Falkenhagen equation

For practical purposes, the most useful equation is that of Robinson and Stokes, who have shown that the Falkenhagen equation can be approximated to... 

M. Della Monica, A. CegUe and A. Agostiano, Extension of the Falkenhagen equation to the conductivity of concentrated electrolyte solutions, /. Phys. Chem., 88,1984,2124-2127. 

The Debye-Huckel-Onsager equation for the dependence of the ordinary diffusion conductance on concentration has been extended by Falkenhagen, Leist and Kelbg [3] to apply to more concentrated solutions and their equation for a 1 1-electrolyte may be written... 

As the dependency does not include any specific property of the ion (in particular its chemical identity) but only its charge the explanation of this dependency invokes properties of the ionic cloud around the ion. In a similar approach the Debye-Huckel-Onsager theory attempts to explain the observed relationship of the conductivity on c1/2. It takes into account the - electrophoretic effect (interactions between ionic clouds of the oppositely moving ions) and the relaxation effect (the displacement of the central ion with respect to the center of the ionic cloud because of the slightly faster field-induced movement of the central ion, - Debye-Falkenhagen effect). The obtained equation gives the Kohlrausch constant ... 

Induced Interaction between Two Multipole Systems. Equation (58) defines in general form the classical electrostatic interaction of two electric systems having permanent multipoles and pj" , in conformity with the classical theory of Keesom. In the classical approach also, as shown by Debye and Falkenhagen, one has to take into consideration energies due to interactions between the permanent multipoles of the one system and electric multipoles induced in the other, and vice versa. Restricting the problem in a first approximation to the energy arising from the mutual interaction of dipoles, we can write ... 

On neglecting, in equations (87a), (88a), and (89a), the anisotropies of polarizabilities i.e. putting k< = 0) one obtains the Debye-Falkenhagen formulae. Similarly, it is possible to calculate induced energies of interaction between higher-order multipole moments. ... 

Tollert attempted to separate the viscosity of an electrolyte into ion viscosities. The viscosities of solutions of two electrolytes are well represented by an equation given by Falkenhagen and Dole ii if ri= rjQ - Ac ) for a single electrolyte, then ... 

Falkenhagen considered a modified distribution function which took account of the finite size of the ions by recognising that the total space available to the ions is less than the total volume of the solution. This implicitly means that (1 - - Ka) is not approximated to unity. A modified Poisson-Boltzmann equation was thus used in the derivation of the relaxation effect, but the solution of this modified Poisson-Boltzmann equation was approximated to the first two terms. These modifications gave higher order terms in Cacmai of the type which had been empirically observed. 

Equation (12-29) provides a confirmation of Lewis ionic-strength principle. (More details concerning the thermodynamic treatment of electrolyte solutions can be found in Falkenhagen, Electrolyte, S. Hirzel Verlag, Leipzig, 1953, and H. S. Hamed and B. B. Owen, The Physical Chemistry of Electrolytic Solutions, Reinhold Publishing Corporation, New York, 1958.)... 

Later, Falkenhagen and co-workers and Onsager and Fuoss established a method of calculating parameter A starting from the Debye-Huckel theory. However, the above equation is only valid for concentrations up to about 0.01 mol/L. According to the above equation the relative viscosity should always increase with concentration. However, experiments show non-monotonic behavior for several electrolytes such as most of the potassium halides, and several mbidium and cesium halides [12]. 

The extension of the theory to higher concentrations has been undertaken particularly by Falkenhagen and his co-workers, by Pitts, and by Onsager and Fuoss. The theory is very difficult, and the final equations inevitably involve assumptions and mathematical approximations that have been the subject of discussion they are too complicated to reproduce here, and require computer time for their solution. All three can satisfy the best experimental results for uniunivalent salts up to 0.1 g-equiv. dm" for unsymmetrical valence types the mathematical problems are intractable, and above 0.1 g-equiv. dm for any salt the model on which they are based becomes unreliable. 

S.S. Islam, R.L. Gupta and K. Ismail, Extension of the Falkenhagen-Leist-Kelbg equation to the electrical conductance of concentrated aqueous electrolytes, 7. Chem. Eng. Data, 36,1991,102-104. 

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