Thermochemical properties approximation

The next higher order of approximation, the first-order approximation, is obtained by estimating molecular properties by the additivity of bond contributions. In the following, we will concentrate on thermochemical properties only. 

Lee, A., C. K. Law, and A. Makino. 1989. Aerothermochemical studies of energetic liquid materials 3. Approximate determination of some thermophysical and thermochemical properties of organic azides. Combustion Flame 78 263-74. 

The chemical compositions and thermochemical properties of representative NC-NG and NC-TMETN double-base propellants are compared in Table 4.9. Though the NC/NG mass ratio of 0.80 is much smaller than the NC/TMETM mass ratio of 1.38, the combustion performance in terms of Tf and Mg is seen to be similar, and 0 is 109 kmol K kg for both propellants. In the case of rocket motor operation, Igp and pj, are also approximately equivalent for both propellants. 

Fig. 6.18 shows a typical comparative example of the burning rates of two propellants composed of NC-TMETN and NC-NG. The chemical compositions (% by mass) and thermochemical properties are shown in Table 6.5. The energy densities of these two propellants are approximately equivalent. 

As evidenced by diverse chapters in the current volume and other reviews, interest in enamines has been dominated by the convenience and versatility of their numerous synthetic applications As such, numerous enamines have been prepared and their reaction chemistry studied and enjoyed. Regrettably, by contrast, enamines have not particularly attracted the attention of the thermochemical community few enthalpies (heats) of formation (AJ/f) have been reported for enamines, and essentially no other thermochemical properties such as entropies (either S° or ASf), heat capacities (Cp) and phase change enthalpies have been reported. In this chapter we will concern ourselves primarily with enthalpies of formation, and thus the derived concepts of resonance and strain energies. Only occasionally will we employ the long known Gibbs free energy (AG), two accompanying identities (equations 1 and 2) and a commonly employed approximation (equation 3) for its use. 

Recent advances in computational chemistry have made it possible to calculate enthalpies of formation from quantum mechanical first principles for rather large unsaturated molecules, some of which are outside the practical range of combustion thermochemistry. Quantum mechanical calculations of molecular thermochemical properties are, of necessity, approximate. Composite quantum mechanical procedures may employ approximations at each of several computational steps and may have an empirical factor to correct for the cumulative error. Approximate methods are useful only insofar as the error due to the various approximations is known within narrow limits. Error due to approximation is determined by comparison with a known value, but the question of the accuracy of the known value immediately arises because the uncertainty of the comparison is determined by the combined uncertainty of the approximate quantum mechanical result and the standard to which it is compared. 

Different ab initio methods can be characterized by their treatment of electron-electron interactions, called electron correlation. The first practical ab initio method was the HF (Hartree-Fock) method, which treats each electron as if it exists in a nniform field made from the total charge and space occnpied by the other electrons. This treatment is only an approximation to the interactions between electrons as point charges in a dynamics system and exclndes the contribution of excited electronic configurations. This neglect of electron correlation can lead to significant error in determining thermochemical properties. 

The thermochemical property that best reflects the reactivity or stability of a radical cation in solution is the one-electron reduction potential, E°. The corresponding gas-phase property is the ionization potential, IP, of the corresponding neutral molecule. The latter can be considered as the intrinsic solvent independent one-electron reduction potential of the radical cation. The solvent independent ionization potential and the solvent dependent one-electron reduction potential are approximately related via equation (3) where the constant, 4.44 ( 0.02) eV,[23] is the absolute potential of the hydrogen electrode in water. [24]... 

Kinetic interpretation of the recombination portion of the [OH] profile proceeds by means of the partial equilibrium approximation, by which the course of change of the entire system composition with recombination is computed, using the measured shock wave speed and initial gas composition and known thermochemical properties of the expected species. To place the progress of recombination in perspective, the change in N from its original value of unity to the value at full equilibrium, A, is reckoned in terms of the normalized progress variable defined as... 

To our knowledge, only two applications of these techniques have been made to industrial reaction problems. The Chioda Chemical Engineering and Construction Company in Tokyo, Japan has used a program called CHEMONICS in which known specific reactions numbering approximately 100 are stored. The thermochemical properties, and in some cases kinetic parameters, are known for these reactions. The reactions are mixed and matched by the user with the program performing the analysis of the reaction network. 

Zeleznik and Gordon [77] invented the method of simultaneous regression of the thermochemical properties so that more than one property can be approximated by a single polynomial. This work ended up with the famous NASA seven-term polynomials first published by Zeleznik and Gordon [77] and McBride et al. [15], which cover heat capacity Cp, enthalpy, and entropy. 

The kinetic method is an approximate scheme to determine relative thermochemical properties based on the rates of competitive dissociation of mass-selected cluster ions. As an example, consider the proton-bound dimer system ... 

The molecular calculations [550,560] allow us to conclude that the DKH approximation in combination with hybrid DFT functionals provides a reliable tool for the prediction of structural and thermochemical properties of molecules. 

Standard enthalpies of formation of bis(dithiocarbamato)nickel(II) complexes were also reported2019 and the results indicate that Ni—O and Ni—S bond energies in square planar nickel complexes are approximately the same from a thermochemical point of view. The electron-transfer properties of various dithiocarbamato and diselenocarbamato complexes were investigated by voltammetric techniques.2020,2021 The observed processes were found to be irreversible. 

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