Solutions, Bjerrum theory

These large increases in rate might be attributed to the operation of a neutral salt effect, and, in fact, a plot of log k versus the square root of the ionic strength, fi, is linear. However, the reactants, in this case, are neutral molecules, not ions in the low dielectric constant solvent, chloroform, ionic species would be largely associated, and the Bronsted-Bjerrum theory of salt effects51 52, which is valid only for dilute-solution reactions between ions at small n (below 0.01 M for 1 1 electrolytes), does not properly apply. 

Solvent effects in electrochemistry are relevant to those solvents that permit at least some ionic dissociation of electrolytes, hence conductivities and electrode reactions. Certain electrolytes, such as tetraalkylammonium salts with large hydrophobic anions, can be dissolved in non-polar solvents, but they are hardly dissociated to ions in the solution. In solvents with relative permittivities (see Table 3.5) s < 10 little ionic dissociation takes place and ions tend to pair to neutral species, whereas in solvents with 8 > 30 little ion pairing occurs, and electrolytes, at least those with univalent cations and anions, are dissociated to a large or full extent. The Bjerrum theory of ion association, that considers the solvent surrounding an ion as a continuum characterized by its relative permittivity, can be invoked for this purpose. It considers ions to be paired and not contributing to conductivity and to effects of charges on thermodynamic properties even when separated by one or several solvent molecules, provided that the mutual electrostatic interaction energy is < 2 kBT. For ions with a diameter of a nm, the parameter b is of prime importance ... 

Another attempt to go beyond the cell model proceeds with the Debye-Hiickel-Bjerrum theory [38]. The linearized PB equation is used as a starting point, however ion association is inserted by hand to correct for the non-linear couplings. This approach incorporates rod-rod interactions and should thus account for full solution properties. For the case of added salt the theory predicts an osmotic coefficient below the Manning limiting value, which is much too low. The same is true for a simplified version of the salt free case. 

What is the significance of these results on dimer and trimer formation for ionic solution theory In the post-Debye and HUckel world, particularly between about 1950 and 1980 (applications of the Mayer theory), some theorists made calculations in which it was assumed that aU electrolytes were completely dissociated at least up to 3 mol dm. The present work shows that the degree of association, even for 1 1 salts, is -10% at only 0.1 mol dm . One sees that these results are higher than those of the primitive Bjerrum theory. 

Haymet and co-workers have calculated the mole fraction of dimers (associated ions) in electrolytic solutions, and some of their results are shown in Fig. 3.51. Use the equations of the Bjerrum theory applied to NajP04 and compare the results with those of the correlation function approach used by Haymet et al. The essential difference between the Haymet approach and that of Bjerrum is that... 

Consider KCl and take a to be the sum of the ionic radii. Use data from tables to get these. Thus, one can calculate d of the Bjerrum theory over a reasonable concentration range and, using appropriate tables, obtain the value of the fraction of associated ions. Now recalculate the values of log/. for KCl for 0.1 to 2 Af solutions from the full Debye-Hlickel theory involving allowance for ion size and hydration — but now also taking into account 0. In this approach, Cq(1 - 0) is the concentration of the ions that count in the expressions. (See Appendix 3.6.) Does this accounting for 0 improve the fit ... 

When treating the association of counterions one may also apply the association statistics (AS) model which is equivalent to the Bjerrum theory for ion pairing in an electrolyte solution [29,30]. However, in the case of surface association spaee is available only on the side of the liquid. Another difference is due to the critical distance which depends on direction and is a function of the surface potential. This theory explains why two ionic species may associate at the surface despite the fact that they do not undergo ion pairing in the bulk of solution. According to the Bjerrum theory, ions of large effective size cannot approach the critical distance and such an electrolyte is completely dissociated. At the surface the critical distance extends by increasing surface potential and once the surface potential exceeds the critical value, at which the critical distance matches the minimum separation, association at the interface proceeds. 

There have been attempts to modify Bjerrum s treatment to remove this arbitrariness, but none has been used universally to any great extent in the interpretation of experimental data. Nevertheless, despite this artificiality, the Bjerrum theory coupled with the Debye-Hiickel theory has proved a very useful and relatively successfiil tool in discussing electrolyte solutions. This success is especially noteworthy when the Bjerrum-Debye-Huckel theory is compared with the alternative approach of Guggenheim s numerical integration which gives similar results (see Section 10.13.1). Table 10.2 gives values of K ssoc for various charge types and for various values of a and q. 

Another example of specific ion adsorption was discussed in terms of the formation of interfacial ion pairs between ions in the aqueous and the organic phase. The contribution of specific ionic adsorption to the interfacial capacitance can be calculated using the Bjerrum theory of ion-pair formation. The results show that a phase boundary between two immiscible electrolyte solutions can be described as a mixed solvent region with varying penetration of ion pairs into it, depending on their ionic size. The capacitance increases with increasing ionic size in the order Ii+ < Na+ < K" " < Rb < Cs" ". Yufei et al. [22] found that significant specific ion adsorption occurs at the interface between two immiscible electrolytes... 

In solution theory the specialized distribution functions of this kind should appear in the theory of ion pairs in ionic solutions, and a form of the Bjerrum-Fuoss ionic association theory adapted to a discrete lattice is generally used for the treatment of the complexes in ionic crystals mentioned above. In fact, the above equation is not used in this treatment. Comparison of the two procedures is made in Section VI-D. 

Bjerrum, J., Metal Ammine Formation in Aqueous Solution Theory of Reversible... 

Feb. 22,1879, Varde, Denmark - Dec. 17,1947, Copenhagen, Denmark) Ph.D. Copenhagen 1908, since 1908 Professor of Chemistry (the 3rd chair, i.e., the chair of Physical Chemistry at the Univ. of Copenhagen). 1926/27 visiting Professor at Yale Univ., New Haven, Connecticut, USA. Famous for his work on chemical reaction kinetics, chemical affinity, indicators, and thermodynamics of solutions. He could explain the effect of activity coefficients on reaction rates in solutions. In 1923 he developed independently of - Lowry, and - Bjerrum a new -> acid-base theory, the so-called Bronsted acid-base theory. 

Applied to ionic solutions by Mayer in 1950, this theory aimed to express the activity coefficient and the osmotic pressure of ionic solutions while neglecting the effects of solvation that had been introduced by Bjerrum and developed by Stokes and Robinson to give experimental consistency of such impressive power at high concentrations. 

Bjerrum s theory of ionic association gives rise to an expression for the fraction of ions in an ionic solution which are associated. Use the theory to calculate the degree of association of a 0.01 M MgClj solution in ethanol (e = 32). 

What is the total charge on an ionic atmosphere around an anion of valence z From the data in the text, examine logy vs. Vm, where tn is the molality of the solution, from 0 to 1 mol dm". The plots always pass through a minimum. Use the fully extended Debye-Hlickel theory, including the Bjerrum-Stokes and Robinson terms, to find the significance of the minimum at which the electrolyte concentration increases with the increase of the cation radius. 

The theory of ion-pair formation in nonaqueous solutions has been substantially advanced by the work of Barthel, who demonstrated how important it is to take into account the non-Coulombic forces at small ionic distances in addition to the Coulom-bic ones used by Bjerrum. These non-Coulombic forces are represented by the mean force potential W (r) in the region a[Pg.551]

In 1926, Bjerrum [137] used Debye-Hiickel theory to describe ion association and took into account the interaction of ions within a short range. He introduced an ion-pair concept, gave a definition of ion pairs as neutral species formed by electrostatic attraction between oppositely charged ions in solution, and showed how ion-pair formation was dependent on the ions size (radius of ions), solvent (dielectric constant), and temperature. 

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