Born equation ionic radius

Born equation Jphys chemJ An equation for determining the free energy of solvation of an ion in terms of the Avogadro number, the ionic valency, the ion s electronic charge, the dielectric constant of the electrolytic, and the ionic radius. born i kwa zhan J... 

The values for the enthalpies of hydration of ions may be forced to conform to the expectations of the Born equation (2.43) by estimating a suitable value for each ionic radius or by estimating an apparent ionic charge. 

The very negative value of the estimated enthalpy of hydration of the proton is consistent with a Born radius of 63 pm (from equation 2.43). Since that equation overestimates the ionic radius by —67 pm it follows that a bare proton (radius —0 pm) would be expected to have such a very negative enthalpy of hydration. Studies of the proton and water in the gas phase have shown that the stepwise additions of water molecules in the reaction ... 

Figure 3.4 shows that the values of Ahyd// become less negative as the radius of the cation increases and as the anions increase in radius. Such a variation would be expected from the Born equation (2.43), suitably modified for cations by the addition of 65 pm (the mean value for the Group 1 cations, see Table 2.9) to the ionic radius ... 

In this case the reason tor the correlation is fairly obvious. The parameter refr is equal to the ionic radius plus a constant, 85 pm, the radius of the oxygen atom in water. Therefore, rt(S is effectively the interatomic distance in the hydrate, and the Born-Lande equation (Eq. 4.13) can be apphed. 

The redox potentials These are measured by electrochemical methods such as cyclic voltametry which impose restrictions on the solvents since solvation of ionic species must be obtained. In practice, highly polar solvents such as acetonitrile (MeCN), methanol (MeOH), or water are used in most cases, and corrections must then be made when e.t. takes place in less polar solvents. Here it is assumed that the only difference is due to the solvation energy of the ions — this is calculated from the Born equation which gives the solvation energy of a spherical ion of charge q and radius a in a solvent of static dielectric constant D as [34]... 

Ionic potential — Function defined by = zjr, where z and r are the valence and radius of an ion, respectively. This function was introduced by G.H. Cartledge [i,ii], who used it as a quantitative basis of the periodic classification of elements. The ionic potential is directly connected with the heat of hydration of ions (see - Born equation), and thus related to the heat of solution of salts, acidic properties of ions, and others. It is also known that the ionic potential is correlated with electrochemical redox potentials (e.g., for solid metal hexacyanomet-allates [iii]). 

One of the diflSculties in applying the Born equation is that the effective radius of the ion is not known further, the calculations assume the dielectric constant of the solvent to be constant in the neighborhood of the ion. The treatment has been modified by Webb who allowed for the variation of dielectric constant and also for the work required to compress the solvent in the vicinity of the ion further, by expressing the effective ionic radius as a function of the partial molal volume of the ion, it was possible to derive values of the free energy of solvation without making any other assumptions concerning the effective ionic radius. 

A much-discussed electrostatic treatment of hydration based on the Born equation relates the Gibbs energy of solvation AG to the ionic radius and the solvent dielectric constant [128], For the hydration process [Eq. (1)] we take hydration as a specific case of solvation and set AGh = AGs- The change in Gibbs energy may be obtained readily if the ions are treated as hard spheres in a continuous dielectric ... 

The other model for the ionic friction concerns the dielectric response of solvent to the solute perturbation. When an ion is fixed in polar solvent, the solvent is polarized according to the electrostatic field from the ion. If the ion is displaced, the solvent polarization is not in equilibrium with a new position of the ion, and the relaxation of the polarization should take place in the solvent. The energy dissipation associated with this relaxation process may be identified as an extra friction. The extra friction, called the dielectric friction, decreases with increasing ionic radius, thereby, with decreasing electrostatic field from the ion. The dielectric friction model developed by Born [66], Fuoss [67], Boyd [68] and Zwanzig [69, 70] has taken a complete theoretical form due to the work by Hubbard and Onsager [71, 72] who proposed a set of continuum electrohydrodynamic equations in which the electrostatic as well as hydrodynamic strains are incorporated. 

A number of theoretical difficulties in equating the Born function with this process are believed to be accommodated in the j parameter, which in the Bom model is the ion radius, but in the HKF model is an adjustable parameter called the effective ionic radius. The r j parameters were originally related to crystallographic ionic radii (r ) and ionic charge Zj in a simple linear fashion in the HKF model, and were independent of T and P... 

There has been some speculation that an ionic noble-gas compound with the stoichiometry Xe F can be prepared. Using both the Born-Lande and Kapustinsldi equations, estimate the lattice energy for this hypothetical compound. Carefully state all assumptions that you make to establish a value for the ionic radius of Xe. Atomic radii are given in Table 7.3. 

Construct a Born-Haber cycle that will enable a calculation of a reasonable value for the AH of Ne Cl . Estimate the lattice energy using the Kapustinskii equation. Rationalize the value you use for the ionic radius of Ne". Discuss the principal reasons why NeCl would or would not be thermodynamically feasible [lE(Ne) = 2080 kJ/mol]. 

Thus, with the help of Marcus equation, we can obtain some useful estimates and predictions. The quantitative accuracy of this theory, however, should not be overstated. It was shown above that this theory is based on the same physical model as the Born theory of ion solvation and hence suffers from the same drawbacks. We do not know whether any attempts have been made to take into account the effect of dielectric saturation of the medium in the vicinity of ions in kinetics. An attempt to take into account the spatial dipole correlation while considering the redox reaction MnOi+ /MnO was made by Dolin et al,[237]. As mentioned in section 3.2, the correlation in dipole orientation leads, as it were, to an increase in the effective ionic radius. Consequently, it should somewhat decrease the activation energy. According to estimates in [237], this effect is not strong, but it must increase with decreasing ionic radius. 

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