Debye-Huckel model constants

Fig. 3.7. The Debye-Huckel model is based upon selecting one ion as a reference ion, replacing the solvent molecules by a continuous medium of dielectric constant e and the remaining ions by an excess charge density (the shading usually used in this book to represent the charge density is not indicated in this figure).

Although reasonable activation energies may be obtained, it is still often difficult to predict accurate thermal rate constants. One reason for this is the deviation of the real system from ideality, which introduces parameters that are not computationally well-defined in the conventional MO-TST approach. Recall that the quasi-equilibrium constant in Equation (6) is in terms of activities. Thus, the rate constant equation (Eqn. 12) is a function of activity coefficients of reactants and transition states, and these coefficients cannot be computed with the usual Debye-Huckel model. 

Most models use dilute solution assumptions and former models [93] assumed unit values [2,19,93,94] of all activity coefficients (except in some cases for H+ ions). Bernhardsson et al. [4] reached a compromise by using two sets of equilibrium constants, one for dilute solutions and the other for concentrated solutions. Other authors used Debye-Huckel, the truncated Davies model [96,98], or the B-dot Debye-Huckel model [98] to derive the activity coefficients in concentrated solutions. 

The statistical thermodynamic approach of Pitzer (14), involving specific interaction terms on the basis of the kinetic core effect, has provided coefficients which are a function of the ionic strength. The coefficients, as the stoichiometric association constants in our ion-pairing model, are obtained empirically in simple solutions and are then used to predict the activity coefficients in complex solutions. The Pitzer approach uses, however, a first term akin to the Debye-Huckel one to represent nonspecific effects at all concentrations. This weakens somewhat its theoretical foundation. 

Rate constant for homogeneous self exchange, corrected for electrostatic work terms using Debye-Huckel-Bronsted model. Data taken from sources quoted in ref. 15 unless otherwise stated. 

A modification of GB that includes the effects of dissolved electrolytes in the formalism, i.e., an extension analogous to the Poisson-Boltzmann extension of the Poisson equation, has been proposed by Srinivasan et al. (1999). In this model, the dielectric constant is a function of the interatomic distance and the Debye-Huckel parameter (Eq. (11.7)). 

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 ... 

Table B.2. The Debye-Huckel constants used in the FREZCHEM model. T is temperature (K), and P is pressure (bars). (Numbers are in computer scientific notation, where e xx stands for 10 l )...

Temperature Effects. The temperature range for which this model was assumed to be valid was 0°C through 40°C, which is a range covering most natural surface water systems (28). Equilibrium constants were adjusted for temperature effects using the Van t Hoff relation whenever appropriate enthalpy data was available (23, 24, 25). Activity and osmotic coefficients were temperature corrected by empirical equations describing the temperature dependence of the Debye-Huckel parameters of equations 20 and 21. These equations, obtained by curve-fitting published data (13), were... 

Thirdly, another corollary of the first limitation, is the inconsistency and inadequacy of activity coefficient equations. Some models use the extended Delbye-Huckel equation (EDH), others the extended Debye-Huckel with an additional linear term (B-dot, 78, 79) and others the Davies equation (some with the constant 0.2 and some with 0.3, M). The activity coefficients given in Table VIII for seawater show fair agreement because seawater ionic strength is not far from the range of applicability of the equations. However, the accumulation of errors from the consideration of several ions and complexes could lead to serious discrepancies. Another related problem is the calculation of activity coefficients for neutral complexes. Very little reliable information is available on the activity of neutral ion pairs and since these often comprise the dominant species in aqueous systems their activity coefficients can be an important source of uncertainty. 

The components of an ion-association aqueous model are (1) The set of aqueous species (free ions and complexes), (2) stability constants for all complexes, and (3) individual-ion activity coefficients for each aqueous species. The Debye-Huckel theory or one of its extensions is used to estimate individual-ion activity coefficients. For most general-purpose ion-association models, the set of aqueous complexes and their stability constants are selected from diverse sources, including studies of specific aqueous reactions, other literature sources, or from published tabulations (for example, Smith and Martell, (13)). In most models, stability constants have been chosen independently from the individual-ion, activity-coefficient expressions and without consideration of other aqueous species in the model. Generally, no attempt has been made to insure that the choices of aqueous species, stability constants, and individual-ion activity coefficients are consistent with experimental data for mineral solubilities or mean-activity coefficients. 

We have from our study on pyrovanadate equilibria in the pH range 10.8 - 12 at 25 °C found that the medium dependence in Na(Cl), TBA(Cl), and Na,TBA(Cl) media can be explained with medium cation complexation to the vanadate species. Although vast medium concentration ranges have been covered, no Debye-Huckel parameters have to be used. Moreover, since Na, TBA and medium independent equilibrium constants have been determined, the pyrovanadate system can be modeled at any Vtot, [Na ], and [TBA ]. An analogous study on the H - HV04 system in the pH range 7 - 12 is in progress and it seems that medium cation complexes can explain all EMF/NMR data. 

The thermodynamic formation constant and heat of formation of Ni(CN)4" in aqueous solution have been determined at 25°C potentiometrically and calorimetrically, respectively. No background electrolyte was used, and the Debye-Huckel equation was applied to extrapolate the experimental thermodynamic data to zero ionic strength. Although, the activity model used is not compatible with the SIT, most of the experiments referred to / < 0.007 M therefore, the reported value = - 180.7 kJ moT at... 

The thermodynamic parameters for the formation of several metal-cyanide complexes, among others those of Ni(CN)4 , have been determined using pH-metric and calorimetric methods at 10, 25 and 40°C. In case of nickel(II), the thermodynamic data were determined by titration of Ni(C104)2 solutions with NaCN solutions. The ionic strength of the solutions were 1 < 0.02 M in all cases. The Debye-Huckel equation, related to the SIT model, was used to correct the formation constants to thermodynamic constants valid at 7 = 0. Since previous experiments indicated that the dependence of A,77° in the ionic strength in dilute aqueous solutions is small compared to the experimental error, the measured heats of reaction (A,77 = - 189.1 kJ mol at 10°C A,77 ,= -183.7 kJ mol at 40 C) were taken to be valid at 7 = 0, but the uncertainties were estimated in this review as 2.0 kJ moT. From the values of A,77 , as a function of temperature, average A,C° values were calculated. 

The correction factor,/, relates the actual mobility of a fully charged particle at the ionic strength under the experimental conditions to the absolute mobility. It takes ionic interactions into account and is derived for not-too-concentrated solutions by the theory of Debye-Huckel-Onsager using the model of an ionic cloud around a given central ion. It depends, in a complex way on the mean ionic activity coefficient. The resulting equation contains the solvent viscosity and dielectric constant in the denominator. In all cases, the factor is < 1. The actual mobility is always smaller than the absolute mobility. 

All the assumptions involved in the Debye-Huckel approximation (DH) are incorporated in this model because approximations have been used to establish the relationship between the electrostatic transfer constant Kj and (Tb/Tf)j (where Tj is the activity coefficient of the j-th species) in terms of measurable parameters. 

The model used to represent the ionic solution is that of Debye and Huckel spherical rigid ions with charges at their centres, immersed in a continuum having the properties of a macroscopic fluid with dielectric constant and viscosity identical to those of the solvent. The closest distance at which two ions may approach will be denoted by a. 

Xhe Debye-Hiickel (DH) theory (Debye and Huckel, 1923) gives a simple expression for the excess volume in the framework of the primitive model, which consider the systems as ions immersed in a continuum, structureless solvent of dielectric constant, ,... 

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