Debye-Huckel theory constants

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

From the Debye-Huckel theory for the potentiSI)(in the vicinity of an ion [96], Scatchard derived an expression for the effect of dielectric constant of the solvent ... 

The work terms wl (/ = r or p) are associated with the electrostatic work done when the reactants are brought together from infinity to a distance separated from rigid spheres. For ions of charges Zj and z2 in a medium with a dielectric constant D, w , i r or p, can be calculated on the basis of the Debye-Huckel theory (Equation 6.110). 

The Debye-Huckel theory is accurate in solutions in which the interactions between ions are not too great (i.e., at low ionic strengths in solutions of monovalent ions in solvents with large dielectric constants). In Fig. 2, the predictions of Eq. (21) are compared with experimental data for some strong electrolytes with different ionic charges. 

Debye-Huckel parameter. (V2 Laplace operator, o -> permittivity of vacuum, er -> dielectric constant of the electrolyte solution, cf bulk concentrations of all ions i, zp charges of the ions i, f electric potential, k - Boltzmann constant, and T the absolute temperature). See also -5- Debye-Huckel theory. 

It is a function expressing the effect of charge of the ions in a solution. It was introduced by -> Lewis and Randall [iii]. The factor 0.5 was applied for the sake of simplicity since for 1 1 electrolytes I = c (electrolyte). It is an important quantity in all electrostatic theories and calculations (e.g., - Debye-Huckel theory, - Debye-Htickel limiting law, - Debye-Huckel-Onsager theory) used for the estimation of -> activity coefficients, -> dissociation constants, -> solubility products, -> conductivity of -> electrolytes etc., when independently from the nature of ions only their charge is considered which depends on the total amount (concentration) of the ions and their charge number (zj). 

When the proper choice of the ponstants a and b are made, the function (Em° + Eext) should be constant within the limits of the extended Debye-Huckel theory. In calculating Em° the value of the equation for log y (Equation 6) which must be substituted into Equation 4 becomes... 

In many calculations the hydrogen ion concentration is more accessible than the activity. For example, the electroneutrality condition is written in terms of concentrations rather than activities. Also, from stoichiometric considerations, the concentrations of solution components are often directly available. Therefore, the hydrogen ion concentration is most readily calculated from equilibrium constants written in terms of concentration. When a comparison of hydrogen ion concentrations with measured pH values is required (in calculation of equilibrium constants, for example), an estimate of the hydrogen ion activity coeflScient can be made by application of the Debye-Huckel theory if necessary, an estimate of liquid-junction potentials also can be made. Alternatively, the glass electrode can be calibrated with solutions of known hydrogen ion concentration and constant ionic strength. " ... 

An optical study s of Ce(III) indicated the existence of a complex, CeC104 ". The formation constant was evaluated as about 80 at zero ionic strength and was found to decrease rapidly with increasing ionic strength, in accordance with the Debye-Huckel theory. If this interpretation is correct, it would seem that Ce(IV) must also form a perchlorate complex of comparable stability to account for the lack of effect of perchlorate on the potential. 

The dielectric constant of cyclohexanol is 15.0 and its freezing point is 23.6 C. Calculate the limiting slope of 1 — 4> against Vtf, according to the Debye-HUckel theory, and compare the result with that in Fig. 31. 

Table II. Constants for the Third and Fifth Approximations of the Gronwall, LaMer and Sandved Extension of the Debye-Huckel Theory...

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. 

The water species involved in this reaction must be neutral (and not OH") because of the fact that the rate of uracil photohydrate formation is independent of NaCl concentration up to 1M, and is the same in unbuffered water as in 0.1M phosphate buffer. The rate constant for photohydrate formation in CU was also observed, in a series of runs all made in the same day with the same initial CU concentration, to be 0.0418 0.010 at NaCl concentrations of 0, 0.001M, 0.01M, 0.1 M, and 1M. The lack of salt effect is consonant, according to Debye-Huckel theory (3) with the reaction of a charged species (UH+) with an uncharged species, as written in Reaction f, and eliminates reaction between two charged species in the product-forming process. 

A very interesting application of Eq. 1.7-12 is the Br nsted-Bjerrum equation for rate constants in solutions where the Debye-Huckel theory is applicable. The latter provides an equation for the activity coefficient, Rutgers [38] ... 

A key quantity in the Debye-Huckel theory, leading to the values of the constants A and B, is the screening length, k, the average reciprocal of the radius of the ionic atmosphere surrounding an ion in the solution, made up essentially by ions of the opposite charge. The square of this quantity is proportional to the ionic strength of the solution and also to the reciprocal of the product w T ... 

We shall just mention here that the simple association theory may be extended by considering the interactions between defects in solution in a medium with dielectric constant a [14]. This is analogous to the Debye-Huckel theory of electrolytic solutions. As a result, the mole fractions of charged point defects of sort i in the mass action laws have to be replaced by their corresponding activities which according to Debye-Huckel are of the form... 

The ionic strength dependence of k is essentially a property of the rate law. Therefore, the ionic strength dependence seldom affords new mechanistic information unless the complete rate law cannot be determined. These equations more often are used to "correct" rate constants from one ionic strength to another for the purpose of rate constant comparison. Ionic strength effects have been used to estimate the charge at the active site in large biomolecules, but the theory is substantially changed because the size of the biomolecule violates basic assumptions of Debye-HUckel theory. 

The interactions between charged defects may be accounted for by using the Debye-Huckel theory in analogy with the interactions of ions in aqueous solutions. This requires knowledge of the relative dielectric constant, the smallest distance between charged defects, and other parameters for the solid. Debye-Huckel corrections have, for instance, been worked out and tested for cation vacancy defects in metal-deficient Coi-yO and Nii-yO. At infinite dilution the... 

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