Calculation procedures, 369 related

An outline of the calculational procedures related to the application of Eq. (1) may be found in the books by Griffith [67] and Low [14]. Concerning the theory of the free ion, the text by Condon and Shortley [63] should be consulted. A basic introduction into the theory of the ligand field and spin-orbit coupling is contained in the treatment by Ballhausen [57]. 

The suggested fractionation theory is based on the LLE of a copolymer solution therefore, first the calculation procedure related to the LLE is discussed. Additionally, the calculation results are compared with experimental LLE data for ethylene vinyl acetate copolymer (EVA) in methyl acetate taken from literature [90]. 

Mannhold, R., Dross, K. Calculation procedures for molecular lipophilicity a comparative study. Quant. Struct.-Act. Relat. 1996, 15, 403 09. 

The calculation procedures described above to evaluate integrals from discrete experimental response data to a pulse input may be modified to take tailing into account. This is done by dividing the data into time periods before and after tT. The data for t < tr are treated as already described, and the data for t > tT are treated analytically based on an exponential relation. We consider various quantities and the corresponding equations and integrals in turn. 

In this paper, Section 2 is devoted to describe calculational procedures and models. Section 3 presents calculated results for the DME steam reforming and related processes. Section 4 summarizes the results. 

Related Calculations. This basic calculation procedure can be extended to the case of countercurrent multistage extraction with reflux. A schematic of the basic extractor is shown in Fig. 9.5. For this extractor there are N stages in the extracting section, 1E to NE, and there are M stages in the stripping section, 15 to MS. 

Equation 53 consists of three unknown quantities, viz., P2( s)> P3( g), and P4( s) Fortunately, for fluidized bed operations these quantities are inter-related and this simplifies the calculation procedure. The relationships between these quantities are discussed below. 

All proportional detectors are designed to provide a response that is as close to linear as possible in order to facilitate calculation procedures in quantitative analysis. In many detectors the output from the detector sensor is not linearly elated to the solute concentration, in which case appropriate signal modifying circuits must be used to furnish a linear output. For example the output from a light adsorption sensor will be exponential and consequently it must be used with a logarithmic amplifier to produce an output that is linearly related to solute concentration. 

The calculation procedures ascribed above have practical importance. They can be employed to predict the distribution ratio of a metal ion, DJJ, between the bulk solution phase and the ion-exchanger phase. The distribution proRles at various pH s and salt concentrations can be estimated just by use of the unique microscopic stability constant, (Pi)q, if the monodentate complex formation reaction is predominant. With dehned as the ratio of the amount of the bound metal ions to the total capacity of the carboxydate ion exchanger is related to the intrinsic binding constant, K, as shown... 

Fortunately, the solution to both of these problems has become available via ab initio molecular orbital calculations. Procedures are now available for calculating the second derivatives of the total energy with respect to the coordinates, which are the force constants The values are generally about 20 % too large, but can readily be scaled to fit the experimental data. Similarly, the calculations may yield the dipole moment derivatives. The values are approximate, but invariably have the correct signs and magnitudes. A number of cycloalkanes and related compounds have been examined in this fashion ... 

One should be aware that the determined QL (or DL) is strongly related to the equipment used at the time of determination. They may represent more system parameters than characteristics of the analytical proce-dure.f They are also dependent on the calculation procedure applied. 

Mannhold, R. and Dross, K. (1996). Calculation Procedures for Molecular Lipophilicity A Comparative Study. Quant.Struct.-Act.Relat., 75,403-409. 

The calculation procedure is as follows For the chosen values of the dissociation degrees of the pure components oi and ao2, the values of ai and 2 are calculated according to Eqs. (8.29) and (8.30) for each composition of the mixture with a known value of the molar conductivity, A, exp. The theoretical value of the molar conductivity, i, calc is calculated according to Eq. (8.36), in such a way for each couple of oi and 02 that a set of theoretical values of molar conductivities for the given composition is obtained. The criterion for selection of the right values of aoi and ao2 is given by the relation... 

The thermodynamic modeling and calculation procedures for S-L-V equilibrium in binary systems for RESS/PGSS involve simultaneous solution of the phase equilibrium relations for the two components, namely, the SCF solvent, 1, and the solid solute, 3, for all three phases, S, L, and V, as given by the following equations ... 

In some cases, an association constant and related interaction coefficients have been used where it might have been possible to make do with a different set of interaction coefficients. We make no apologies for this so long as the calculation procedure is well defined and consistent. 

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