Coefficients rational

Isotherm parameter Molar selectivity coefficient Rational selectivity coefficient Bed length, m... 

Ion-exchange isotherms assume different shapes depending on the selectivity factor and the variations in with the level of exchange The rational selectivity coefficient includes the ionic charge and is given by... 

Every polynomial equation Oqx + aix + ---+a = Q with rational coefficients may be rewritten as a polynomial, of the same degree, with integral coefficients by multiplying each coefficient by the least common multiple of the denominators of the coefficients. 

In contrast molecular interaction kinetic studies can explain and predict changes that are brought about by modifying the composition of either or both phases and, thus, could be used to optimize separations from basic retention data. Interaction kinetics can also take into account molecular association, either between components or with themselves, and contained in one or both the phases. Nevertheless, to use volume fraction data to predict retention, values for the distribution coefficients of each solute between the pure phases themselves are required. At this time, the interaction kinetic theory is as useless as thermodynamics for predicting specific distribution coefficients and absolute values for retention. Nevertheless, it does provide a rational basis on which to explain the effect of mixed solvents on solute retention. 

The theoretical rationalization described by FMO theory has to do with the value of the coefficients of the MO s on the atoms of the reactants. Atoms having p-orbitals of... 

One of the most rational means for displacing a broad zone is electrolyte desorption under the conditions of decreasing degree of ionization, i.e., when counterions are converted into dipolar ions, uncharged molecules and coions. This conversion corresponds to a sharp decrease in distribution coefficients of the desorbed substance. Hence, the displacement of equilibrium parame ters at a high rate of mass-exchange is one of the methods of selective stepwise chromatography. 

For olefins with Ji-substitucnts, whether electron-withdrawing or electron-donating, both the HOMO and LUMO have the higher coefficient 021 the carbon atom remote from the substituent. A predominance of tail addition is expected as a consequence. However, for non-conjugated substituents, or those with lone pairs (e.g. the halo-olefins), the HOMO and LUMO are polarized in opposite directions. This may result in head addition being preferred in the case of a nucleophilic radical interacting with such an olefin. Thus, the data for attack of alkyl and fluoroalkyl radicals on the fluoro-olefins (Table 1.2) have been rationalized in terms of FMO theory.16 Where the radical and olefin both have near neutral philicity, the situation is less clear.21... 

In principle, the situation can be simplified to some extent by comparing temperature coefficients for the same metal in different solvents,81 and for different faces of the same metal in the same solvents.32,34 In these cases, correlations are possible which allow some rationalization of the experimental picture. Specific discussions will be provided later on. 

Table I reports the observed NMR linewidths for the H/3 protons of the coordinating cysteines in a series of iron-sulfur proteins with increasing nuclearity of the cluster, and in different oxidation states. We have attempted to rationalize the linewidths on the basis of the equations describing the Solomon and Curie contributions to the nuclear transverse relaxation rate [Eqs. (1) and (2)]. When dealing with polymetallic systems, the S value of the ground state has been used in the equations. When the ground state had S = 0, reference was made to the S of the first excited state and the results were scaled for the partial population of the state. In addition, in polymetallic systems it is also important to account for the fact that the orbitals of each iron atom contribute differently to the populated levels. For each level, the enhancement of nuclear relaxation induced by each iron is proportional to the square of the contribution of its orbitals (54). In practice, one has to calculate the following coefficient for each iron atom ...

List some adsorption systems with extremely low and very high sticking coefficients. Can you rationalize these values with transition state theory (Chapter 3) ... 

Important parameters involved in the Volmer-Butler equation are the transfer coefficients a and (1. They are closely related to the Bronsted relation [Eq. (14.5)] and can be rationalized in terms of the slopes of the potential energy surfaces [Eq. (14.9)]. Due to the latter, the transfer coefficients a and P are also called symmetry factors since they are related to the symmetry of the transitional configuration with respect to the initial and final configurations. 

The theoretical approach by Samec based on the ion-free compact layer model established that the true apparent transfer coefficient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide-Fc system provided values of a smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on defining effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that k i is... 

The membrane permeabilities Pm may be converted to intrinsic permeabilities P(h when the pKa is taken into consideration. An ionizable molecule exhibits its intrinsic permeability when it is in its uncharged form and there is no water layer resistance. The relationship between Pm and P0 is like that between the pH-dependent apparent partition coefficient (log Kd) and the true partition coefficient (log Kp), respectively. This relationship can be rationalized by the mass balance. Take, for example, the case of a monoprotic acid, HA. The total substance concentration is... 

Activity ax is termed the rational activity and coefficient yx is the rational activity coefficient This activity is not directly given by the ratio of the fugacities, as it is for gases, but appears nonetheless to be the best means from a thermodynamic point of view for description of the behaviour of real solutions. The rational activity corresponds to the mole fraction for ideal solutions (hence the subscript x). Both ax and yx are dimensionless numbers. 

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