True thermodynamic constant

True thermodynamic constants use a species activity in place of its molar concentration a). 

Since AG° can be calculated from the values of the chemical potentials of A, B, C, D, in the standard reference state (given in tables), the stoichiometric equilibrium constant Kc can be calculated. (More accurately we ought to use activities instead of concentrations to take into account the ionic strength of the solution this can be done introducing the corresponding correction factors, but in dilute solutions this correction is normally not necessary - the activities are practically equal to the concentrations and Kc is then a true thermodynamic constant). 

The concentration-dependent thermodynamic constant Kc can be expressed as a function of the true thermodynamic constant K° as follows (Pankow, 1991) ... 

The importance of equilibrium measurements cannot be overly stressed. They provide true thermodynamic constants to evaluate the role of substrate binding in catalysis, they provide the background with which kinetic experiments can be properly designed and interpreted to establish the pathway of catalysis, and they provide additional constraints to be used in the fitting of kinetic data. 

As the overall composition of the system may be described by two variables, such as [H2O] and [COOH], a dependence on [COOH] might be added in Eq. (56). However, this is not needed, as no effect of the mole ratio [COOH)/[NH2] on the apparent equilibrium constant has ever been detected. Insertion of the above relationship into the mass action law provides a relationship between apparent equilibrium constant Ka and true thermodynamic constant K [Eq. (57)). 

Actually, applying Gran s strategy is more complicated than stated, because the pH value is an activity value. Hence, the activities of species HA and hr must be considered and /fa must be the true thermodynamic constant. As a result, activity coefficients must be used and Gran s equation must be written as follows ... 

Second, Berner uses the argument that his solubility for calcite is consistent with that calculated from the true thermodynamic constant whereas the value of Ingle et al. is not. The relationship between these constants is as follows ... 

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. 

The true thermodynamic equilibrium constant, Ksp, for the solubility of AglOa, therefore, is... 

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, 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... 

The conditional equilibrium constant may be defined in terms of the true thermodynamic equilibrium constant KML and the appropriate values of a. 

The retention of the band or peak beyond what V0 predicts depends on the magnitude of the equilibrium constant and logically on the volume Vs or area As of the stationary phase. The equation of importance is Vr — V0+KVS and the net retention V/ = KVS. Two main factors influence the value of the equilibrium constant and these are the chemical nature of the mobile and stationary phases. Chemistry is molecules and while true thermodynamics knows no molecules or forces between molecules, chemists think in terms of molecular properties. Among those properties, there is a consideration of the kinds of forces that exist between molecules. Granted that thermodynamics are energy not force considerations but it is useful to understand the main forces involved in the interaction between molecules. Put another way,... 

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. 

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 ... 

This means that the basicity constant measured in solution represents the total basicity of the dissolved aromatic substance. In order therefore to obtain the true basicity constant the measured figure evidently has to be divided by the number of active C-atoms in the molecule. This number, z, which is related to the symmetry of the molecule, is six for benzene, four for p-xylene, one for pentamethylbenzene, six for hexa-methylbenzene, fom for naphthalene, two for anthracene, etc. (see Tables 19 and 22). Thermodynamically, this correction can be justified as an entropy contribution (Mackor et al., 1958a). 

In order to derive a thermodynamic Haldane relation for this mechanism, the true dissociation constants for B (i.e., kjks) and for P (i.e., k lkd) are needed. From the definitions for the various kinetic parameters (See Ordered Bi Bi Mechanism) it is readily seen that... 

The notion of an ideal behavior also is defined here for those cases in which Pi is constant over a range of solution compositions, while variations with solution composition are said to characterize nonideal behavior. In the present studies values of purification factors are affected by the kinetics of the process. Accordingly, these quantities may not be true thermodynamic properties. 

This is called a Langmuir adsorption isotherm for a species A, and the function 9a( Pa) isi shown in Figure 7-23. The KjS are the adsorption-desorption equilibrium constants for species A and B. By historical convention we call these the adsorption isotherms. Before i we proceed let us note that this is a true thermodynamic equilibrium relation so that... 

However, if the valences of the exchanging cations are equal, the selectivity coefficient or pseudo-equilibrium constant is not affected by concentration. As already mentioned, one isotherm corresponds to a specific temperature in the case of adsorption or ion exchange of equal valence ions, whereas additionally, the same normality is required for the existence of only one isotherm in the case of ion exchange of different valence ions, due to the concentration-valence effect (Helfferich, 1962). The determination of the true equilibrium constant should be based on the thermodynamic activities (activity coefficients) of the species rather than concentrations. It is clear that the difficulties in the determination of activity coefficients also complicate the determination of the true equilibrium constant (Culfaz and Yagiz, 2004). 

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). 

The stability constants are defined here in terms of concentrations and hence have dimensions. True thermodynamic stability constants K° and (3° would be expressed in terms of activities (Section 2.2), and these constants can be obtained experimentally by extrapolation of the (real) measurements to (hypothetical) infinite dilution. Such data are of limited value, however, as we cannot restrict our work to extremely dilute solutions. At practical concentrations, the activities and concentrations of ions in solution differ significantly, that is, the activity coefficients are not close to unity worse still, there is no thermodynamically rigorous means of separating anion and cation properties for solutions of electrolytes. Thus, single-ion activity coefficients are not experimentally accessible, and hence, strictly speaking, one cannot convert equations such as 13.6 or 13.8 to thermodynamically exact versions. 

In Fig. 3 c the schematic volume-temperature curve of a non crystallizing polymer is shown. The bend in the V(T) curve at the glass transition indicates, that the extensive thermodynamic functions, like volume V, enthalpy H and entropy S show (in an idealized representation) a break. Consequently the first derivatives of these functions, i.e. the isobaric specific volume expansion coefficient a, the isothermal specific compressibility X, and the specific heat at constant pressure c, have a jump at this point, if the curves are drawn in an idealized form. This observation of breaks for the thermodynamic functions V, H and S in past led to the conclusion that there must be an internal phase transition, which could be a true thermodynamic transformation of the second or higher order. In contrast to this statement, most authors... 

Equation (5) is greatly simplified the true thermodynamic partition coefficient would be the quotient of analyte activities, not concentrations. Furthermore, the equation assumes that analyte A is present in only one form (one molecular structure or ion). When this is not realized in practice, a more complex equilibrium constant must be used. 

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