Debye-Huckel constant

It then also follows that the rate constant for a first-order reaction, whether or not the solvent is involved, is also independent of ionic strength. This statement is true at ionic strengths low enough for the Debye-Huckel equation to hold. At higher ionic strengths, predictions cannot be made about reactions of any order because all of the kinetic effects can be expected to show chemical specificity. 

Hard wall Point ions (Debye-Huckel) Constant dielectric background... 

Table 8.3 Constants of the Debye-Huckel Equation from 0 to 100°C 8.5...

Coefficients cl-c4 are used to approximate the integral function "J" aphi is the Debye-Huckel constant at 25 C /... 

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 ]... 

A apparent molality of acid (mole/kg of water) DEBYE - HUCKEL constant... 

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. 

Very few generalized computer-based techniques for calculating chemical equilibria in electrolyte systems have been reported. Crerar (47) describes a method for calculating multicomponent equilibria based on equilibrium constants and activity coefficients estimated from the Debye Huckel equation. It is not clear, however, if this technique has beep applied in general to the solubility of minerals and solids. A second generalized approach has been developed by OIL Systems, Inc. (48). It also operates on specified equilibrium constants and incorporates activity coefficient corrections for ions, non-electrolytes and water. This technique has been applied to a variety of electrolyte equilibrium problems including vapor-liquid equilibria and solubility of solids. 

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. 

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. 

Table 8.4 Debye-Huckel constants for H2O in T range 0 to 300 °C at saturation P (from Helgeson and Kirkham, 1974). A is in kg X mole and B is in kg X mole X cm. ...

Taking ionic strength into consideration, the modified dissociation constant pK may be calculated by the Debye-Huckel relationship ... 

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)). 

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 ... 

Even if we know all reactions and equilibrium constants for a given system, we cannot compute concentrations accurately without activity coefficients. Chapter 8 gave the extended Debye-Huckel equation 8-6 for activity coefficients with size parameters in Table 8-1. Many ions of interest are not in Table 8-1 and we do not know their size parameter. Therefore we introduce the Davies equation, which has no size parameter ... 

Equation 6-33 suggests that extrapolation of equilibrium constants to infinite dilution is done appropriately by plotting log Kc vs-01. For example, Fig. 6-1 shows plots of pK a for dissociation of H2P04-, AMP, and ADP2-, and ATP3 vs fp. The variation of pK a with- p at low concentrations (Eq. 6-35) is derived by application of the Debye-Huckel equation (Eq. 6-33) ... 

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 ... 

A factor in Arrhenius equation Debye-Huckel constant activity... 

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 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 )...

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