Mixed deviations from

CLASSES MIXED DEVIATION FROM raoult s law CHANGE IN H BONDING ON MIXING EXAMPLES ... 

The two-parameter van Laar equation cannot represent maxima or minima in the activity coefficients, nor can it represent the mixed deviations from ideality exemplified by the benzene-hexaflnorobenzene system of Fig. 1.4-1. However, it is suparior to the Margules equation for some extremely nonideal systems such as alcohol-hydrocarbon mixtures, for example, the ethanol-n-haptane system of Fig. 1.4-1. For such mixtures the two-parameter Margules equation often incorrectly predicts liquid-liquid phase splitting. Higher order Margules equations can sometimes be u red for these systems, but at the expense of many additional parameters. 

Flow Pattern Ideality. A straightforward interpretation of the observed kinetics can only be made if the flow pattern in the reactor used corresponds to an ideal flow pattern. In particular for plug flow reactors, deviations from the ideal reactor behavior can be encountered. For perfectly mixed reactors such as a batch reactor and a continuous stirred tank reactor, the rotation speed of the stirrer is the key parameter that needs to be set sufficiently high to ensure complete mixing. Deviations from the ideal plug flow pattern can, for example, be caused by a less-dense packing of the catalyst pellets near the reactor wall, by a too high dilution of the catalyst bed with inert pellets or by the importance of effective axial diffusion compared to convection (15). 

A deaning chamber is substantiaiiy iess weii mixed than perfect - at least because the racked parts block fluid flow and cause the flow patterns to be non-uniform. And the chamber shape, while often radially symmetrical, is not longitudinally symmetrical. So, the less than perfectly mixed vessel will retain a fluid component longer than would be expected from the assumption of perfect mixing. Deviation from the well-mixed residence time will be different for every vessel shape and loading of parts, and will be specifically unpredictable (Chapter 2.13.1). 

It should be emphasized that this expression of the entropy of mixing is applicable only to athermic systems or to mixtures exhibiting only weak interactions between molecules—that is, solutions with low enthalpy of mixing. Deviations from ideality could arise in particular in the following situations, which will be... 

Solutions can deviate from ideality because they fail to meet either one or both of these criteria. In reference to polymers in solutions of low molecular weight solvents, it is apparent that nonideality is present because of a failure to meet criterion (2), whether the mixing is athermal or not. 

Flow in tubular reactors can be laminar, as with viscous fluids in small-diameter tubes, and greatly deviate from ideal plug-flow behavior, or turbulent, as with gases, and consequently closer to the ideal (Fig. 2). Turbulent flow generally is preferred to laminar flow, because mixing and heat transfer... 

The foregoing discussion has dealt with nonideahties in the Hquid phase under conditions where the vapor phase mixes ideally and where pressure-temperature effects do not result in deviations from the ideal gas law. Such conditions are by far the most common in commercial distillation practice. However, it is appropriate here to set forth the completely rigorous thermodynamic expression for the Rvalue ... 

Equation (2-38) is valid for every region of the surface. In this case only weight loss corrosion is possible and not localized corrosion. Figure 2-5 shows total and partial current densities of a mixed electrode. In free corrosion 7 = 0. The free corrosion potential lies between the equilibrium potentials of the partial reactions and U Q, and corresponds in this case to the rest potential. Deviations from the rest potential are called polarization voltage or polarization. At the rest potential = ly l, which is the corrosion rate in free corrosion. With anodic polarization resulting from positive total current densities, the potential becomes more positive and the corrosion rate greater. This effect is known as anodic enhancement of corrosion. For a quantitative view, it is unfortunately often overlooked that neither the corrosion rate nor its increase corresponds to anodic total current density unless the cathodic partial current is negligibly small. Quantitative forecasts are possible only if the Jq U) curve is known. 

In the pure concerted reaction there is no need to invoke the cationic or anionic intermediates in describing the transition state, but it now becomes evident that some deviation from this idealized route may be possible, and then we need a way to comment upon and to measure the extent to which the cationic or anionic character is mixed in in the transition state. This is now widely accomplished with the aid of energy surfaces of the type shown schematically in Fig. 5-19. Depending on the nature of the surface, the reaction path may follow a route far from the diagonal representing the pure concerted reaction, and the primary goal is to identify the location of the transition state on this surface. 

Although the above treatment is based on the assumption of perfect mixing, it was found experimentally that deviations from this ideal situation can be taken into account by introducing the additional parameters of Wolf and Resnick (W5) into the kernel (253). 

The reason is that classical thermodynamics tells us nothing about the atomic or molecular state of a system. We use thermodynamic results to infer molecular properties, but the evidence is circumstantial. For example, we can infer why a (hydrocarbon + alkanol) mixture shows large positive deviations from ideal solution behavior, in terms of the breaking of hydrogen bonds during mixing, but our description cannot be backed up by thermodynamic equations that involve molecular parameters. 

The mixing time will be that required for the mixture composition to come within a specified deviation from the equilibrium value and this will be dependent upon the way in which the tracer is added and the location of the detector. It may therefore be desirable to record the tracer concentration at several locations, and to define the variance... 

The index ms indicates that j s transforms according to the mixed symmetry representation of the symmetric Group 54 [33]. 7 5 is an irreducible tensor component which describes a deviation from Kleinman symmetry [34]. It vanishs in the static limit and for third harmonic generation (wi = u>2 = W3). Up to sixth order in the frequency arguments it can be expanded as [33] ... 

The dispersion coefficients for the mixed-symmetry component 7 5 which describes the deviation from Kleinman symmetry are for methane more than an order of magnitude smaller than coefficients of the same order in the frequencies for 7. Their varations with basis sets and wavefunction models are, however, of comparable absolute size and give rise to very large relative changes for the mixed-symmetry dispersion coefficients. 

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