Hiickel Constant

The Hiickel constant k has been inserted here as one more adjustable parameter. Note that the integrated form of equation (126) is exact. 

The constant k can be adjusted to give best agreement with experiment. It is found that a good value to use is somewhat larger than would be indicated by the Mulliken approximation and a very standard value used by many groups is  

Alternatively, a slight modification to this formula makes k a function of the specific orbital pair, kj y, rather than identical for each matrix element H. 

The derivation of this result introduces a generalization of the Mulliken approximation  

In the Extended Hiickel approximation, the charges in the unselected part are treated like classical point charges. The correction of these classical charges to the diagonal elements of the Hamiltonian matrix may be written as  

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The dielectric constants , which are also needed to evaluate the Debye-Hiickel constants A and B, were measured from 283.15° to 318.15°K at intervals of 5°K, using spectrograde acetone and freshly prepared, doubly distilled water as reference materials. The Janz-Mclntyre bridge (18) with Balsbaugh con-... 

Earlier, when discussing historical development, we mentioned that different workers have used different equations to describe the Debye-Hiickel constant (A, Eq. 2.35) as a function of temperature. For example, at 0°C, the value of this constant is 0.3781, 0.3764, and 0.3767 kg1/2 mol-1/2 for the FREZCHEM, Archer and Wang (1990), and Pitzer (1991) models, respectively. At NaCl = 5 m and 0 °C, the calculated mean activity coefficients using these three parameters evaluated with the FREZCHEM model are 0.7957, 0.7995, and 0.7988, respectively. The largest discrepancy is 0.48%, which is within the range of model errors for activity coefficients (Table 3.5). 

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Table 3.1 Debye-Hiickel Constant and Limiting Slopes of AfG(, AfH., and Cpm(i) as Functions of Temperature...

Use the values of the Debye-Hiickel constants A and B at 25 , given in Table XXXV, to plot — log f for a uni-univalent electrolyte against Vv for ionic strengths 0.01, 0.1, 0.5 and 1.0, assuming in turn that the mean distance of approach of the ions, a, is either zero, or 1, 2, 4 and 8A. Investigate, qualitatively, the effect of increasing the valence of the ions. 

To calculate the adjustments shown in equation 1.4-1 as a function of temperature, we need the temperature depe-dence of the Debye-Hiickel constant a. Clarke and Glew (10) have provided tables that show that... 

Debye-Hiickel constant (1.17582 kg mol at 298.15 K) activity coefficient of species i surface tension (N m )... 

Table 3.8 Values of the Debye-Hiickel Constants on the Molarity Scale Together with the Density and Relative Permittivity of Water in the Temperature Range 0-50°C...

It should be noted that redefining the Debye-Hiickel constants so that they change with electrolyte concentration to reflect the corresponding change in does not extend the concentration range over which this model fits experimental data. This result emphasizes that it is important to include the finite size of all ions in a model which is applied in a concentration range greater than 0.1 M. 

Table B-2 Debye-Hiickel constants as a function of temperature at a...

A = Hiickel constant I = ionic strength i = any ion present z, = number of charges on ion I Fi is an interaction parameter term... 

Debye-Hiickel constant Constant for ion interaction Concentration of solution Saturation concentration Specific heat at constant pressure Specific heat at constant volume Diffusion coefficient Self-diffusion coefficient of the solvent... 

Table B-2 Debye-Hiickel constants as a ftmction of temperatiue at a pressure of 1 bar below 100°C and at the steam saturated pressure for t > 100°C. The uncertainty in the A parameter is estimated by this review to be + 0.001 at 25°C, and 0.006 at 300°C, while for the B parameter the estimated uncertainty ranges from 0.0003 at 25 °C to+ 0.001 at300°C.

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