Debye-Huckel formula

In order to combine equation (14) with the Debye-Huckel formula, which accounts for the long-range force contribution, it is necessary to normalize to the infinite dilution reference state for the ions ... 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

The mean activity coefficient for a salt can be calculated from experimental data, but the individual-ion activity coefficients used in ion-association aqueous models cannot be determined experimentally. Several formulas were used for individual-ion activity coefficients in the calculations presented in this report. Three formulas were used in the WATEQ model the extended Debye-Huckel formula including an ion-size parameter, a[ (Equation 2) modified extended Debye-Huckel formula with two fitted parameters, a[ and 6i (Equation 3) and the Davies equation (Equation 4). 

The interaction between ions, mainly between those of opposite charge, can lead to a variation of activity coefficients with the composition of mixed electrolyte solutions and thus contradict the Debye-Huckel formula prediction that log ft is proportional to In dilute solutions the conflict is minimal, but at higher concentrations (>0.1 mol dm ) the influence of ion interactions can, for example, alter the significance of the ionic size parameter, d, in the flrst term of Equations (12) and (13), namely ... 

From equation 2.55 we recover the Debye-Hiickel approximation for 4 j/4 << 1. The factor accounts for the numerical accuracy of the Debye-Huckel formula for dimensionless potentials somewhat larger than unity. For large positive surface potentials I j >> 1, and a > 0,... 

This equation can be used when no experimental information is available. In some cases it can give usable results for activity coefficients up to ionic strengths of 0.5 mol kg or beyond, but it is ordinarily in error by several percent in this region. Table A. 11 in Appendix A gives experimental values of the mean ionic activity coefficients of several aqueous electrolytes at various concentrations. It also gives the predictions of the Debye-Huckel formula with fia taken equal to 1.00kg / mol /, and of the Davies equation. 

In water, at ordinary concentrations, the hydrogen chloride is practically all present as the hydrated ions. The infrared absorption bands characteristic of HCl, and shown by the liquid hydride and its solutions in nonionizing solvents do not appear in the aqueous solutions.451 In dilute solutions, the conductivities agree with the Debye-Huckel-Onsager formula. 

Abstract, The solution of the Debye-Huckel equation for a system of spheres with arbitrary radii and surface charge in electrolyte solutions is described. The general theoretical approach to describe such systems is elaborated. The practically important case of two spheres is considered in detail. Finite closed formulae to calculate the interaction energy of two spherical particles with constant surface charges are obtained from general expressions in zero approximation. Known relationships follow from our formulae in limiting cases. 

The Debye-Huckel theory gives a calculation of the activity coefficients of individual ions. However, although the individual concentrations of the ions of an electrolyte solution can be measured, experiment cannot measme the individual activity coefficients. It does, however, furnish a sort of average value of the activity coefficient, called the mean activity coefficient, for the electrolyte as a whole. The term mean is not used in its common sense of an average quantity, but is used in a different sense which reflects the number of ions which result from each given formula. Such mean activity coefficients are related to the individual activity coefficients in a manner dictated by the stoichiometry of the electrolyte. 

Applying the formula of Debye-Huckel-Br0nsted for the activity coefficient and the graphic extrapolation method, the basic values of the electromotive force of a cell for each nickel preparation were determined. Introducing, according to known data, the normal potential of a reference electrode, equal to 0.6151 v, the... 

We will not discuss the details of the Debye-Huckel theory. The main idea of the theory was to pretend that the ions in a solution could have their charges varied reversibly from zero to their actual values. This charging process created an ion atmosphere around a given ion with an excess of ions of the opposite charge. The reversible net work of creating the ion atmosphere was calculated from electrostatic theory. According to Eq. (4.1-32) the reversible net work is equal to AG, which leads to equations for the electrostatic contribution to the chemical potential and the activity coefficient for the central ion. The principal result of the Debye-Hiickel theory is a formula for the activity coefficient of ions of type i ... 

Uncertainty also arises in the accuracy of the measured chemical or physical data (field or experimental) that may be used as model input for a particular problem for example, measurements of pressure, temperature, alkalinity, pH, and Eh, petrographic descriptions, and mineral chemistries of phases all have uncertainty associated with them. Analytical incompleteness is also a concern if missing compositions must then be estimated. Additional uncertainty arises when formulae and supporting parameters are extrapolated beyond their range of applicability. The use of the Debye-Huckel expression to calculate ion activity coefficients at ionic strengths greater than 1 molal provides an example. 

H. von Halban and G. Kortum, The dissociation constants of weak and moderately strong electrolytes. I The dissociation constant of a-dinitrophenol and the range and validity of the limitation formula of Debye and Huckel, Z.fur. Physik. Chem., 1934,170, 351-379. 

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