Equilibrium parameters

In summary, T j, gives a truer approximation to a valid equilibrium parameter, although it will be less than T owing to the finite dimensions of the crystal and the finite molecular weight of the polymer. We shall deal with these considerations in the next section. For now we assume that a value for T has been obtained and consider the simple thermodynamics of a phase transition. 

Band broadening is also affected by the gradient steepness. This effect is expressed in Table 16-14 by a band compression factor C, which is a fnuctiou of the gradient steepness and of equilibrium parameters. Since C < 1, gradient elution yields peaks that are sharper than those that would be obtained in isocratic elution at

[Pg.1536]

Solute equilibrium parameters (X5,S for RPC and (Xz,Z for lEC Solute retention factor for initial mobile phase A ... 

The model parameters, in addition to the adsorption equilibrium parameters, are ... 

This is the general expression for film growth under an electric field. The same basic relationship can be derived if the forward and reverse rate constants, k, are regarded as different, and the forward and reverse activation energies, AG are correspondingly different these parameters are equilibrium parameters, and are both incorporated into the constant A. The parameters A and B are constants for a particular oxide A has units of current density (Am" ) and B has units of reciprocal electric field (mV ). Equation 1.114 has two limiting approximations. 

Figure 15. Data from single channel experiments, plotted to show the relationship between kinetic and equilibrium parameters for several of the saxitoxins, tetrodotoxin, and Conus geographus toxin GIIIA. Compound numbering corresponds to that in Figure 1. The vertical axis is and the horizontal axis is dwell time, the reciprocal of k j. The dissociation constant, the ratio of k jj/k, therefore corresponds to distance along the diagonal. Data primarily from Ref. 95.

For non-volatile components A, = 0 the equilibrium parameter (A,) is expressed by Henry s constant as follows... 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Manganese transformations can be seen from changes in the equilibrium parameters of the various fractions (Utf,) and the whole soil (Ute) with time of incubation under saturation (Fig. 6.25). In both soils incubated under the saturation condition, the Utf parameters of the EXC and the CARB fractions increased and departed from the native state (Utf.Exc and... 

The soil equilibrium parameter, Uts, measures the departure from the Mn fractionation in the oxic native soil, which is caused by the saturation and incubation of the soil. This parameter can acquire values equal to or larger than one. Compared to the native state, an increase in the Uts indicates that some fraction(s) have been grossly enriched in Mn. Note the fact that a fraction that has lost some Mn will only reduce its own contribution to the Uts value, but its contribution will not be subtracted from that of the other fraction(s) since the product F, xUtfi can not acquire negative values. 

Change the chemical equilibrium parameters (K and Cmax) to see how they effect the distribution and transport of the solute (see Lyman et al. (1982) for a comprehensive set of data). Experiment by using a different model for the adsorption of the solute, e.g., Freundlich linear adsorption. 

The constraints on m1 and m4 are explicit. The lower limit of m, however, does not depend on the other flow rate ratios, whereas the upper limit of m4 is an explicit function of the flow rate ratios m2 and m3 and of the feed composition respectively [25]. The constraints on m2 and m3 are implicit (see Eq. 4), but they do not depend on m1 and m4. Therefore, they define a unique region of complete separation in the (m2, m3) plane, which is the triangle-shaped region abw in Fig. 4. The boundaries of this region can be calculated explicitly in terms of the adsorption equilibrium parameters and the feed composition as follows [25] ... 

Vogl, T., C. Jatzke, H.J. Hinz, J. Benz, and R. Huber. 1997. Thermodynamic stability of annexin V E17G equilibrium parameters from an irreversible unfolding reaction. Biochemistry 36 1657-1668. 

Selected entries from Methods in Enzymology [vol, page(s)] Add-base catalysis [with site-directed mutants, 249, 110-118 altered pH dependencies, 249, 110] commitment to [in determination of intrinsic isotope effects, 249, 343, 347-349 in interfacial catalysis, 249, 598-599 equilibrium isotope exchange in, 249, 443-479 hydrogen tunneling in, 249, 373-397] interfacial [competitive inhibitors, kinetic characterization, 249, 604-605 equilibrium parameters, 249, 587-594 forward commitment to, 249, 598-599 interpretation, 249, 578-586 (constraining variables for high processivity, 249, 582-586 kinetic variables at interface,... 

Table 1.2 Examples of important mixing rate and equilibrium parameters in environmental process...

Process Mixing rate-related parameter Equilibrium parameter... 

The selectivity and equilibrium parameters for the C6 system are given in Table IX, the activity parameters in Table X, and the deactivation parameters in Table XI. 

Then, the relationship between tfA B and the Langmuir equilibrium parameter (La) is... 

Another important equilibrium parameter is the distribution coefficient (Aj) defined as... 

Finally, /fUneal, is the equilibrium parameter in the expression of the linear equilibrium ... 

In Table 1 values of thermodynamic equilibrium parameters and values of Kp and Kpi at 25 are given. 

Equilibrium parameters derived from kinetics will differ from those measured at equilibrium because of the effects of proline isomerization. The additional equilibria between cis- and rans-peptidyl-proline bonds in the denatured state add to its stability and so favor denaturation (equation 18.1). 

The next step is the choice of the basis set of these operators. The choice of the basis set depends on the ensemble. Kadanoff and Swift have considered a grand canonical ensemble with the temperature, chemical potential, and the velocity as the equilibrium parameters. The states that describe a situation where these equilibrium parameters vary slowly are the local equilibrium states. Linear combinations of the densities of the conserved operators acting on the equilibrium state ( ), where L ) =0) provide the desired local... 

The equations (20) to (30) provide the basis for predicting the adsorption rate profiles for the binary system. The input parameters required for the model are the single-solute film transfer and surface diffusion coefficients, the single-solute isotherm constants and the mixture equilibria coefficients. The rate parameters were obtained from single solute rate data (20), and the equilibrium parameters were obtained from single and multi-solute equilibrium data. 

---