Debye-Huckel expression

At moderate ionic strengths a considerable improvement is effected by subtracting a term bl from the Debye-Huckel expression b is an adjustable parameter which is 0.2 for water at 25°C. Table 8.4 gives the values of the ionic activity coefficients (for z, from 1 to 6) with a taken to be 4.6A. 

The original Debye-Huckel expression for the calculation of the activity coefficients of ions is... 

Although more complex pair-correlation functions are available, the Debye-Huckel expression is adequate for our present purpose. It is valid when the work required to bring the reactants... 

EXAMPLE 12.1 Debye-Huckel Expression for Ionic Activity Coefficients. The Debye-Hiickel limiting law attributes all of the nonideality of an electrolyte solution to electrostatic effects... 

At finite concentrations the effect of the solvent on the ion-ion interactions are superimposed on the solvent effect discussed above for infinite dilution. The former effect can be expressed as the mean ionic activity coefficient, y again, expressed conventionally on the molal scale, relative to infinite dilution in the solvent in question, which in dilute solutions, where the extended Debye-Huckel expression is deemed to hold, is ... 

Thus arose the Debye-HUckel expression for the experimentally inaccessible individual ionic-activity coefficient. This expression could be transformed into the Debye-Htickel limiting law for the experimentally measurable mean ionic-activity... 

The term a can be taken as the same as a,- in the Debye-Huckel expressions, T is defined in the text. 

The salt correction may be calculated quantitatively with the help of the Debye-Huckel expression. However, certain factors operating especially at higher ionic strengths tend to produce deviations between the calculated and experimentally determined values. These factors are enumerated below. 

Experimental determinations made in terms of concentrations give concentration quotients which are non-ideal constants. Corrections for non-ideality are made in terms of the calculated ionic strength and the various Debye-Huckel expressions. However, emf experiments, including pH measurements, can sometimes furnish equilibrium constants directly in terms of activities, and as such these will be ideal equilibrium constants. 

Dissociation is slight at the aqueous concentrations for which partial pressures have been measured, and where it has been calculated, a simple Debye-Huckel expression was used to obtain ion activity coefficients. 

In the search for medium complexes we first treated Na data at the lowest possible Na concentrations (self-medium solutions at low V,oi) to establish the medium independent constants and obtained log(3o,2,o = -0.30. This value was not allowed to vary in subsequent calculations. Then all Na data were treated. As previously found at high Vioi, two extremely minor resonances arising from an unprotonated linear trimer V. Oio " is discernable in such solutions. However, at the present high pH values, the amount is too low to make it possible to determine its formation constant. An approximate value of a monosodium complex, that fairly well explained these resonances, was used in the calculation in the search for all other complexes. All 35 experimental points were perfectly explained with non-sodium and sodium complexes of mono- and divanadates. An attempt to explain the data with extended Debye-Huckel expressions was not successful. 

Acidity of Solutions 835 b. The following extended Debye-Huckel expression is used ... 

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. 

Debye-Huckel Expression for Long-Range Interactions... 

---