Partial properties calculation

The chirality code of a molecule is based on atomic properties and on the 3D structure. Examples of atomic properties arc partial atomic charges and polarizabilities, which are easily accessible by fast empirical methods contained in the PETRA package. Other atomic properties, calculated by other methods, can in principle be used. It is convenient, however, if the chosen atomic property discriminates as much as possible between non-equivalent atoms. 3D molecular structures are easily generated by the GORINA software package (see Section 2.13), but other sources of 3D structures can be used as well. 

This definition is the means by which partial properties are calculated from solution properties. Equation 115 can now be written as equation 117 ... 

This summability equation, the counterpart of equation 116, provides for the calculation of solution properties from partial properties. Differentiation of equation 122 yields equation 123 ... 

The basis for calculation of partial properties from solution properties is provided by this equation. Moreover, the preceding equation becomes... 

Equation (4-49) is merely a special case of Eq. (4-48) however, Eq. (4-50) is a vital new relation. Known as the summahility equation, it provides for the calculation of solution properties from partial properties. Thus, a solution property apportioned according to the recipe of Eq. (4-47) may be recovered simply by adding the properties attributed to the individual species, each weighted oy its mole fraction in solution. The equations for partial molar properties are also valid for partial specific properties, in which case m replaces n and the x, are mass fractions. Equation (4-47) applied to the definitions of Eqs. (4-11) through (4-13) yields the partial-property relations ... 

In apphcatious to equilibrium calculations, the fugacity coefficients of species iu a mixture are required. Given au expression for G /RT as aetermiued from Eq. (4-158) for a coustaut-compositiou mixture, the corresponding recipe for In is found through the partial-property relation... 

Careful consideration was taken in the parameterization process to insure that the parameters were deemed reasonable for the atom types, using the OPLS-AA force field atom types as a comparison. As one of the goals of this project was to ensure that robustness was achieved in many different calculated properties of the newly developed model, several sets of simulations were also performed to ensure that the parameters could achieve a reasonable agreement with experiment. Some of the properties calculated included the gas phase density, the partial molar volume in aqueous solution, and the bulk solvent structure as well. The calculation of the solubility was discussed in the previous section for the parameterization process and the viewing of these results, the solubility will be reported in log S values, as many of the literature values are reported as log S values, and therefore, the comparison would not lose any sensitivity due to rounding error from the log value. 

The Lee-Kesler (7) generalized equation of state, which also applies to both phases, is the basis for the sixth thermodynamic properties method. As originally developed, the Lee-Kesler equation was for predicting bulk properties (densities, enthalpies etc.) for the entire mixture and not for calculating partial properties for the components of mixtures. Phase equilibrium was not one of the uses that the authors had in mind when they developed the equation. Recognizing the other possibilities of the Lee-Kesler equation, Ploecker, Knapp, and... 

The definition of a partial molar property, Eq. (11.2), provides the me-for calculation of partial properties from solution-property data. Implicit in definition is a second, equally important, equation that allows the calculation solution properties from knowledge of the partial properties. The derivation this second equation starts with the observation that the thermodynamic propertl of a homogeneous phase are functions of temperature, pressure, and the numb of moles of the individual species which comprise the phase. For thermodyna property M we may therefore write... 

Equation (11.4) is in fact just a special case of Eq. (11.3), obtained by setting n = 1, which also makes nt = xt. Equations (11.5) and (11.6) on the other hand are new and vital. They allow the calculation of mixture properties from partial properties, playing a role opposite to that of Eq. (11.2), which provides for the calculation of partial properties from mixture properties. 

These equations allow calculation of the effect of temperature and pressure on the partial Gibbs energy (or chemical potential). They are the partial-property analogs of two equations that follow by inspection from Eq. (10.2) ... 

Thus for binary systems, the partial properties are readily calculated directly from an expression for the solution property as a function of composition at constant T and P. The corresponding equations for multicomponent systems are much more complex, and are given in detail by Van Ness and AbbotLt... 

Thus for a binary solution, the partial properties are given directly as functions of composition for given T and F For multicomponent solutions such calculations are complex, and direct use of Eq. (4-47) is appropriate. 

Partial pressure, 300, 333 Partial properties, 321-325, 416-418 calculation of, 423-428 excess, 422-425... 

Eq. (14.50). This is a complexiterative step, consisting of annmberof parts. Fora specific phase (liqnid or vapor), application of Eq. (14.50) requires prior calculationof mixture properties Z, P, and / and partial properties qi- The mixture properties come from solution of the equation of state, Eq. (14.38) or (14.39), bntthis requires knowledge of q as calculated from values by Eq. (14.56). Moreover, Eq. (14.55) for Cji includes the pure-species properties Z, and qi, wliich must therefore be determined first. The sequence of calcnlations is as follows ... 

Vapor-liquid distribution coefficients (/ -values) may be calculated from equations of state using Equations 1.21, 1.23, and 1.25. These calculations require the evaluation of partial properties of individual components, defined as the change in the total solution property resulting from the addition of a differential amount of the component in question to the solution, while holding constant the remaining component amounts and the temperature and pressure. Mathematically, the partial property fl of component i is given by... 

If equations of state are available for both the vapor and liquid phases, the above equations may be used to calculate the component fugacity coefficients in both phases by Equation 1.23, and the /f-values by Equation 1.25. Alternatively, the fugacity coefficient of a component in solution may be derived from the total fugacity coefficient expression (Equation 1.21) via the definition of partial properties ... 

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