In both cases the GPF formalism can, in principle, give the BI of a nonideal system, with respect to either the adsorbent or the ligand molecules. This is not possible if one uses the phenomenological approach as described in Section 2.3. [Pg.320]

Although M(i j i j) = M Sj 5j) for both ideal and nonideal systems, the enantiomers and 5j are differentiated by the presence of a second different chir molecule (e.g., either i jj or 5jj). Two pairs of enantiomers are capable of four other types of intermolecular association, in addition to the three already mentioned in Table 1. These are conveniently diagrammed in Figure 1, [Pg.200]

Experimental determination of the surface composition in nonideal systems, in which the gradients extend over several layers inwards the crystal is as difficult as the exact calculations. Therefore, one has to make again rather unpleasant assumptions. [Pg.269]

Thermodynamics cannot provide the extension to the BP for nonideal systems (with respect to either the ligands or the adsorbent molecules). The statistical mechanical approach can, in principle, provide corrections for the nonideality of the system. An example is worked out in Appendix D. [Pg.359]

This method handles narrow-boiling, wide-boiling, and highly nonideal systems efficiently. [Pg.131]

Where constant molar overflow does not work well, such as with nonideal systems or where there is a drastic difference between internal vapor and liquid rates. Section 2.2.2 discusses the applicability of constant molal overflow. [Pg.148]

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus, [Pg.1293]

For some systems, the initial values have to be near the expected solution results. For superfractionators, and columns with purity specifications and highly nonideal systems, the initial temperature profile should be near the expected results. For narrow-boiling systems, an accurate reflux estimate is necessary. [Pg.148]

Payens, T.A.J., Brinkhuis, J.A., van Markwijk, B.W. (1969). Self-association in nonideal systems. Combined light scattering and sedimentation measurements in p-casein solutions. Biochimica etBiophysica Acta, 175, 434 137. [Pg.227]

This means from the Boltzmann equation follows only the conservation of the kinetic energy. But, in nonideal systems, the average of kinetic and potential energy as a sum should be covered. [Pg.191]

Constant molal overflow from stage to stage (theoretical) for simple ideal systems following Raoult s Law. More complicated techniques apply for nonideal systems. [Pg.15]

As also seen in Table I, the micellar composition can be a-f-fected substantially by nonideality. In -fact, azeotropic behavior in the monomer—micelle equilibrium is possible -for these nonideal systems i.e., as the monomer composition varies -from pure A to pure B, the micelle can vary -from Xn > y to Xn = y (azeotrope) to Xa < yA. This azeotrope -formation is illustrated -for the cationic/nonionic system in Figure 2, where an azeotrope -forms at Xa = yA = 0.3. The minimum CMC -for a mixture corresponds to the azeotropic composition i-f an azeotrope is present (32.37). For an ideal system, azeotropic behavior is not observed. [Pg.11]

As mentioned in Section 2.1, the usual Boltzmann equation conserves the kinetic energy only. In this sense the Boltzmann equation is referred to as an equation for ideal systems. For nonideal systems we will show that the binary density operator, in the three-particle collision approximation, provides for an energy conservation up to the next-higher order in the density (second virial coefficient). For this reason we consider the time derivative of the mean value of the kinetic energy,12 16 17 [Pg.196]

At low or moderate pressure, when the liquid phase is incompressible, an activity coefficient model (y model) is more flexible to use than an equation of state. This method often works, even for strongly nonideal systems involving polar and associating components. [Pg.425]

Equations 3 and 4 are derived from Equation 5 (31) which has been Found to be invalid For the systems oF interest. However, Equations 3 and 4 have been shown to accurately describe mixture CMC values and monomer-micelle equilibrium. The resolution is that Equations 3 and 4 should be considered as valuable empirical equations to describe these nonideal systems. The Fact that they were originally derived From regular solution theory is a historical coincidence. [Pg.13]

By virtue of the function (3.6), concentrations, which are readify determined parameters, can be used instead of chemical potentials in the thermodynamic equations for ideal systems. The simple connection between the concentrations and chemical potentials is lost in real systems. To facilitate the changeover from ideal to nonideal systems and to avoid the use of two different sets of equations in chemical thermodynamics, [Pg.38]

When monomers with dependent groups are involved in a polycondensation, the sequence distribution in the macromolecules can differ under equilibrium and nonequilibrium regimes of the process performance. This important peculiarity, due to the violation in these nonideal systems of the Flory principle, is absent in polymers which are synthesized under the conditions of the ideal polycondensation model. Just this circumstance deems it necessary for a separate theoretical consideration of equilibrium and nonequilibrium polycondensation. [Pg.189]

Gas solubihty has been treated extensively (7). Methods for the prediction of phase equiUbria and actual solubiUty data have been given (8,9) and correlations of the equiUbrium iC values of hydrocarbons have been developed and compiled (10). Several good sources for experimental information on gas— and vapor—hquid equiUbrium data of nonideal systems are also available (6,11,12). [Pg.20]

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