Bases equilibrium constants and

The relationship between the concentration-based equilibrium constant and the thermodynamic equilibrium constant is therefore ... 

One can write acid-base equilibrium constants for the species in the inner compact layer and ion pair association constants for the outer compact layer. In these constants, the concentration or activity of an ion is related to that in the bulk by a term e p(-erp/kT), where yp is the potential appropriate to the layer [25]. The charge density in both layers is given by the algebraic sum of the ions present per unit area, which is related to the number of ions removed from solution by, for example, a pH titration. If the capacity of the layers can be estimated, one has a relationship between the charge density and potential and thence to the experimentally measurable zeta potential [26]. 

Equilibria in Solution The stability of a protein-ligand complex in solution is measured in terms of the equilibrium constant and the standard free energy of association based on it. For association of species P and L in solution to form a complex PL, i.e., for... 

The equilibrium constant of the proton transfer (125), omitting the activity of the H20, is known as the base dissociation constant and is denoted by K , to distinguish it from the KA of (124). 

The general approach illustrated by Example 18.7 is widely used to determine equilibrium constants for solution reactions. The pH meter in particular can be used to determine acid or base equilibrium constants by measuring the pH of solutions containing known concentrations of weak acids or bases. Specific ion electrodes are readily adapted to the determination of solubility product constants. For example, a chloride ion electrode can be used to find [Cl-] in equilibrium with AgCl(s) and a known [Ag+]. From that information, Ksp of AgCl can be calculated. 

The acid-base equilibrium constant for the Me residue can be determined by spectroscopic pH titration. An example for the titration is shown in Fig. 2. The electrostatic potential

difference between the apparent pK on the charged surface (pKobs) and that on an intrinsic neutral surface (pK1) by... 

Next, an exploration of thermodynamics and equilibrium, based on a conceptual understanding of entropy and Gihbs free energy. This integrated presentation lays a common foundation for these concepts and provides a basis for understanding the origin and form of the equilibrium constant and the behavior of equilibrium systems. 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

The pH of a buffer solution depends on the weak acid equilibrium constant and the concentrations of the weak acid and its conjugate base. To show this, we begin by taking the logarithm of the acid equilibrium constant ... 

Direct measurements of solute activity are based on studies of the equilibria in which a given substance is involved. The parameters of these equilibria (the distribution coefficients, equilibrium constants, and EMF of galvanic cells) are determined at different concentrations. Then these data are extrapolated to very low concentrations, where the activity coincides with concentration and the activity coefficient becomes unity. 

In the case of an acid HX titrated with a quarternary ammonium base R4NOH there are a few complications as a consequence of some additional equilibrium constants and of a certain degree of instability of the titrant tetramethylammonium hydroxide (TMAOH) in pyridine for this reason the titrant solution was standardized against benzoic acid and used only on the day of preparation. Now, in addition to KHX and ifHX > we had to deal with... 

An indication of the nature of the transition state in aromatic substitution is provided by the existence of some extrathermodynamic relationships among rate and acid-base equilibrium constants. Thus a simple linear relationship exists between the logarithms of the relative rates of halogenation of the methylbenzenes and the logarithms of the relative basicities of the hydrocarbons toward HF-BFS (or-complex equilibrium).288 270 A similar relationship with the basicities toward HC1 ( -complex equilibrium) is much less precise. The jr-complex is therefore a poorer model for the substitution transition state than is the [Pg.150]

Table 5 lists equilibrium data for a new hypothetical gas-phase cyclisation series, for which the required thermodynamic quantities are available from either direct calorimetric measurements or statistical mechanical calculations. Compounds whose tabulated data were obtained by means of methods involving group contributions were not considered. Calculations were carried out by using S%g8 values based on a 1 M standard state. These were obtained by subtracting 6.35 e.u. from tabulated S g-values, which are based on a 1 Atm standard state. Equilibrium constants and thermodynamic parameters for these hypothetical reactions are not meaningful as such. More significant are the EM-values, and the corresponding contributions from the enthalpy and entropy terms. 

Various other methods have therefore been employed in an attempt to identify species more directly. An equilibrium study based on the change in the UV spectra of acidified molybdate solutions in 1.0 M NaCl medium showed that the data can be satisfactorily explained in terms of a reaction model including [MoyCfy]6, [HMo7024]6 , [H2Mo7 O24]4-, and [Mo8026]4- (82). However, due to the many unknown parameters (equilibrium constants and spectra) to be calculated a totally independent evaluation of the data was not possible. 

The small difference between the successive pK values (cf. values below) of tungstic acid was previously explained in terms of an anomalously high value for the first protonation constant, assumed to be effected by an increase in the coordination number of tungsten in the first protonation step (2, 3, 55). As shown by the values of the thermodynamic parameters for the protonation of molybdate it is actually the second protonation constant which has an abnormally high value (54, 58). An equilibrium constant and thermodynamic quantities calculated for the first protonation of [WO, - pertaining to 25°C and zero ionic strength (based on measurements from 95° to 300°C), namely log K = 3.62 0.53, AH = 6 13 kJ/mol, and AS = 90 33 J, are also consistent with a normal first protonation (131) (cf. values for molydate, Table V). 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

The p/<, of a base is actually that of its conjugate acid. As the numeric value of the dissociation constant increases (i.e., pKa decreases), the acid strength increases. Conversely, as the acid dissociation constant of a base (that of its conjugate acid) increases, the strength of the base decreases. For a more accurate definition of dissociation constants, each concentration term must be replaced by thermodynamic activity. In dilute solutions, concentration of each species is taken to be equal to activity. Activity-based dissociation constants are true equilibrium constants and depend only on temperature. Dissociation constants measured by spectroscopy are concentration dissociation constants." Most piCa values in the pharmaceutical literature are measured by ignoring activity effects and therefore are actually concentration dissociation constants or apparent dissociation constants. It is customary to report dissociation constant values at 25°C. 

For various alkanes over TON, MFI, MOR and FAU framework types the entropy of adsorption was calculated based on the measured values for the adsorption equilibrium constant and for the heat of adsorption. Figure 13.13 indicates that each time a linear relation is found between the entropy and the heat of adsorp-... 

Yang and Schulz also formulated a treatment of coupled enzyme reaction kinetics that does not assume an irreversible first reaction. The validity of their theory is confirmed by a model system consisting of enoyl-CoA hydratase (EC 4.2.1.17) and 3-hydroxyacyl-CoA dehydrogenase (EC 1.1.1.35) with 2,4-decadienoyl coenzyme A as a substrate. Unlike the conventional theory, their approach was found to be indispensible for coupled enzyme systems characterized by a first reaction with a small equilibrium constant and/or wherein the coupling enzyme concentration is higher than that of the intermediate. Equations based on their theory can allow one to calculate steady-state velocities of coupled enzyme reactions and to predict the time course of coupled enzyme reactions during the pre-steady state. 

A quantitative measure of the degree of dissociation is given by the equilibrium constant for the acid or base. The higher the equilibrium constant is, the greater the percent dissociation of the acid or base. Therefore, a higher equilibrium constant means a stronger acid or base. Equilibrium constants, K and K, are listed for several com-mon weak acids and bases in Table 13.4. 

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