Born exponents calculations, 172

The variable n is knovra as the Born exponent, which depends upon the electronic configuration of the ions present. The Born-Lande equation calculates on the basis of the electrostatic attraction between... 

The enthalpy of formation of an ionic compound can be calculated with an accuracy of a few percent by means of the Born-Land equation (Eq. 4.13) and the Born-Haber cycle. Consider NaCI. for example. Wc have seen that by using the predicted internuclear distance of 283 pm (or the experimental value of 281.4 pm), the Madelung constant of 1.748, the Born exponent, n, and various constants, a value of —755kJmor could be calculated for the lattice energy. The heat capacity correction is 2.1 kJ mol", which yields = —757 kJ moP. The Bom-Haber summation is then... 

Calculated by using Madelung constants of 1.748 and 5.039 for the NaCl and CaF2 structures, respectively, with rCi- = 1.81 A and n (the Born exponent) equal to 9. 

To prevent misunderstanding (94), we emphasize that neither experimental hydration energies nor experimental coordination numbers are necessary for these calculations. Moreover, the coordination numbers obtained are generally not comparable to empirical hydration numbers. The only experimental quantities that enter the calculations are a) cationic radius and charge b) van der Waals radius of water c) dipole and quadrupole moment of water d) polarizabilities e) ionization potentials and f) Born repulsion exponents as well as fundamental constants (see Ref. (92)). 

Besides this electrostatic attraction there is the repulsion which arises when the ions begin to touch each other. This repulsion originates in the general mutual repulsion of the electron clouds of atoms and ions, which always occurs when the clouds penetrate each other and the electrons do not form any atomic bond with a common electron pair (p. 147). The repulsion is difficult to calculate and so Born represented the repulsion energy by B rn, a function which, provided n is large, increases very rapidly with decreasing distance r, corresponding to almost hard spheres. B in this expression is a still undetermined factor of proportionality while the value of the exponent can be deduced from the compressibility n amounts to about 9. 

Problem 5.4 LiH is a colorless solid at room temperature. The melting point is about 700 and the melt conducts electricity. Both the solid and the hquid are therefore believed to consist of Li" " and H (hydride) ions. The electric dipole moment of the gaseous LiH is 5.88 D, the dissociation energy at zero K is 234 kJ moP, the bond distance is 160 pm, and the vibrational wavenumber 1406 cm. Calculate the electric dipole moment from the spherical ion model. Show that the dissociation energy calculated from the spherical ion model is in good agreement with the experimental if the exponent in the Born repulsion term is reduced from n = 10 to 5. Is there any reason... 

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