Debye-Huckel parameters

Debye-Huckel parameter H = Henry s constant for molecular solute I = ionic strength = o.5 K = equilibrium constant m = molality, mole kg-1 P = pressure, Pa R = gas constant, J mol K T = temperature, K 3 ]... 

For the Debye-Huckel parameter A in this work the following equation was used ... 

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)). 

EXAMPLE 11.1 Dependence of the Debye-Huckel Parameter k on Temperature and Type of Electrolytes. Evaluate the numerical factor in Equation (41) for aqueous solutions at 25°C. At this temperature er = 78.54 for water. Calculate k and k Mor 0.01 M solutions of 1 1,2 1, and 3 1 electrolytes. Suggest how these values can be adapted to other temperatures (or media) without complete recalculation. 

Describe the physical significance of the Debye-Huckel parameter k. How does it vary with the bulk concentration nx for a 1 1 electrolyte How does it vary with ionic charge for a constant bulk concentration ... 

Table 18.1 Debye-Huckel parameters for the osmotic coefficient, volume, enthalpy,... 

In this appendix, we summarize the coefficients needed to calculate the thermodynamic properties for a number of solutes in an electrolyte solution from Pitzer s equations.3 Table A7.1 summarizes the Debye-Huckel parameters for water solutions as a function of temperature. They provide the leading terms for Pitzer s equations, and can also be used to calculate the Debye-Huckel limiting law values from the equations... 

Again, the coefficients are the same as defined earlier, with Afl, Aj, and Av as the Debye-Huckel parameters, and T as the temperature and Mw as the molecular weight of the solvent (water) in kg-mol-1. Values for the thermal coefficients for a number of electrolytes are given in Tables A7.8 to A7.10. 

Debye length — (also - Debye-Huckel length) In the formulation of the - Debye-Huckel theory the counter ions surrounding the sample ion under consideration are substituted in an attempt of simplification by an ionic cloud. The radius of this ionic cloud or atmosphere giving the distance between the ion under consideration and the location where dq/ (1/k) is at maximum (dq is the charge enclosed in a shell of dr thickness around the ion, and k is the - Debye-Huckel parameter). The Debye length rD (LD and other symbols are also used) also is given by... 

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. 

Debye-Huckel parameter — The Debye-Hiickel parameter k of an electrolyte solution is calculated as... 

See also -> Huckel equation of electrophoretic mobility, -> Debye-Huckel approximation, -> Debye-Huckel length, -> Debye-Huckel limiting law, -> Debye-Huckel-Onsager theory, -> Debye-Huckel parameter. 

The quantity I /at has units of length and is called the Debye length it defines the extent of the double layer, i.e., the distance in which the potential decays to I je of its initial value k is called the Debye-Huckel parameter. Hence within validity of this approximation (low surface potentials < 25 mV) the potential decreases exponentially away from the surface. 

Here we treat a planar plate surface immersed in an electrolyte solution of relative permittivity e,. and Debye-Huckel parameter k. We take x- and y-axes parallel to the plate surface and the z-axis perpendicular to the plate surface with its origin at the plate surface so that the region z>0 corresponds to the solution phase (Fig. 2.1). First we assume that the surface charge density a varies in the x-direction so that a is a function of x, that is, cr = cr(x). The electric potential ij/ is thus a function of x and z. We assume that the potential i/ (x, z) satisfies the following two-dimensional linearized Poison-Boltzmann equation, namely,... 

The asymptotic expression for the potential of a spherical particle of radius a in a symmetrical electrolyte solution of valence z and Debye-Huckel parameter k, a large distance r from the center of the sphere may be expressed as... 

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... 

Helgeson, H. C. and Kirkham, D. H. Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures II. Debye-Huckel parameters for activity coefficients and relative partial molal properties, Amer. J. Sci. 274, 1199-1261 (1974). 

The electrostatic methods just discussed suitable for nonelectrolytic solvent. However, both the GB and Poisson approaches may be extended to salt solutions, the former by introducing a Debye-Huckel parameter and the latter by generalizing the Poisson equation to the Poisson-Boltzmann equation. The Debye-Huckel modification of the GB model is valid to much higher salt concentrations than the original Debye-Hiickel theory because the model includes the finite size of the solute molecules. 

Values of the Debye-Huckel parameters A and B in Eqs. (B.2) and (B.l 1) are listed in Table B-2 for a few temperatures at a pressure of 1 bar below 100°C and at the steam saturated pressure for t> 100°C. The values in Table B-2 may be calculated from the static dielectric constant and the density of water as a function of temperature and pressure, and are also found for example in Refs. [74HEL/K1R], [79BRA/PIT], [81HEL/KIR], [84ANA/ATK], [90ARC/WAN]. 

Dielectric properties of water and Debye-Huckel parameters to 350°C and 1 kbar, J. Phys. Chem., 83, (1979), 1599-1603. Cited on page 594. 

Fig. 7. Dependence of Relative Rate on Ionic Strength ("Salt ). Solid and dotted lines connect monopole + quadrupole and monopole rates, respectively. The electrostatic potential energy between the charge on 0 Wj) aI ra particular SOD charge Q2 separated by r was taken to Tie Q-C e r/er where e Is the dielectric constant (=78) and < Is the Debye-Huckel parameter.

The dependence of selectivity on the ionic strength of the solution has been related through the mean activity coefficient to be inversely proportional to the Debye-Huckel parameter,... 

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