Thermodynamic computational calculation

Discusses the thermodynamic basis for computer calculations for vapor-liquid equilibria computer programs are given. Now out of date. 

Chapter 10, the last chapter in this volume, presents the principles and applications of statistical thermodynamics. This chapter, which relates the macroscopic thermodynamic variables to molecular properties, serves as a capstone to the discussion of thermodynamics presented in this volume. It is a most satisfying exercise to calculate the thermodynamic properties of relatively simple gaseous systems where the calculation is often more accurate than the experimental measurement. Useful results can also be obtained for simple atomic solids from the Debye theory. While computer calculations are rapidly approaching the level of sophistication necessary to perform computations of... 

A major goal was to investigate the solid state structures of such compounds by single crystal X-ray diffraction. It was found that Lewis acid-base adducts R3M—ER3 show general structural trends, which allow estimations on the relative stability of the adducts. The experimental results were confirmed by computational calculations, giving even deeper insights into the structural parameters and the thermodynamic stability of simple Lewis acid-base adducts. In addition, their thermodynamic stability in solution was investigated by temperature-dependent NMR spectroscopy. 

A number of problems formulated with data from the literature are given next as exercises. In addition, to the objective function given by Equation 15.11 the reader who is familiar with thermodynamic computations may explore the use of implicit objective functions based on fugacity calculations. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

These experimentally observed structural trends were confirmed by computational calculations on H3A1 and Me3Al adduct families. In each adduct family, the amount of increase of the M-X bond lengths and decrease of the X M-X bond angles (X = H, Me) compared to uncomplexed MX3 diminishes with the atomic number of the group 15 element. The structural trends very well reflect the trends observed for the thermodynamic stability of such adducts, as is illustrated in Tables XI and XII. 

Burcat [ Thermochemical Data for Combustion Calculations, in Combustion Chemistry. (W. C. Gardiner, Jr., ed.), Chapter 8. John Wiley Sons, New York, 1984] discusses in detail the various sources of thermochemical data and their adaptation for computer usage. Examples of thermochemical data tit to polynomials for use in computer calculations are reported by McBride, B. J Gordon, S., and Reno, M. A., Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, NASA, NASA Langley, VA, NASA Technical Memorandum 4513, 1993, and by Kee, R. J., Rupley, F. M and Miller, J. A., The Chemkin Thermodynamic Data Base, Sandia National Laboratories, Livermore, CA, Sandia Technical Report SAND87-8215B, 1987. 

It is hoped that the present findings may give those untrained in the details of the thermodynamic-hydrodynamic calculations a better feel for the results as well as the limitations of the computer output. 

One other serious criticism regarding the data on Cu speciation is the neglect of the cysteine present in blood plasma. Cu11 and cysteine undergo a facile redox reaction (Chapter 20.2). Since the reaction is irreversible, no quantitative thermodynamic quotient is available for use in the computer calculations. Another assumption often made is that the overwhelming concentration of other amino acids may prevent cysteine coordination and, as a result, stabilize the Cu11 state. Recent studies show that this assumption is totally unjustified48 and so the dilemma still has to be resolved. 

The thermodynamic data as well as the detonation parameters can nowadays be very reliably obtained by using quantum-mechanical computer calculations. On the one hand it is important to check experimental results, and on the other hand and even more importantly - it is important to predict the properties of potential new energetic materials without any prior experimental parameters, for example during the planning of synthetic work. Moreover, such computational methods are ideal for the estimation of the detonation parameters of newly synthesized compounds, which have not been obtained in the 50 100 g quantities which are necessary for the experimental determination of such detonation parameters (e.g. detonation velocity). 

Equation (7.8) offers a clear separation of inner-shell and outer-shell contributions so that different physical approximations might be used in these different regions, and then matched. The description of inner-shell interactions will depend on access to the equilibrium constants K. These are well defined, observationally and computationally (see Eq. (7.10)), and so might be the subject of either experiments or statistical thermodynamic computations. Eor simple solutes, such as the Li ion, ab initio calculations can be carried out to obtain approximately the Kn (Pratt and Rempe, 1999 Rempe et al, 2000 Rempe and Pratt, 2001), on the basis of Eq. (2.8), p. 25. With definite quantitative values for these coefficients, the inner-shell contribution in Eq. (7.8) appears just as a function involving the composition of the defined inner shell. We note that the net result of dividing the excess chemical potential in Eq. (7.8) into inner-shell and outer-shell contributions should not depend on the specifics of that division. This requirement can provide a variational check that the accumulated approximations are well matched. 

In correspondence with this scheme and classification of facies, we adopted these parameters in the thermodynamic analysis and in plotting the diagrams of mineral equilibria, but some isothermal sections of the diagrams were plotted for temperatures expressed in degrees Kelvin (500, 700, 900, 1100°K), which was due to the constraints of the computer calculations. 

FIG. 2-7 Enthalpy-concentration diagram for aqueous ammonia. From Thermodynamic and Physical Properties NH3-H20, Int Inst. Refrigeration, Paris, France, 1994 (88 pp.). Reproduced by permission. In order to determine equilibrium compositions, draw a vertical from any liquid composition on any boiling line (the lowest plots) to intersect the appropriate auxiliary curve (the intermediate curves). A horizontal then drawn from this point to the appropriate dew line (the upper curves) will establish the vapor composition. The Int. Inst. Refrigeration publication also gives extensive P-v-xtah es from —50 to 316°C. Other sources include Park, Y. M. and Sonntag, R. E., ASHRAE Trans., 96,1 (1990) 150-159 x, h, s, tables, 360 to 640 K) Ibrahim, O. M. and S. A. Klein, ASH E Trans., 99, 1 (1993) 1495-1502 (Eqs., 0.2 to 110 bar, 293 to 413 K) Smolen, T. M., D. B. Manley, et al.,/. Chem. Eng. Data, 36 (1991) 202-208 p-x correlation, 0.9 to 450 psia, 293-413 K)i Ruiter, J. P, 7nf. J. R rig., 13 (1990) 223-236 gives ten subroutines for computer calculations. 

Many thermodynamic cycles contain the hydrogen proton and anions, which often leads to a large error in the computational calculation of the free energy of solvation of the anion. As a result, cycles with water molecules or additional acids [5,27-31] are often used to try and remove these sources of error. If accurate free energy values are used, pKa calculations can be fairly accurate, but many papers report pKa calculations with less accurate free energy values for H+. These publications would need to be recalculated with more accepted values to produce reliable and accurate data. 

Theoretical (computational) calculations can also offer quantitative descriptors of physicochemical properties of the molecular structures, molecular interactions, and thermodynamics of interactions. Principally, extensive studies on the catalytic site of GP have been exploited in theoretical QSAR studies [4]. The techniques engaged correlate biochemical behaviors with the known crystallographic structures, and map regions around the inhibitor molecule and added water molecules to improve the in silico prediction [106-110]. 

Thermodynamic property calculations based upon the solution of the molecular OZ equation using spherical harmonic expansions have not been extensive. This is probably due to the computational effort required in the implementation of these methods. However, quite promising results have been obtained for the equation of state of hard sphere diatomics (Chen and Steele, Freasier, Lado ) and for 12-6 diatomics (Lado ). Again, as we noted earlier in Section III.A, more extensive tests of this approach need to be made. 

Values of AG° are required for a multitude of reactions at many different temperatures, and in general one can calculate these from the appropriate values of AH0 and S°. Today, such calculations can be carried out very accurately with thermodynamic computer programs in a minimum of time. For example, let us have a closer look at the decomposition of cupric oxide (section 6.4.3). If we take into account the temperature dependence of AS" and AH0, the outcome of a computed calculation with the program Micro Term [1] gives a temperature of 1339 K, above which AG° becomes negative. This temperature is of course more accurate than that from section 6.4.3, and the difference is quite considerable. 

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