Normalized Debye-Huckel solution

Understandably, it is much more common to see analyses of problems based on Eq. (32) since for simple geometries the solution can be written down in closed form, expressed in terms of simple functions. For plane surfaces, for example, the solutions are elementary hyperbolic functions while for an isolated spherical surface the Debye-Huckel potential expression prevails. For two charged spherical surfaces the general solution can be written down as a convergent infinite series of Legendre polynomials [16-19]. The series is normally truncated for calculation purposes [16] K For an ellipsoidal body ellipsoidal harmonics are the natural choice for a series representation [20]. (The nonlinear Poisson Boltzmann equation has been solved numerically for a ellipsoidal body... 

Another well-known example of a medium effect in solution kinetics is the effect of ionic strength on reactions between ions [38, 39]. This is normally treated using the extended Debye-Huckel theory to estimate the activity coefficients in equation (7.10.1). The activity coefficient for species i is given by... 

In order to obtain activity coefficients or standard potentials from measurements on cells of the type shown in equation (1) it is necessary, as described in Chapters 8 and 10, to make some form of extrapolation. Furthermore in the test of the Debye-Huckel relations for these solutions it has been found that, because of the higher molecular weight of the non-aqueous solvents, the difference between the activity coefficient, f, and the rational coefficient, f, based on Raoult s law, cannot be neglected, even below a concentration of 0.1 normal, as it usually can with aqueous solutions. This difference was overlooked by the workers just mentioned, who found only partial agreement of their results with the Debye-Huckel theory. Their data have therefore been recomputed as follows. For the ethyl alcohol solutions, for instance, a reference solution with a molality, mu of 0.09501, was chosen. The relation... 

Normally, the validity of the Debye—HUckel theory extends little further than kR <1. At room temperature, this requires ionic concentrations < 0.1 mol dm for univalent ions in water, 0.03 mol dm for univalent ions in ethanol or <0.01 moldm for univalent ion in ethers. In these cases, ions may be regarded as point particles and the strong repulsive core potential ignored. Furthermore, the time taken for non-reactive ions to diffuse far enough to establish an ionic-atmosphere around an ion, which was suddenly formed in solution containing only univalent ions, is... 

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. 

It is at this point that a problem appears in Cherfs method as outlined in his thesis. In order to duplicate his results, the Imig range contribution was calculated on a molality basis, and the local composition model was calculated on a mole fraction basis. This discrepancy was corrected in the paper published in the AIChE Journal (C4) for single electrolyte sdutions. As can be seen in Chapter IV, the Pitzer-Debye-Hiickel expression used for the long range contribution was normalized to the mole fraction basis. Due to these differences, the interaction parameters presented in the paper for use with the Pitzer Debye-Huckel version differ from those presented in the thesis. The AIChE Journal paper notes that a paper on multicomponent solutions was being prepared so this section will be updated later. The Chen method cannot be used in the multicomponent test systems until then. 

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