Thermodynamic calculations

HYBOT-Plus (hydrogen bonding thermodynamics, calculation of local and molecular physicochemical descriptors) http //www.timtec.net/soJiware/hybot-plus.htm... 

The techniques listed above are dynamical simulations. It is also possible to use bead interaction potentials for strictly thermodynamic calculations. For example, the following steps have been used for protein-folding problems ... 

After initial heating and equilibration, the trajectory may be stable for thousands of time points. During this phase of a simulation, you can collect data. Snapshots and CSV files (see Collecting Averages from Simulations on page 85) store conformational and numeric data that you can later use in thermodynamic calculations. 

Molality is used in thermodynamic calculations where a temperature independent unit of concentration is needed. Molarity, formality and normality are based on the volume of solution in which the solute is dissolved. Since density is a temperature dependent property a solution s volume, and thus its molar, formal and normal concentrations, will change as a function of its temperature. By using the solvent s mass in place of its volume, the resulting concentration becomes independent of temperature. 

Thermodynamic calculations for reactions forming carbon disulfide from the elements are compHcated by the existence of several known molecular species of sulfur vapor (23,24). Thermochemical data have been reported (12). Although carbon disulfide is thermodynamically unstable at room temperature, the equiHbtium constant of formation increases with temperature and reaches a maximum corresponding to 91% conversion to carbon disulfide at about 700°C. Carbon disulfide decomposes extremely slowly at room temperature in the absence of oxidizing agents. 

Both equations (2-28) and (2-29) are also extrapolatable above the critical temperature where necessary for thermodynamic calculations. 

Calculations Potential energy that can be released by a chemical system can often be predicted oy thermodynamic calculations. If there is little energy, the reaction stiU may be hazardous if gaseous produces are produced. Kinetic data is usually not available in this way. Thermodynamic calculations should be backed up by actual tests. 

To make the necessary thermodynamic calculations, plausible reaction equations are written and balanced for production of the stated molar flows of all reactor products. Given the heat of reaction for each applicable reaction, the overall heat of reaction can be determined and compared to that claimed. However, often the individual heats of reaction are not all readily available. Those that are not available can be determined from heats of combustion by combining combustion equations in such a way as to obtain the desired reaction equations by difference. It is a worthwhile exercise to verify this basic part of the process. 

Three conceptual steps can be discerned in the definition of the ionic structure of fluoride melts containing tantalum or niobium. Based on the very first thermodynamic calculations and melting diagram analysis, it was initially believed that the coordination numbers of tantalum and niobium, in a molten system containing alkali metal fluorides, increase up to 8. 

If there are no standard conditions or in the case where it is not be possible to measure the standard potential, the value can be determined by thermodynamic calculations (see Sec. 1.3.2). 

The conditions favorable for carbon formation from these sources can be predicted by straightforward thermodynamic calculations. However, because a number of other chemical reactions can occur simultaneously and... 

The relationships summarized in Table 3.1. expanded to include differences and molar properties, serve as the starting point for many useful thermodynamic calculations. An example is the calculation of AZ for a variety of processes in which p, V, and T are changed.e For any of the extensive variables Z = S, U, H, A or G, we can write... 

For thermodynamic calculations, gas-phase equilibria are expressed in terms of K but, for practical calculations, they may be expressed in terms of molar concentrations by using Eq. 12. 

At the moment there exist no quantum chemical method which simultaneously satisfies all demands of chemists. Some special demands with respect to treatment of macromolecular systems are, the inclusion of as many as possible electrons of various atoms, the fast optimization of geometry of large molecules, and the high reliability of all data obtained. To overcome the point 4 of the disadvantages, it is necessary to include the interaction of the molecule with its surroundings by means of statistical thermodynamical calculations and to consider solvent influence. 

The following example shows that the influence of statistical thermodynamical calculations on qualitative assertions is often insignificant. The reactions (3) <5) describe three of the first propagation steps of the cationic copolymerization of ethene and isobutene. 

There is also no significant influence of statistic thermodynamical calculations on the reaction parameters. That can be seen in the Tables 3 and 4. In Table 4 the calculated reaction enthalpies and free reaction enthalpies are faced with experimental values estimated by means of thermochemical methods. 

In summary, it can be pointed out that in our cases the great expense of statistical thermodynamical calculations yields only improvements in detail. For this reason they will be discussed in the following parts only in special cases. 

The changes in free energy of formation of Reaction (1) are shown in Fig. 2.1 as a function of temperature. " The values of AG were calculated using Eq. (1) above for each temperature. The Gibbs free-energy values of the reactants and products were obtained from the JANAF Tables.1 Other sources of thermodynamic data are listed inRef 6. These sources are generally accurate and satisfactory forthe thermodynamic calculations of most CVD reactions they are often revised and expanded. 

All of this is valuable information, which can be of great help. Yet, it must be treated with caution since, in spite of all the progress in thermodynamic analysis, the complexity of many CVD reactions, is such that predictions based on thermodynamic calculations, are still subj ect to uncertainty. As stated above, these calculations are based on chemical equilibrium which is rarely attained in CVD reactions. 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

While alkane metathesis is noteworthy, it affords lower homologues and especially methane, which cannot be used easily as a building block for basic chemicals. The reverse reaction, however, which would incorporate methane, would be much more valuable. Nonetheless, the free energy of this reaction is positive, and it is 8.2 kj/mol at 150 °C, which corresponds to an equihbrium conversion of 13%. On the other hand, thermodynamic calculation predicts that the conversion can be increased to 98% for a methane/propane ratio of 1250. The temperature and the contact time are also important parameters (kinetic), and optimal experimental conditions for a reaction carried in a continuous flow tubiflar reactor are as follows 300 mg of [(= SiO)2Ta - H], 1250/1 methane/propane mixture. Flow =1.5 mL/min, P = 50 bars and T = 250 °C [105]. After 1000 min, the steady state is reached, and 1.88 moles of ethane are produced per mole of propane consmned, which corresponds to a selectivity of 96% selectivity in the cross-metathesis reaction (Fig. 4). The overall reaction provides a route to the direct transformation of methane into more valuable hydrocarbon materials. 

True equilibrium cannot be established at the interface between two different electrolytes, since ions can be transferred by diffusion. Hence, in thermodynamic calculations concerning such cells, one often uses corrected OCV, % ... 

Equilibrium potentials can be calculated thermodynamically (for more details, see Chapter 3) when the corresponding electrode reaction is known precisely, even when they cannot be reached experimentally (i.e., when the electrode potential is nonequilibrium despite the fact that the current is practically zero). The open-circuit voltage of any galvanic cell where at least one of the two electrodes has an nonequilibrium open-circuit potential will also be nonequilibrium. Particularly in thermodynamic calculations, the term EMF is often used for measured or calculated equilibrium OCV values. 

Experimentally undefined parameters, which have a real physical meaning that is, they reflect an actual physical phenomenon but cannot be determined from the experimental data (even a thought experiment to measure them cannot be conceived) or by a thermodynamic calculation. In isolated cases such parameters can be calculated on the basis of nonthermodynamic models. The equations used for calculations generally contain sums, differences, or other combinations of such parameters that are measurable. The Galvani potential at the interface between two dissimilar conducting phases is an example. 

The diffusion-potential reduction thus attained is entirely satisfactory for many measurements not demanding high accuracy. However, this approach is not feasible for the determination of the accurate corrected OCV values of cells with transference that are required for thermodynamic calculations. 

The value of polarization defined by Eq. (2.21) is referred to a calculated value of equilibrium potential of the reaction, rather than to the electrode s effective open-circuit potential, when the latter is not the equilibrium potential. Sometimes a thermodynamic calculation of the equilibrium potential is not possible for instance, when several electrode reactions occur simultaneously. In this case one either uses, conditionally, the concept of a polarization which via Eq. (2.21) refers to the effective open-circuit potential, or (since the latter is often irreproducible) one simply discusses electrode potentials at specified current densities rather than the potential shift away from some original value. 

The calculation of y and P in Equation 14.16a is achieved by bubble point pressure-type calculations whereas that of x and y in Equation 14.16b is by isothermal-isobaric //cm-/(-type calculations. These calculations have to be performed during each iteration of the minimization procedure using the current estimates of the parameters. Given that both the bubble point and the flash calculations are iterative in nature the overall computational requirements are significant. Furthermore, convergence problems in the thermodynamic calculations could also be encountered when the parameter values are away from their optimal values. 

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