Equilibrium constants activity based

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. 

In terms of the equilibrium constant K based on molar densities of reactants and the activated complex in step 1, (14-174) yields... 

This equilibrium constant is based on activity, not concentration. It now must be converted to a concentration-based equilibrium constant. For a gas,... 

The thermite reaction is an oxidation-reduction reaction that uses powdered aluminum metal as a reducing agent to reduce a metal oxide, such as Fe203, to the free metal. The thermodynamic equilibrium constant, K, is an equilibrium constant expression based on activities. In dilute solutions activities can be replaced by the numerical values of molarities and in ideal gases, by the numerical values of partial pressures in bar. The activities of pure solids and liquids are 1. 

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]. 

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... 

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). 

For (acid + base) reactions, expressions can be written for the equilibrium constant that involve activity coefficients as well. For example, for the reactions... 

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. 

All equilibrium constants in the present discussion are based on the concentration (not activity) scale. This is a perfectly acceptable thermodynamic scale, provided the ionic strength of the solvent medium is kept fked at a reference level (therefore, sufficiently higher than the concentration of the species assayed). This is known as the constant ionic medium thermodynamic state. Most modern results are determined at 25 °C in a 0.15 M KCl solution. If the ionic strength is changed, the ionization constant may be affected. For example, at 25 °C and 0.0 M ionic strength, the pXj of acetic acid is 4.76, but at ionic strength 0.15 M, the value is 4.55 [24]. 

Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-H20 system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 

It has already been pointed out that the calculated equilibrium constants are known better than the analytical data on which they are based. So we may not attribute the observed difference in provisional equilibrium values and experimental values (Table VI) to uncertainties in the aqueous model. There are, however, uncertainties in estimating 31og K(x)/3x from Figure 1. Slopes estimated from Figure 1 are probably known within 20%. Uncertainties of 20% In 3 log K(x)/3x translate directly to uncertainties of 20% in solid phase activities and activity coefficients. 

Finally, it is not appropriate to derive thermodynamic properties of solid solutions from experimental distribution coefficients unless it can be shown independently that equilibrium has been established. One possible exception applies to trace substitution where the assumptions of stoichiometric saturation and unit activity for the predominant component allow close approximation of equilibrium behavior for the trace components (9). The method of Thorstenson and Plummer (10) based on the compositional dependence of the equilibrium constant, as used in this study, is well suited to testing equilibrium for all solid solution compositions. However, because equilibrium has not been found, the thermodynamic properties of the KCl-KBr solid solutions remain provisional until the observed compositional dependence of the equilibrium constant can be verified. One means of verification is the demonstration that recrystallization in the KCl-KBr-H20 system occurs at stoichiometric saturation. 

However, the Henderson-Hasselbach equation results from an oversimplification that deserves special attention. In fact, the equilibrium constant K characterizing the acid-base equilibrium must be written with activities ... 

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. 

J K A factor in equation 17.58 An equilibrium constant based on activities various —... 

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 the moment, we can consider the activated complex as a type of intermediate (although not isolatable) reached by the reactants as the highest energy point of the most favorable reaction path. The activated complex is in equilibrium with the reactants and is commonly regarded as an ordinary molecule, except that movement along the reaction coordinate will lead to decomposition. The activated complex can be assumed to have the associated properties of molecules, such as volume, heat content, acid-base behavior, entropy, and so forth. Indeed, formal calculations of equilibrium constants involving reactions of the activated complex to form another activated complex can be carried out (Sec. 5.6 (b)). ... 

In this expression, K is the thermodynamic equilibrium constant, which can be multiplied by Na/p (with Na equal to Avogadro s number) to obtain the commonly used equilibrium constants based on the molar bulk concentration reference state. It is important to note that the exponential term in the right-hand side of Equations 2.20 and 2.21 is an activity coefficient term. This term depends on the interaction field n z), which is nonlocal and therefore it couples with all the interactions and chemical equilibria in all regions of the film. 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

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