Thermodynamic equilibrium constant-based

The values of /3 for each C, were obtained by iteration from the total thermodynamic equilibrium constants based on conductivity measurements. The activity coefficients f2- and / were evaluated from the extended Debye-Hiickel theory. 

In Chapter 6, we discussed the thermodynamic equilibrium constant based on activities rather than on concentrations. Diverse salts affect the activities and therefore the extent of dissociation of weak electrolytes such as weak acids or bases. 

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. 

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. 

ADCA 7-Amino-3-desacetoxycephalosporanic acid APA 6 Aminopenicillanic acid HPG D-p-Hydroxyphenylglycine HPGA D-p-Hydroxyphenylglycine amide Keq Concentration based equilibrium constant Kth Thermodynamic equilibrium constant... 

The very low value of Ashmore and Burnett is difficult to explain. It is easy to demonstrate that the discrepancy is not resolved by assuming the N03 intermediate in nitrogen dioxide decomposition is the pernitrite radical, in contradistinction to the symmetric nitrate radical. Their calculation of k5 depended on an experimentally obtained value for k 5 and an equilibrium constant K5- 5 calculated from thermodynamic properties for N03 measured by Schott and Davidson and Ray and Ogg. These results, obtained in a nitrogen pentoxide system, pertain to the nitrate radical, not the pernitrite radical. Guillory and Johnston176 reported an equilibrium constant based on estimated... 

Based on these considerations, it is possible to write the expressions for the carbonic acid system thermodynamic equilibrium constants (Kj). 

Another important application is the use of potentiometric measurements for the evaluation of thermodynamic equilibrium constants. In particular, the dissociation constants for weak acids and weak bases in a variety of solvents are... 

Since equilibrium constants are defined by ion activities, which are defined by their concentrations and coefficients (see equation 4.15), they do not include ion pairing or complexation effects. In a multi-ion and multiligand solution, where ion pairing is common, it is necessary to use thermodynamic equilibrium constants to convert the ion-pair concentrations to concentrations of free ions. This equilibrium constant (Kc) is defined by concentrations, making it useful to compute ion speciation. The thermodynamic equilibrium constant (K q) used in calculating Kc is based on the following conditions I = 0 m, 25°C and 1 atm. Thus, Kc is defined by the following equation ... 

These programs are able to model the geological systems soil/rock-aqueous solution systems that is the concentration and distribution of the thermodynamically stable species can be determined based on the total concentrations of the components and the parameters just mentioned. In addition, the programs can also be used to estimate thermodynamic equilibrium constants and/or surface parameters from the concentrations of the species determined through experiments. Thermodynamic equilibrium constants can be found in tables (Pourbaix 1966) or databases (e.g., Common Thermodynamic Database Project, CHESS, MINTEQ, Visual MINTEQ, NEA Thermodynamical Data Base Project (TDB), JESS, Thermo-Calc Databases). Some programs (e.g., NETPATH, PHREEQC) also consider the flowing parameters. 

The thermodynamic equilibrium constants shown by Equations 3.15 and 3.16 match the stoichiometric (or concentration based-) constants of stoichiometric models (see Equations 1 and 3 of Reference 1). Since the latter neglect the modulation of the adsorption of a charged species by the surface potential, they are not constant [19] after the addition of the IPR in the mobile phase. Stoichiometric relationships [19] represent only the ratio of equilibrium concentrations and cannot describe equilibrium in the presence of electrostatic interactions. In their stoichiometric approach. 

Using activity coefficients, it is possible to examine in greater detail the effect of solvents on acid and base strengths. Equilibrium constants expressed in terms of concentration are solvent-dependent. Solvent-independent, so-called thermodynamic equilibrium constants are obtained when the concentration terms are replaced by concentration-based activity terms. The thermodynamic equilibrium constant K for the reaction HA H + A is given by the following equation ... 

This approach is based on classical thermodynamics and statistical mechanics the latter makes the link to the microscopic picture of the adsorption processes. From the point of view of thermodynamics, adsorption can be treated like a chemical reaction. It will be shown that adsorption can proceed with or without a change of the number of gaseous molecules, so that the thermodynamic equilibrium constant expressed in partial pressures may or may not equal the constant expressed in concentrations. Notice that the standard values of some quantities accepted here when deriving formulae for the adsorption characteristics are not the standard states commonly used in chemical thermodynamics. In particular, it concerns the concentrations. 

In Eqs. (3) and (4), overbars denote the ion-exchanger phase. For a cation-exchange reaction as shown here, the exchangeable ions (Na" " and H+) are termed counterions and the negatively charged ions in solution are called colons. K is the thermodynamic equilibrium constant, and denotes ionic activity. For convenience of measurement, concentrations are used in practice in place of activities. In this case, in Eq. (4), based on concentration, the selectivity... 

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

For weak acids, the magnitude of is very small, and as a result the resulting H3O+ and A ions will be produced in small amounts. Under those conditions, both Yjj+ and y will be approximately equal to one, and then one can approximate the thermodynamic equilibrium constant, K, by the concentration-based ionization constant, Ka. 

Based on this information, it is possible to proceed with development of a first-order reversible reaction. As suggested by Harter (1989), it is convenient to convert sorbate concentration in solution to fraction remaining at time, t. Using this approach, the data were adequately modeled by a single reaction (Fig. 6-2b) with apparent rate coefficients k = 3.26 A / = 1.848 and the apparent thermodynamic equilibrium constant, K 1.76. Considering that the reaction appears to be completed within 2 min, cation exchange is the probable sorption mechanism. 

Also, aj = YjZj for each species, jj is the true mole fraction-based activity coefficient for the 7th species, and is the thermodynamic equilibrium constant. 

As the apparent equilibrium constant is more easily measured in the laboratory than the thermodynamic equilibrium constant, most reported data on biochemical reactions are apparent equilibrium constants. Since the thermodynamic equilibrium constant here is based on ideal 1-molal standard states, so that the activity coefficients are unity at infinite dilution, we have... 

Also we can define Ka = -logA a based on the tnie thermodynamic equilibrium constant. 

It should be remembered that that situation is more complicated when chemical equilibrium constants based on normalizations of the type shown in equations (4.6)-(4.8) are used. Even though those chemical equilibrium constants are thermodynamically consistent, they are functions of the composition of the reacting liquid phase. For example, if a dissolved gas k normalized according to equation... 

Table A-II. Logarithms (base 10) of the Thermodynamic Equilibrium Constants of Aqueous Phase Association Reactions and Solid Phase Dissolution Reactions (Kgp) Used in this Study...

The thermodynamic equilibrium is based on the UNIQUAC model [100], The liquid-phase binary diffusivities are determined using the method of Tyn and Calus (see [94]) for the diluted mixtures corrected by the Vignes equation [42] to account for finite concentrations. The vapor-phase diffusion coefficients are assumed constant. The reaction kinetics parameters are taken from [101]. The vapor and liquid binary mass-transfer correlations were calculated for the inert packing and the catalytic rings with the correlation of Onda et al. [102]. 

The concept of pH, however, is not applicable in such nonaqueous systems or in concentrated acid solutions. A new quantitative scale, therefore, was needed (5,9-11). The most useful and widely accepted method was proposed by Hammett and Deyrup in 1932 (12). They defined ho by equation 24, which can be determined experimentally by adding the neutral base B in low concentrations to an acid solution (BH+ is the acidic form of the indicator, Ksa+ is the thermodynamic equilibrium constant for BH+, and [BH+]/[B] is the ionization ratio generally determined spectrophotometrically). Equation 24 is usually written in the logarithmic form (eq. 25), where the quantity Hq is termed the Hammett acidity function. Since in dilute solutions of acids Abh+ is expressed as in equation 26, the Hammett acidity function becomes equal to pH. In concentrated solutions, however, Hq differs considerably from pH and this can be formally expressed by inserting activity coefficients in equation 24 (eq. 27). 

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