Heat-of-formation

The heat of formation for a reaction containing explosive chemicals can be described as the total heat evolved when a given quantity of 

Explosive substance Empirical formula percent weight 

The heat of formation is the energy released as heat when atoms situated at theoretically infinite distance approach, bind, and form the molecule of interest. The core includes, by definition, the atomic nucleus and the electrons that do not participate in chemical bonds, that is, the nonvalence electrons. The semiempirical method PM6 estimates the heat of formation as the sum of the total repulsion energy of the cores and the total heat of formation of the atoms. Each semiempirical quantum mechanics method calculates, in its own manner, the energy of repulsion of the cores and utilizes a different set of values for the atomic heat of formation. Consequently, the values of the heat of formation determined for the same molecule by different semiempirical 

The value of this descriptor depends on the number and type of atoms, and on the number and type of chemical bonds in the analyzed species. Accordingly, the heat of formation weighted by the number of atoms and the heat of formation weighted by the number of chemical bonds are also used as descriptors. 

The values of the diverse geometrical descriptors depend only on the type of atoms and on the Cartesian coordinates of these atoms in the minimum energy conformer. The type of a particular atom can be identified by the tabulated values of the atomic number, mass, or van der Waals radius. Often included in this category are descriptors whose value depends on other characteristics of atoms. For instance, topological indices are sometimes considered geometrical descriptors. However, topological indices can only be calculated after the identification of the way in which atoms are connected. 

The principal moments of inertia are simple geometrical descriptors defined as the sum of products of the atomic masses with the distance to the main rotation axis X. 

The three principal moments of inertia characterize the mass distribution in the analyzed molecule. The maximum and minimum values of the inertia moments, Im and allow the calculation of eccentricity (Arteca 1991), which is a measure of the deviation from the spherical shape. 

N2F4 (20.9 0.4 kcal/mol) and the heat of formation of NF2 (7.8 1.0 kcal/mol) [1]. This value differs from AH°298= 2.0 2.5 kcal/mol, which was determined by measuring the heat of reaction of N2F4 (only about 94% pure) with NH3 [2]. The latter value appears in the JANAF Tables [3]. AH 298= 5 kcal/mol was derived [4] from AH 298(NF3,g) = -31.75 kcal/mol [4] and Armstrong s [2] values of heats of reaction for NF3 and N2F4 with NH3. Semiempirical MO calculations (MNDO) gave AH°=-18.3 kcal/mol [5]. 

We shall recall that the enthalpy change for a process (e.g., a chemical reaction), AH, is equal to Ihe value of the heat absorbed or evolved when the process (e.g., reaction) takes place at a constant pressure  

We shall also recall that it is not possible to measure the absolute value of a thermodynamic property such as the enthalpy of a substance. 

Nevertheless, let s consider a hypothetical system in that it is assumed we know absolute enthalpies of substances at constant temperature and pressure, say, 

Those enthalpy values listed in the table are in fact not possible to measure. However, the enthalpy changes of the reactions discussed above can be obtained by measuring heats evolved or absorbed from the reactions. As we are more interested in enthalpy changes rather than absolute enthalpies, a new term called enthalpy of formation (AHJ) or heat of formation is introduced. 

The enthalpy of formation is defined as the enthalpy change for the reaction in which one mole of the substance is formed for the elements at the temperature of interest 

Chain Reactions in]. Nevertheless, the energy evolved depends only on the initial and final states and not on intermediate ones. Once the reaction is completed, the net heat evolved is exactly the same as if the reactant molecules were first dissociated into their atoms, and then reacted directly to form the final products (Hess Law). If a compd be formed directly from the atoms, the heat of atomization (Qa.) which was required to generate them from the molecules 

It might be interesting to note, that as early as 1780, it was shown by Fr scientists A.L. Lavoisier P.S. Laplace that the heat of formation is equal to the heat required to decompose a compound into its elements, which they called heat of decomposition. 

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S = Heat of sublimation of sodium D = Dissociation energy of chlorine / = Ionization energy of sodium = Electron affinity of chlorine Uq = Lattice energy of sodium chloride AHf = Heat of formation of sodium chloride. 

For pure organic materials, it is also possible to calculate the heating value starting from the heats of formation found in tables of thermodynamic data. The NHV is obtained using the general relation of thermochemistry applicable to standard conditions of pressure and temperature (1 bar and 25°C)) f 9j... 

For many purposes, for example the estimation of approximate heats of formation (p. 63), it is sufficient to have an average value. This average of the bond dissociation energies is called the average thermochemical bond energy or (more commonly) simply the bond energy. ... 

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. 

Investigations to find such additive constituent properties of molecules go back to the 1920s and 1930s with work by Fajans [6] and others. In the 1940s and 1950s lhe focus had shifted to the estimation of thermodynamic properties of molecules such as heat of formation, AHf, entropy S°, and heat capacity, C°. 

To summarize, such a scheme seems to be sirffident for the estimation of Cp° and S°, but does not give sufficiently accurate values for the heat of formation, AHf. 

Table 7-2 also contains, besides the values for heats of formation, values for... 

In order to develop a quantitative interpretation of the effects contributing to heats of atomization, we will introduce other schemes that have been advocated for estimating heats of formation and heats of atomization. We will discuss two schemes and illustrate them with the example of alkanes. Laidler [11] modified a bond additivity scheme by using different bond contributions for C-H bonds, depending on whether hydrogen is bonded to a primary (F(C-H)p), secondary ( (C-H)g), or tertiary ( (C-H)t) carbon atom. Thus, in effect, Laidler also used four different kinds of structure elements to estimate heats of formation of alkanes, in agreement with the four different groups used by Benson. 

Another scheme for estimating thermocheraical data, introduced by Allen [12], accumulated the deviations from simple bond additivity in the carbon skeleton. To achieve this, he introduced, over and beyond a contribution from a C-C and a C-H bond, a contribution G(CCC) every time a consecutive arrangement of three carbon atoms was met, and a contribution D(CCC) whenever three carbon atoms were bonded to a central carbon atom. Table 7-3 shows the substructures, the symbols, and the contributions to the heats of formation and to the heats of atomization. 

Inspection of the values for the structure elements and their contribution to the heats of formation again allows interpretation The B-terms correspond to the energies to break these bonds, and a sequence of three carbon atoms introduces stabihty into an alkane whereas the arrangement of three carbon atoms around a central carbon atom leads to the destabilization of an alkane. 

Table 7.3. The Allen scheme substructures, notations, and contributions to heats of formation and heats of atomization (values in kj/mol).

Any one of these additivity schemes can be used for the estimation of a variety of thermochemical molecular data, most prominently for heats of formation, with high accuracy [13]. A variety of compilations of thermochemical data are available [14-16]. A computer program based on Allen s scheme has been developed [17, 18] and is included in the PETRA package of programs [19]. 

Until now, we have discussed the use of additivity schemes to estimate global properties of a molecule such as its mean molecular polarizability, its heat of formation, or its average binding energy to a protein receptor. 

Heats of formation can be estimated with reasonable accuracy by additivity of group increments and corrections for ring effects. 

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. 

MINDO/3, MNDO, and AM 1 wxrc developed by the Dervar group at the University of i exasat Austin. This group ehose many parameters, such as heats of formation and geometries of sample molecules, to reproduce experimental quantities. The Dewar methods yield results that are closer to experiment than the CN DO and IN DO methods. 

M dlecular Formula Name Heat of Formation (experiment, kcal/mol) Heat of Formation (AM1, kcal/mol)... 

MIXDO/3 is the earliest of the Dewar methods. It provides more accurate geometries and heats of formation than CNDO or INDO. and has been used widely. The limitations of the INDO approximation, on which MI lhO/3 is based, frequently lead to problems of accuracy wdi cri dealing w i th m olecules con tain ing h eteroatorn s. 

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. 

HEAT OF FORMATION AND STRAIN ENERGY CALCULATIONS (UNIT=KCAUMOLE)... 

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