Ionic association Bjerrum model

It can be seen that the added complexity of ion association is likely to make any simple model of ion-ion interactions very difficult to apply without a number of ad hoc assumptions concerning ionic radii. This is particularly true for ionic strengths in excess of 0.01 M or for low-dielectric-constant media. However, a further difficulty is raised by the problem of the nature of an ion pair. If we consider the simple case of univalent ions A+ B forming an ion pair, it is possible to picture the pair as varying in character from one in which the charges remain separated by the sum of the ionic radii of A+ + B to a molecule in which A and B form a covalent bond, not necessarily even polar in character. Nor is it necessarily true that a given species will behave the same in different solvents. If there is a tendency to covalent bond formation, then it is quite possible that the polarity of the A—B bond will depend on the dielectric constant of the solvent. Covalently bound molecules which ionize are considered as weak electrolytes, and they are not treated by the methods of Bjerrum, which are meant for strong electrolytes. The differences may not always be clear, but the important interactions for the weak electrolyte are with the solvent, and these we shall consider next. 

One could use the Debye-Hiickel ionic-atmosphere model to study how ions of opposite charges attract each other, (a) Derive the radial distribution of cation ( +) and anion (nj concentration, respectively, around a central positive ion in a dilute aqueous solution of 1 1 electrolyte, (b) Plot these distributions and compare this model with Bjerrum s model ofion association. Comment on the applicability of this model in the study of ion association behavior, (c) Using the data in Table 3.2, compute the cation/anion concentrations at Debye-HUckel reciprocal lengths for NaCl concentrations of lO and 10 mol dm", respectively. Explain the applicability of the expressions derived. (Xu)... 

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. 

Considerable effort has been made to develop a model for the parameter on the basis of statistical theories using simple electrostatic concepts. The first of these was proposed by Bjerrum [25]. It contains important ideas which are worth reviewing. He assumed that all oppositely charge ions within a certain distance of a central ion are paired. The major concept in this model is that there is a critical distance from the central ion over which ion association occurs. Obviously, it must be sufficiently small that the attractive Coulombic forces are stronger than thermal randomizing effects. Bjerrum assumed that at such short distances there is no ionic atmosphere between the central ion and a counter ion so that the electrostatic potential due to the central ion may be calculated directly from Coulomb s law. The value of this potential at a distance r is... 

Seidenstickers model (138) accounts for the d.c. and a.c. conductivity measurements on NHs-doped ice in terms of hybrid levels, that is, levels where both Bjerrum (D) and ionic defects are present at the same nitrogen site. If, further, the D defects associated with ammonia are only slightly dissociated, the model predicts that both a.c. and d.c. conduc-... 

The association constants of table III can be compared with those from conductance measurements, and are found to be in perfojt agreement, e.g. K (MgS04/H20) = 160 dm mol . The agreement of the R -values of Table III for aqueous solutions with those of the ion-pair model, Eq. (20), ould be stressed as an important result. The calculated values, Rcaic. correspond to R = a + 2s (here s = don. dimension of OH) according to this model. The agreement of R with Bjerrum s distaiKe parameter q, which is often used as the upper limit of association and which depends only on the permittivity of the solvent [cf. Eq. (19b)], is less satisfactory. For aqueous solutions of 2,2-electrolytes at 25 °C q equals 1.43 nm, independent of the ionic radii. 

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