Enthalpy calculation methods

A few compounds wili be chosen to test the method with various types of structures. Compounds wiil be chosen for which enthalpy can, for the purpose of comparison, be found in the tables and the enthalpy calculated in the liquid state oniy when this value is needed to be known. 

So far we have not touched on the fact that the important topic of solvation energy is not yet taken into account. The extent to which solvation influences gas-phase energy values can be considerable. As an example, gas-phase data for fundamental enolisation reactions are included in Table 1. Related aqueous solution phase data can be derived from equilibrium constants 31). The gas-phase heats of enolisation for acetone and propionaldehyde are 19.5 and 13 keal/mol, respectively. The corresponding free energies of enolisation in solution are 9.9 and 5.4 kcal/mol. (Whether the difference between gas and solution derives from enthalpy or entropy effects is irrelevant at this stage.) Despite this, our experience with gas-phase enthalpies calculated by the methods described in this chapter leads us to believe that even the current approach is most valuable for evaluation of reactivity. 

The different solvation energetics of R and R- will also lead to errors in the bond dissociation enthalpies calculated with equation 16.33. For instance, in the case of phenol, whose interactions with proton-acceptor solvents (like DMSO) are obviously stronger than those for the phenoxy radical, a negative correction should be applied to the value of Z)//°(PhO-H) calculated from equation 16.33 (see also equation 16.32). It is probably unwise to ascribe the 7 kJ mol-1 difference between the electrochemical and the recommended DH° (PhO—R) value to the differential solvation effects. Although this discrepancy is in the correct direction, it lies within the suggested uncertainty of the method. 

Figure 16.9 The ratio of the effective calorimetric enthalpy to the enthalpy calculated by the van t Hoff method from optical measurements, plotted against the temperature of denaturation. The symbols represent the following proteins , metmyoglobin A, ribonuclease O, cytochrome c O, a-chymotrypsin , lysozyme. Reproduced by permission from P. L. Privalov, Adv. Prot. Chem., 33, 167 (1979).

Valence tautomers, benzene oxide 1 and oxepine 2 (Equation 1), as well as relative tautomeric systems, benzene sulfide-thiepine and o-xylene-2,7-dimethyloxepine, have been studied by a post-Hartree-Fock (HF) ab initio QCISD(r)/6-31G //MP2/6-31G method. In particular, the enthalpy calculated for a benzene oxide-oxepine system is 0.59 kj moF1 <1997PCA3371>. The calculated molecular orbital (MO) energies are in linear relationship to those from the photoelectron (PE) spectra <1996JCF1447>. Barrier to tautomerization for a benzene oxide-oxepine system is 29.4 kj mol-1. Protonation stabilizes the oxide form versus the oxepine <1997PCA3371>. 

The net adsorption enthalpies and the predicted sublimation enthalpies (see Method 1) were used to calculate the adsorption enthalpies of transactinides on selected metal surfaces (Method 11). The metals, which are presented in Table 4, can be used as stationary phase in gas adsorption chromatographic experiments for selective gas chemical separations or, in the case of high adsorption interaction, as strong fixation materials for the sample preparation in the measurement of transactinides. 

Write and solve an energy balance on a chemical reactor using either the heat of reaction method (taking reactant and product species as references for enthalpy calculations) or the heat of formation method (taking elemental species as references), and specify which method is preferable for a given process. Write the process path implicitly adopted when each method is used. 

Two methods are commonly used to choose reference states for enthalpy calculations and to calculate specific enthalpies and AW. We outline the two approaches below, using a propane combustion process to illustrate them. For simplicity, the material balance calculations for the illustrative process have been performed and the results incorporated into the flowchart. 

Choose reference states for enthalpy calculations. (This is the step that distinguishes the preceding method from this one.) The choices should be the elemental species that con-... 

The heat of formation method, which involves taking elemental constituents of the reactants and products in their naturally occurring states as references for enthalpy calculations, is usually convenient for processes that involve several simultaneous reactions. TTie next example illustrates this approach. 

Calculational methods for the accurate determination of thermodynamic parameters (particularly for solution-phase calorimetry) have only recently become available through the BCHMP chemical test and reference reaction. It is likely therefore that values reported for enthalpy, for example, are likely to be significantly in error for some of the earlier work using flow calorimetry. These errors can be rectified, however, through the calculation of the thermal volume and relevant adjustment of the calorimetric data. 

The Kesler-Lee correlations for liquid and vapour phase heat capacities of petroleum fluids are used for estimating the respective enthalpies at temperatures of interest. The Lee-Kesler corresponding-states method is used for obtaining estimates of the heats of vaporization and for developing the saturation envelope enthalpies. This method uses the Curl and Pitzer approach and calculates various thermodynamic properties by representing the compressibility factor of any fluid in terms of a simple fluid and a reference fluid as follows ... 

The molecular composition of sulfur vapor is much more complex than had been thought by all authors before the year 1990. Not only the molecular size can vary between 2 and—at least—10, but there are cyclic and chain-Hke isomers as well as branched rings and chains and even clusters to be taken into account. This makes experimental investigations rather difficult. However, the reaction enthalpies calculated by the most sophisticated ab initio MO methods (Table 5) are in good agreement with the most rehable experimental data obtained by mass spectrometry and vapor pressure measurements (Table 1, column 5). 

To calculate the free enthalpy of an ion, we need to know its symmetry number and its intrinsic free enthalpy. The symmetry number can be calculated methodically and algorithmically. The intrinsic free enthalpy is obtained from the assumptions of the single-events theory. For an ion, the intrinsic free enthalpy calculations involve two parameters ... 

Thus the integral is verihed to agree with the total enthalpy calculation. Although only is used in the integral method of calculation, information about Hp and the molar of the mixture are implied in and can be explicitly revealed by integrating to yield and subsequently adding the two partials to obtain the molar of the mixture. 

Recently, establishment of the equilibrium between all three isomers 1-3 has been followed in the gas phase from each individual isomer, and the activation parameters and reaction enthalpies, given in Table 5 for the individual steps, have been deduced125. Differences in experimental activation enthalpies are in good agreement with reaction enthalpies, calculated by force-field methods. 

Table V shows the computations by Hwu for FT — H in a methane-propane mixture in comparison with the predictions of Mollerup (16,17, 18) using the VDW one-fluid theory with shape factors. The improvement of the HSE method is very slight. The theoretical advantages of the HSE method for enthalpy calculations may be offset here by using a generally poorer reference equation of state than that used by Mollerup.

Table 16.10 Experimental data on sublimation of Sn02 in Langmuir and Knudsen studies [22] and the molar enthalpies calculated by the third-law method... 

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