 1953 from x-ray diffraction studies (22). There is considerable strain energy in the buckled aromatic rings and distorted bond angles. The strain has been experimentally quantified at 130 kj/mol (31 kcal/mol) by careful determination of the formation enthalpy through heat of combustion measurements (23). The release of this strain energy is doubtiess the principal reason for success in the particularly convenient preparation of monomer in the parylene process. 

Values for the free energy and enthalpy of formation, entropy, and ideal gas heat capacity of carbon monoxide as a function of temperature are listed in Table 2 (1). Thermodynamic properties have been reported from 70—300 K at pressures from 0.1—30 MPa (1—300 atm) (8,9) and from 0.1—120 MPa (1—1200 atm) (10). 

Table 23 contains the formation enthalpies for individual points of the potential energy hypersurface of the C4H9BF4 supermolecule, that is, a molecule which can be considered to be made up of the following components C2H, C2H4 and BF4. The same table provides further possibilities to divide the supermolecule C4HgBF4 into logical constituents. 

How do we determine the energy and enthalpy changes for a chemical reaction We could perform calorimetry experiments and analyze the results, but to do this for every chemical reaction would be an insurmountable task. Furthermore, it turns out to be unnecessary. Using the first law of thermodynamics and the idea of a state function, we can calculate enthalpy changes for almost any reaction using experimental values for one set of reactions, the formation reactions. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

Some experimental values for the formation enthalpy of Frenkel defects are given in Table 2.2. As with Schottky defects, it is not easy to determine these values experimentally and there is a large scatter in the values found in the literature. (Calculated values of the defect formation energies for AgCl and AgBr, which differ a little from those in Table 2.2, can be found in Fig. 2.5.)... 

Since the possible violence of reactions lies in the heat liberated and the temperature which may be reached, the energy change during the reaction has been selected to present the reaction safety in the ISI. This is a feasible approach since the formation enthalpies are known for most substances. 

Second law entropy free energy of formation free energy of reaction dependence of change in free energy on enthalpy and entropy changes... 

The ionic model, developed by Bom, Lande, and Lennard-Jones, enables lattice energies (U) to be summed from inverse square law interactions between spherically symmetrical charge distributions and interactions following higher inverse power laws. Formation enthalpies are related to calculated lattice energies in the familiar Bom-Haber cycle. For an alkali fluoride... 

The types of values reported in the database standard enthalpies of formation at 298.15 K and 0 K, bond dissociation energies or enthalpies (D) at any temperature, standard enthalpy of phase transition—fusion, vaporization, or sublimation—at 298.15 K, standard entropy at 298.15 K, standard heat capacity at 298.15 K, standard enthalpy differences between T and 298.15 K, proton affinity, ionization energy, appearance energy, and electron affinity. The absence of a check mark indicates that the data are not provided. However, that does not necessarily mean that they cannot be calculated from other quantities tabulated in the database. 

Summaries of G3X(MP3) and G3X(MP2) mean absolute deviations from experiment for the G3/99 test set of 376 energies are given in Table 3.4. The overall mean absolute deviations for G3X(MP3) and G3X(MP2) theories are 1.13 and 1.19 kcal/mol, respectively. These are improvements over G3(MP3) and G3(MP2), which have mean absolute deviations of 127 and 131 kcal/mol, respectively, for the same set of energies. For enthalpies of formation, the mean absolute deviations decrease from 1.29 to 1.07 kcal/mol [G3X(MP3)] and from 1.22 to 1.05 kcal/mol [G3X(MP2)]. Much of the improvement in enthalpies is due to non-hydrogen molecules, although other types of species also improve slightly or stay the same. The G3X(MP3) and G3X(MP2) methods save considerable computational time and have a reasonable accuracy. The ratio of the computational costs for G3X, G3X(MP3), and G3X(MP2) theories is approximately 52 1 for a molecule such as benzene. 

Miedema s model and parameters and prediction of compound formation capability. A semi-empirical approach to the evaluation of the compound formation capability and of the heats of formation of alloys was proposed by Miedema and co-workers. This resulted in a model which became very popular and, especially because there was scarcity of experimental data, was frequently used in the evaluation, even if approximate and several times incorrect, of the formation enthalpies. The model suggested for energy effects in alloys is well known essentially it is based on the definition of two parameters. By assigning two coordinates... 

Miedema s theory and structural information. The Miedema model for energy effects in alloys, presented in 2.2.1.3 has been very useful in an evaluation, albeit approximate, of the formation enthalpies and in the prediction of compound formation capability. For an example of the application and limits of this model, see the comments on the thermochemistry of the Laves phases reported in 3.9.3. However notice that the general usefulness of the Miedema approaches has diminished with time, both for its inherent approximation and for... 

Figure 5.8. Lanthanide Ln203 oxides (cubic cI80-Mn2O3 type, on the left side) and Pb alloys (LnPb3, cubic cP4-type, on the right). The trends of the lattice parameter and of the heat of formation are shown (see the text and notice the characteristic behaviour of Eu and Yb). A schematic representation of the energy difference between the divalent and trivalent states of an ytterbium compound is shown. Apromff represents the promotion energy from di- to trivalent Yb metal, A,//11, and Ar/Ynl are the formation enthalpies of a compound in the two cases in which there is no valence change on passing from the metal to the compound the same valence state (II or III) is maintained.

Fig. 1. Born-Haber cycle for the formation of solvated ions from an ionic crystal [M+X ]w. U lattice energy, Affsoiv. enthalpy of ion solvation...

Wiberg. K. B., Group equivalents for converting ab initio energies to enthalpies of formation, J. Comp. Chem. 5, 197 (1984). 

Tardy Y. and Viellard Ph. (1977). Relationships among Gibbs energies and enthalpies of formation of phosphates, oxides and aqueous ions. Contrib. Mineral. Petrol, 63 75-88. 

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