Activity equilibrium constant

The thermodynamic activity equilibrium constant (Ka) is expressed in terms of mole fraction (X) and activity coefficient (y) by the following equation ... 

The rate constants, thermodynamic parameters of activation, equilibrium constant, and the isomerization enthalpy for conversion of cholest-5-en-3-one to cholest-4-en-3-one catalysed by EtONa in absolute ethanol were determined by classic and multivariate kinetic methodologies. The multivariate modelling kinetic treatment allowed the concentrations of the species involved to be calculated, revealed the 3,5-dienolate to be a highly reactive intermediate, and was able to discriminate among several applicable mechanisms, thereby supporting the one comprising two reversible steps.18... 

The ratio n jn n has the form of an equilibrium constant for formation of activated complex. For systems in which the activity of the various species equals their concentration (dilute gases, dilute solutions of nonelectrolytes) (9.41) defines a totally empirical function, the activation equilibrium constant K iT),... 

The activity coefficient of the transition state y enters into the expressions for the reaction rate and rate constant since the concentration of activated complexes comes from the activation equilibrium constant. If the reaction rate depends on the activity of the transition state, = y [X ], then the overall rate of reaction will depend on the activity coefficients of the reactants. 

For the reaction A(solution) + B(solution) AB(solution), the activity equilibrium constant is defined as... 

By proceeding as we did and introducing the activation equilibrium constants, we obtain ... 

Hence, the task of the theory is to calculate the rate constant k of the unimolecular decay of (AB ) and the activation equilibrium constant K. ... 

Except for the reactions between small molecules, the theoretical computation of K is a difficult or even unsolvable task and, because of the short life of the activated complex, the experimental determination of K is hardly imaginable. Fortunately, there is a way out of this frustrating situation, viz. applying a well-known formula of chemical thermodynamics to the activation equilibrium constant (NB the notation used follows the recommendations of lUPAC s Green Book ) ... 

By recalling a well known thermodynamic relations, viz. (dGldp)j = V, and the equation A G° = -RT nK°, it is possible to derive the expression describing the pressure dependence of the activation equilibrium constant ... 

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]. 

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

Perhaps the most extensively studied catalytic reaction in acpreous solutions is the metal-ion catalysed hydrolysis of carboxylate esters, phosphate esters , phosphate diesters, amides and nittiles". Inspired by hydrolytic metalloenzymes, a multitude of different metal-ion complexes have been prepared and analysed with respect to their hydrolytic activity. Unfortunately, the exact mechanism by which these complexes operate is not completely clarified. The most important role of the catalyst is coordination of a hydroxide ion that is acting as a nucleophile. The extent of activation of tire substrate througji coordination to the Lewis-acidic metal centre is still unclear and probably varies from one substrate to another. For monodentate substrates this interaction is not very efficient. Only a few quantitative studies have been published. Chan et al. reported an equilibrium constant for coordination of the amide carbonyl group of... 

In determining the values of Ka use is made of the pronounced shift of the UV-vis absorption spectrum of 2.4 upon coordination to the catalytically active ions as is illustrated in Figure 2.4 ". The occurrence of an isosbestic point can be regarded as an indication that there are only two species in solution that contribute to the absorption spectrum free and coordinated dienophile. The exact method of determination of the equilibrium constants is described extensively in reference 75 and is summarised in the experimental section. Since equilibrium constants and rate constants depend on the ionic strength, from this point onward, all measurements have been performed at constant ionic strength of 2.00 M usir potassium nitrate as background electrolyte . 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

Several features of equation 6.50 deserve mention. First, as the ionic strength approaches zero, the activity coefficient approaches a value of one. Thus, in a solution where the ionic strength is zero, an ion s activity and concentration are identical. We can take advantage of this fact to determine a reaction s thermodynamic equilibrium constant. The equilibrium constant based on concentrations is measured for several increasingly smaller ionic strengths and the results extrapolated... 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

The following experiments involve the experimental determination of equilibrium constants and, in some cases, demonstrate the importance of activity effects. 

In a series of organic acids of similar type, not much tendency exists for one acid to be more reactive than another. For example, in the replacement of stearic acid in methyl stearate by acetic acid, the equilibrium constant is 1.0. However, acidolysis in formic acid is usually much faster than in acetic acid, due to higher acidity and better ionizing properties of the former (115). Branched-chain acids, and some aromatic acids, especially stericaHy hindered acids such as ortho-substituted benzoic acids, would be expected to be less active in replacing other acids. Mixtures of esters are obtained when acidolysis is carried out without forcing the replacement to completion by removing one of the products. The acidolysis equilibrium and mechanism are discussed in detail in Reference 115. 

The physical data index summarizes the quantitative data given for specific compounds in the text, tables and figures in Volumes 1-7. It does not give any actual data but includes references both to the appropriate text page and to the original literature. The structural and spectroscopic methods covered include UV, IR, Raman, microwave, MS, PES, NMR, ORD, CD, X-ray, neutron and electron diffraction, together with such quantities as dipole moment, pX a, rate constant and activation energy, and equilibrium constant. 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

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