Pseudo critical constants

Pseudo Critical Constants and Acentric Factors for Petroleum Fractions... 

Using the principle of corresponding states requires knowledge of pseudo-critical constants of petroleum fractions these should be estimated starting from characteristic properties which are the normal boiling temperature and the standard specific gravity. 

This concept can be extended to mixtures if the pseudo-critical constants of the mixture and a mixture reduction group are defined. This gives the... 

The pseudo-critical constants are calculated and tabulated along with the pure component constants ... 

The principle of corresponding states, and the pseudo-critical constant concept will be used first, then the Peng-Robinson equation of state (program PR1)... 

In order to obtain interaction second virial coefficients for mixtures, some method is required for determining the acentric factor a>y and the pseudo-critical constants T ij and pertaining to the unlike interactions. In the present case, extended van der Waals one-fluid mixing rules are applied in terms of which... 

The estimation of the three parameters —pseudo-critical temperature, pseudo-critical pressure, and the acentric factor— should be done using the same method because these constants should be coherent. 

Compressibility factor (Z) for mixtures when using pseudo-critical mixture constants to detennine ... 

Calculate the volume using Kay s method. In this method, V is found from the equation V = ZRT/P, where Z, the compressibility factor, is calculated on the basis of pseudocritical constants that are computed as mole-fraction-weighted averages of the critical constants of the pure compounds. Thus, T = Z K, 71, and similarly for Pc and Z, where the subscript c denotes critical, the prime denotes pseudo, the subscript i pertains to the ith component, and Y is mole fraction. Pure-component critical properties can be obtained from handbooks. The calculations can then be set out as a matrix ... 

These two bulk properties (TBP data/°API) are then used to calculate other constants such as molecular weight (MW), the pseudo-critical temperature (T ) and pressure (P ), respectively, and the pseudo-acentric factor (m). The other properties generally measured are the kinematic viscosities at 100°F (—311 K) and 200°F (—366 K), respectively, and the Reid Vapor Pressure (RVP) (mainly for the gasoline range cut, defined as the vapor pressure exerted by the cut at 100 °F (—311 K)). All of the above-measured properties and the calculated constants are generally... 

If the pseudo-critical concept is valid, then for each constant composition of the mixture there must exist a hypothetical pure substance with criticals, and which obeys the corresponding states principle and which has... 

The pseudo-critical values were tested, with 0, 6 and set equal to unity, by comparison of predicted compressibility factors with the experimentally determined values for hydrogen and methane mixtures. The value of a was taken from a correlation developed earlier for high temperature systems [7] shown in Table V. The only pure reference substances available with known compressibility factors were methane, hydrogen and deuterium. The critical constants used for these gases are given in Table IV. 

The volume of gaseous mixtures may be computed for any condition that is not close to the envelope in the diagram, from the pressure-volume-temperature relations of the hypothetical material C using the pseudo critical point designated as c (Example 5-5). Lines of constant volume are indicated on the diagram. 

For free radicals which are not involved in termination processes, i.e. those radicals which are the most reactive and, accordingly, the least concentrated, the QSSA can be applied even during the true induction period of the reaction. This is so for chain carrier radicals not involved in termination processes the concentrations of these radicals are not at all constant or slowly varying during the induction period however, the QSSA may be applied to them. For this reason, this special kind of QSSA will be termed pseudo-stationary state approximation (PSSA). As a consequence of the PSSA, the observation of a non-quasi-stationary behaviour for a radical concentration does not necessarily mean that the QSSA cannot be applied. This fact has probably played a role in the criticism of the QSSA. 

The rational design of a reaction system to produce a polymer with desired molecular parameters is more feasible today by virtue of mathematical tools which permit prediction of product distribution. New analytical tools such as gel permeation chromatography are being used to check theoretical predictions and to help define molecular parameters as they affect product properties. There is a laudable trend away from arbitrary rate constants, but systems other than styrene need to be treated in depth. A critical review of available rate constants would be useful. Theory might be applied more broadly if it were more generally recognized that molecular weight distributions as well as rates can be calculated from combinations of constants based on the pseudo-steady-st te assumption. These are more easily determined than the individual constants in chain reactions. 

One of the critical aspects of this approach is that two different experiments have to be performed between which the particular instrument conditions must be carefully kept constant in order not to affect the intensity ratios. This problem can be overcome by the enantiomer-labeled guest method [47]. It is based on the mass spectrometric examination of one enantiomer of the host with a pseudo-racemic mixture of the guest. In order to be able to detect both diastereomers separately, one enantiomer of the guest must be isotopically labeled, usually with deuterium. In the same experiment, both diastereotopic complexes are formed and their intensities can be compared directly. However, the stereochemical effect might additionally be superimposed by an unknown isotope effect. A way to separate stereochemical and isotope effects is to perform the same experiment with the second host enantiomer [4B]. In one experiment both stereochemical and isotope effects disfavor the same complex and thus work in the same direction. In the other experiment, they partly cancel each other. If both experiments have been performed, one can use the two experimental values for the intensity ratios of both diastero-meric complexes to deconvolute both effects [49]. 

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