Calculations of species properties

Calculation of Species Properties at 298.15 K When the Reactant Consists of One, Two, or Three Species... 

We have seen that calculating species properties from experimental values of K and A // ° is more complicated than calculating K and Ar ° from species values. Thermodynamic calculations can be made by alternate paths, and so there is more than one way to calculate species properties from experimental properties. This chapter emphasizes the concept of the inverse Legendre transform discussed by Callen (8). Biochemical reaction systems are described by transformed thermodynamic properties, and the inverse transform given in equation 6.2-1 provides the transformation from experimental reactant properties to calculated species properties. In this ehapter we first considered calculations of species properties at 298.15 K from measurements of K and Ar ° at 298.15 K. Then we considered the more difficult problem of calculating Af G°(298.15 K) and Af //°(298.15 K) from Ar G "(313.15 K) and Ar H (313.15 K). The programs developed here make it possible to go from Ar G and Ar H (F.pH,/) to Af G (298.15 K,/=0) and Af H (298.15 K,/=0) in one step. 

L.J. Broadbelt, S.M. Stark and M.T. Klein, Computer Generated Reaction Modelling On-the-Fly Calculation of Species Properties Using Computational Quantum Chemistry, Chem. Eng. Sci. 49 (1994) 4991-5010. 

The relationship between heat transfer and the boundary layer species distribution should be emphasized. As vaporization occurs, chemical species are transported to the boundary layer and act to cool by transpiration. These gaseous products may undergo additional thermochemical reactions with the boundary-layer gas, further impacting heat transfer. Thus species concentrations are needed for accurate calculation of transport properties, as well as for calculations of convective heating and radiative transport. 

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 ... 

Although the Pitzer correlations are based on data for pure materials, they may also be used for the calculation of mixture properties. A set of recipes is required relating the parameters T, Pc, and (0 for a mixture to the pure-species values and to composition. One such set is given by Eqs. (2-80) through (2-82) in Sec. 2, which define pseudopa-rameters, so called because the defined values of T, Pc, and (0 have no physical significance for the mixture. 

The reliability of molecular mechanics calculations hinges entirely on the validity and range of applicability of the force field. The parameterisation of these functions (the force field) represents the chemistry of the species involved. Many force fields have been developed and the one used in any application usually depends on the molecular mechanics package being used. The force field itself can be validated against experimental and ab initio results. Because of the relative speed of molecular mechanics calculations, it is possible to consider routine calculations of a large number of atoms, certainly tens of thousands, which makes the method amenable to calculations on polymers. To remove surface effects, calculations of bulk properties are normally carried out employing 3D periodic boundaries. In this way it is possible to perform calculations on both amorphous and crystalline systems. 

Although the best source of AH is certainly experimental measurement, this is often unavailable for a species of interest. The standard-state heat of formation is sometimes available from theory. The wide availability of powerful computing platforms has made calculation of thermochemical properties from first-principles practical in many cases. 

For some applications, one may use very simple approximations to the calculation of transport properties, that evaluate mixture properties from pure species properties via certain mixture averaging rules. However, we more often encounter applications in which the approximate averaging rules are not adequate, and multicomponent methods are necessary [103,178],... 

The previous section discussed techniques for obtaining the molecular potential interaction parameters <7 and e based on pure species physical properties of molecule i. Interactions between unlike molecules (i.e., all i-j pairs) must also be considered in the calculation of transport properties (notably, binary diffusion coefficients). The following is a set of combining rules to estimate the i- j interaction parameters, assuming that the pure species values are known. 

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... 

Equations of state have a much wider application. In this chapter we first present a general treatment of the calculation of thermodynamic properties of fluids and fluid mixtures from equations of state. Then the use of an equation of state for VLE calculations is described. For this, the fugacity of each species in both liquid and vapor phases must be determined. These calculations are illustrated with the Redlich/Kwong equation. Provided that the equation of state is suitable, such calculations can extend to high pressures. 

If the apparent equilibrium constant and standard transformed enthalpy of a reaction are measured at a temperature different from 298.15 K and the species properties are known for all the reactants but one at 298.15 K, the question is how to calculate the species properties of that one reactant at 298.15 K for entry into a database. First we consider the simplest case where the reactant with unknown species properties consists of a single species. The reaction chosen as an example is EC 3.5.I.3. 

R. A. Alberty, Calculation of thermodynamic properties of species of biochemical reactants using the inverse Legendre transform, J. Phys. Chem. 109 B, 9132-9139 (2005). 

The present chapter mainly discusses the simplest class of atom-diatom Van der Waals molecules, the molecular hydrogen-inert gas complexes. While experimental information on the vibrational predissociation of these species is as yet relatively limited, our knowledge of the potential energy surfaces which govern their dynamics (9,10) is unequalled for any other systems. Moreover, the small reduced mass and large monomer level spacings make accurate calculations of their properties and propensities relatively inexpensive to perform. For these reasons, these species have come to be treated as prototype systems in theoretical studies of vibrational predissociation (17-25). 

The calculation of the properties of transition structures is more problematic than for stable molecules because TSs involve bond breaking. Thus computations based an the concept of electron pairing may not be applicable, especially for species with radical character. Nevertheless, computational studies have provided insight into many reactions and we frequently use the results of these studies, as well as experimental work, in developing the details of reaction mechanisms. 

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