Thermodynamic equilibrium constant, activity

Apparent equilibrium constant (concentration ratio) Thermodynamic equilibrium constant (activity ratio)... 

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. 

Equations (9.7) and (9.8) define K, the equilibrium constant for the reaction.b It is sometimes referred to as the thermodynamic equilibrium constant. As we shall see, this ratio of activities can be related to ratios of pressure or concentration which, themselves, are sometimes called equilibrium constants. But K, as defined in equations (9.7) and (9.8), is the fundamental form that is directly related to the free energy change of the reaction. 

Figure 9.1 is a graph of equation (9.52) showing how K varies with pressure at 298.15 K. We see that it increases by a factor of approximately 2 as the pressure increases by a factor of 1000. The increase is due to the change in the activity of the water rather than to a change in the thermodynamic equilibrium constant with pressure. 

The reactant mixture may be so nonideal that Equation (7.28) is inadequate. The rigorous thermodynamic approach is to replace the concentrations in Equation (7.28) with chemical activities. This leads to the thermodynamic equilibrium constant. 

Consequences of the Snyder and Soczewinski model are manifold, and their praetieal importance is very signifieant. The most speetaeular conclusions of this model are (1) a possibility to quantify adsorbents ehromatographic activity and (2) a possibility to dehne and quantify chromatographic polarity of solvents (known as the solvents elution strength). These two conclusions could only be drawn on the assumption as to the displacement mechanism of solute retention. An obvious necessity was to quantify the effect of displacement, which resulted in the following relationship for the thermodynamic equilibrium constant of adsorption, K,, in the case of an active chromatographic adsorbent and of the monocomponent eluent ... 

We omit concentrations of pure solids and pure liquids from equilibrium constant expressions because their activity is taken to be 1 and the thermodynamic equilibrium constant involves activities, rather than concentrations. 

In this expression, the square brackets refer to the activity of the component although it is more convenient to use its concentration. This approximation is generally satisfactory, except at very high concentrations, and is particularly suitable for analytical use. Where it is necessary to distinguish between the constant obtained using concentrations and the true thermodynamic equilibrium constant Ka the former may be termed the equilibrium quotient and assigned the symbol Q. The exact relation between Ke and Q has been the subject of much investigation and speculation. In this... 

We assume that the activity coefficient of the ion-pairs is unity and denote the mean ionic activity coefficient by y . The thermodynamic equilibrium constant for the dissociation is then given by the equation... 

Including activity coefficients y, the thermodynamic equilibrium constant K becomes ... 

Salt effects in kinetics are usually classified as primary or secondary, but there is much more to the subject than these special effects. The theoretical treatment of the primary salt effect leans heavily upon the transition state theory and the Debye-Hii ckel limiting law for activity coefficients. For a thermodynamic equilibrium constant one should strictly use activities a instead of concentrations (indicated by brackets). 

Let AT be the true thermodynamic equilibrium constant for formation of the transition-state species T from the reactant-state species R and let k be the experimental rate constant for the reaction of R. Neglecting activity coefficients ... 

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 examples in section 3.1.2 of calculations using stability constants involve concentrations of M, L, and ML . Rigorously, a stability constant, as any thermodynamic equilibrium constant should be defined in terms of standard state conditions (see section 2.4). When the system has the properties of the standard state conditions, the concentrations of the different species are equal to their activities. However, the standard state conditions relate to the ideal states described in Chapter 2, which can almost never be realized experimentally for solutions of electrolytes, particularly with water as the solvent. For any conditions other than those of the standard state, the activities and concentrations are related by the activity coefficients as described in Chapter 2, and especially... 

The superscript 0 in Eq. 2.2 indicates a true thermodynamic equilibrium constant. We use plain K when concentrations replace activities or, for electrolyte solutions, when K refers to a nonzero ionic strength (see Section 2.2). 

Water gas shift and steam reforming reactions producing H2 under rich conditions (reactions R6 and R7 in Table III, respectively) start to be significantly active at the temperatures above 300 °C (cf. Fig. 22c. These reactions result in a different actual CO C3H6 H2 concentration ratio inside the monolith in comparison with the raw exhaust gas, or the synthetic rich inlet gas mixture used in the lab experiments (Koci et al., 2007b). The reactions with water are characterized by the evaluated rate constants kj T) as well as by the thermodynamic equilibrium constants Keq(7). 

If the concentrations of Ca2+ and SO4 are to increase when a second salt is added to increase ionic strength, the activity coefficients must decrease with increasing ionic strength At low ionic strength, activity coefficients approach unity, and the thermodynamic equilibrium constant (8-5) approaches the concentration equilibrium constant (6-2). One way to measure a thermodynamic equilibrium constant is to measure the concentration ratio (6-2) at successively lower ionic strengths and extrapolate to zero ionic strength. Commonly, tabulated equilibrium constants are not thermodynamic constants but just the concentration ratio (6-2) measured under a particular set of conditions. 

Activity coefficients and concentration equilibrium constants. Strictly speaking, Eq. 6-31 applies only to thermodynamic equilibrium constants -that is, to constants that employ activities rather than concentrations. The experimental determination of such constants requires measurements of the apparent equilibrium constant or concentration equilibrium constant21 Kc at a series of different concentrations and extrapolation to infinite dilution (Eq. 6-32). 

After de Forcrand s Clapeyron, and Handa s methods, a third method for the determination of hydrate number, proposed by Miller and Strong (1946), was determined to be applicable when simple hydrates were formed from a solution with an inhibitor, such as a salt. They proposed that a thermodynamic equilibrium constant K be written for the physical reaction of Equation 4.14 to produce 1 mol of guest M, and n mol of water from 1 mol of hydrate. Writing the equilibrium constant K as multiple of the activity of each product over the activity of the reactant, each raised to its stoichiometric coefficient, one obtains ... 

In each case these parameters represent differences between the state function of the activated complex in a particular standard state and the state function of the reactants referred to in the same standard state. One is giving all the characteristics of a thermodynamic equilibrium constant, although it should be multiplied by a transitional partition function. For ideal systems the magnitude of AH° does not depend on the choice of standard state, and for most of the nonideal systems that are encountered the dependence is slight. For all systems, the magnitudes of AG° and AS0 depend strongly on the choice of standard state, so it is not useful to... 

The input of the problem requires total analytically measured concentrations of the selected components. Total concentrations of elements (components) from chemical analysis such as ICP and atomic absorption are preferable to methods that only measure some fraction of the total such as selective colorimetric or electrochemical methods. The user defines how the activity coefficients are to be computed (Davis equation or the extended Debye-Huckel), the temperature of the system and whether pH, Eh and ionic strength are to be imposed or calculated. Once the total concentrations of the selected components are defined, all possible soluble complexes are automatically selected from the database. At this stage the thermodynamic equilibrium constants supplied with the model may be edited or certain species excluded from the calculation (e.g. species that have slow reaction kinetics). In addition, it is possible for the user to supply constants for specific reactions not included in the database, but care must be taken to make sure the formation equation for the newly defined species is written in such a way as to be compatible with the chemical components used by the rest of the program, e.g. if the species A1H2PC>4+ were to be added using the following reaction ... 

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