Ionic strength Debye-Huckel relation

The activity a and concentration c are related by a = (c/c ) x y (equation (3.12)), where y is the mean ionic activity coefficient, itself a function of the ionic strength /. Approximate values of y can be calculated for solution-phase analytes by using the Debye-Huckel relationships (equations (3.14) and (3.15)). The change of y with ionic strength can be a major cause of error in electroanalytical measurements, so it is advisable to buffer the ionic strength (preferably at a high value), e.g. with a total ionic strength adjustment buffer (TISAB). 

Thirdly, another corollary of the first limitation, is the inconsistency and inadequacy of activity coefficient equations. Some models use the extended Delbye-Huckel equation (EDH), others the extended Debye-Huckel with an additional linear term (B-dot, 78, 79) and others the Davies equation (some with the constant 0.2 and some with 0.3, M). The activity coefficients given in Table VIII for seawater show fair agreement because seawater ionic strength is not far from the range of applicability of the equations. However, the accumulation of errors from the consideration of several ions and complexes could lead to serious discrepancies. Another related problem is the calculation of activity coefficients for neutral complexes. Very little reliable information is available on the activity of neutral ion pairs and since these often comprise the dominant species in aqueous systems their activity coefficients can be an important source of uncertainty. 

Electrode response is related to analyte activity rather than analyte concentration. We are usually interested in concentration, however, and the determination of this quantity from a potentiometric measurement requires activity coefficient data. Activity coefficients are seldom available because the ionic strength of the solution either is unknown or else is so large that the Debye-Huckel equation is not applicable. 

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,... 

This tendency to decrease the mobility of the Ba is related directly to the ionic strength of the solution. By incorporating the Debye-Huckel equation, the following correction term is obtained ... 

The explanation of the salting out effect is somewhat more complicated and can be related to the failure of the Debye-Huckel limiting law at higher ionic strengths. At high ionic strengths we may write... 

The thermodynamic parameters for the formation of several metal-cyanide complexes, among others those of Ni(CN)4 , have been determined using pH-metric and calorimetric methods at 10, 25 and 40°C. In case of nickel(II), the thermodynamic data were determined by titration of Ni(C104)2 solutions with NaCN solutions. The ionic strength of the solutions were 1 < 0.02 M in all cases. The Debye-Huckel equation, related to the SIT model, was used to correct the formation constants to thermodynamic constants valid at 7 = 0. Since previous experiments indicated that the dependence of A,77° in the ionic strength in dilute aqueous solutions is small compared to the experimental error, the measured heats of reaction (A,77 = - 189.1 kJ mol at 10°C A,77 ,= -183.7 kJ mol at 40 C) were taken to be valid at 7 = 0, but the uncertainties were estimated in this review as 2.0 kJ moT. From the values of A,77 , as a function of temperature, average A,C° values were calculated. 

In dilute solutions it is possible to relate the activity coefficients of ionic species to the composition of the solution, its dielectric properties, the temperature, and certain fundamental constants. Theoretical approaches to the development of such relations trace their origins to classic papers by Debye and Huckel (6-8). For detailed treatments of this subject, refer to standard physical chemistry texts or to treatises on electrolyte solutions [e.g., that by Hamed and Owen (9)]. The Debye-Hiickel theory is useless for quantitative calculations in most of the reaction systems encountered in industrial practice because such systems normally employ concentrated solutions. However, it may be used together with transition state theory to predict the qualitative influence of ionic strength on reaction rate constants. 

The correction factor,/, relates the actual mobility of a fully charged particle at the ionic strength under the experimental conditions to the absolute mobility. It takes ionic interactions into account and is derived for not-too-concentrated solutions by the theory of Debye-Huckel-Onsager using the model of an ionic cloud around a given central ion. It depends, in a complex way on the mean ionic activity coefficient. The resulting equation contains the solvent viscosity and dielectric constant in the denominator. In all cases, the factor is < 1. The actual mobility is always smaller than the absolute mobility. 

In practice, we consider that Debye and Huckel s law, expressed by relation [4.82], and in particular using its form [4.88] in water, can only be used for solutions in which the ionic strength is no greater than lO mol/1, although in certain cases, ionic strengths of lO mol/l can also yield acceptable results. Certain authors prefer to adjust the law [4.82] by adjusting two experimental conditions ... 

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