Equilibrium constant activity coefficient

Via use of the SED technique, it is possible to determine solute solubilization equilibrium constants (activity coefficients of micellar bound solutes) as well as the surfactant concentration on both sides of the dialysis membrane among other parameters (458-460). 

APPENDIX 6.2 THE VARIOUS SCALES FOR EQUILIBRIUM CONSTANTS, ACTIVITY COEFFICIENTS, AND pH... 

Where, K, r, m, and a express equilibrium constant, activity coefficient, and water activity, and NIO, K4 instead of the minerals of Na2B4C>7 lOHaO, K2B4O74H2O (the same in the following), respectively. Then, the equilibria constants K are calculated with ji /RT and shown in Table 6. 

The pH will depend upon the ionic strength of the solution (which is, of course, related to the activity coefficient — see Section 2.5). Hence, when making a colour comparison for the determination of the pH of a solution, not only must the indicator concentration be the same in the two solutions but the ionic strength must also be equal or approximately equal. The equation incidentally provides an explanation of the so-called salt and solvent effects which are observed with indicators. The colour-change equilibrium at any particular ionic strength (constant activity-coefficient term) can be expressed by a condensed form of equation (4) ... 

Equations 4 and 7 of Table 2.2 suggest that a plot of the logarithm of the equilibrium constant (or a representative equilibrium activity) of a reaction versus the reciprocal of absolute temperature can yield information concerning AH°. For many reactions ACp is close to zero and AH° is essentially independent of temperature, and a linear plot of log K versus JT is obtained over an appreciable temperature range. The equilibrium constant can then be computed readily by the simple relationship of equation 3 in Table 2.2. When ACp is constant over a range of temperature, equation 6 of Table 2.2 can be used to compute the equilibrium constant-temperature coefficient. 

Rather than attempting to allow for the concentration dependence of activity coefficients of ions M" " " and when we calculate an equilibrium constant K, we can vary and [X ] with constant activity coefficients... 

This handbook contains extensive tables of data for the more common Inorganic and organic aqueous electrolyte solutions. Properties covered include dielectric constants, activity coefficients, relative partial molar enthalpies, equilibrium constants, solubility products, conductivities, electrochemical potentials, Gibbs energies and enthalpies of formation, entropies, heat capacities, viscosities, and diffusion coefficients. Unfortunately, only a few of the tables contain references to the sources of the data. 

K and K will also include the activity coefficients y,-. In a first approach one can assumed concentration independent equilibrium constants and thus constant activity coefficients. The ratio between the equilibrium constants of (8.14) and (8.16) is introduced as a parameter a. 

Here the N b denote the mole fraction of glycine in water and benzene, respectively, and the fs denote proportionality constants, (activity coefficients) relating activity to mole fraction. One of these constants may be arbitrarily chosen it is convenient to make the choice so that = 1 in a very dilute aqueous solutionf. At equilibrium (o ), = ag)g, and hence from (2) ... 

If we vary the composition of a liquid mixture over all possible composition values at constant temperature, the equilibrium pressure does not remain constant. Therefore, if integrated forms of the Gibbs-Duhem equation [Equation (16)] are used to correlate isothermal activity coefficient data, it is necessary that all activity coefficients be evaluated at the same pressure. Unfortunately, however, experimentally obtained isothermal activity coefficients are not all at the same pressure and therefore they must be corrected from the experimental total pressure P to the same (arbitrary) reference pressure designated P. This may be done by the rigorous thermodynamic relation at constant temperature and composition ... 

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. 

In an attempt to explain the nature of polar interactions, Martire et al. [15] developed a theory assuming that such interactions could be explained by the formation of a complex between the solute and the stationary phase with its own equilibrium constant. Martire and Riedl adopted a procedure used by Danger et al. [16], and divided the solute activity coefficient into two components. 

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

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

The equilibrium composition of a reaction mixture is described by the equilibrium constant, which is equal to the activities of the products (raised to powers equal to their stoichiometric coefficients in the balanced chemical equation for the reaction) divided by the activities of the reactants (raised to powers equal to their stoichiometric coefficients). 

The powers to which the activities are raised in the expression for an equilibrium constant must match the stoichiometric coefficients in the chemical equation, which is normally written with the smallest whole numbers for coefficients. Therefore, if we change the stoichiometric coefficients in a chemical equation (for instance, by... 

Suppose we successfully measured the sticking coefficient and the activation energy for adsorption of a certain molecule, as well as the rate of desorption. Is it then possible to estimate the equilibrium constant for adsorp-tion/desorption ... 

Sheppard and Brown have evaluated the rate coefficient k as 4180 l.mole. sec with 0.53 M HCIO4 at 20 °C. The overall activation energy and entropy corresponding to the term /f,7 17, where Ky-, is the equilibrium constant of the reaction... 

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. 

Because of uncertainties of equilibrium constants, ES, pH, temperature, /02 and other parameters (activity coefficient, ionic strength, activity of water, pressure), the estimated values of concentrations may have uncertainties of 1 in logarithmic unit. However, it can be concluded from the thermochemical calculations and fluid inclusion data that the Kuroko ore fluids have the following chemical features. 

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