Question

7. Divalent ionic crystals. Barium oxide has the NaCl structure. Estimate the cohesive energies per molecule of the hypothetical crystals Batoº and Bato- referred to separated neutral atoms. The observed nearest-neighbor internuclear distance is Ro = 2.76 Ă; the first and second ionization potentials of Ba are 5.19 and 9.96 eV; and the electron affinities of the first and second electrons added to the neutral oxygen atom are 1.5 and -9.0 eV. The first electron affinity of the neutral oxygen atom is the energy released in the reaction 0 + e +0%. The sec- ond electron affinity is the energy released in the reaction 0- +e0Which valence state do you predict will occur? Assume R, is the same for both forms, and neglect the repulsive energy.

Answer 1

For crystal Ba+O​​​​​​-​​

Ba+5.19 ----- Ba+ + e​​​​-​​​ ___(1)

O + e​​​​​​- + 1.5 ------- O​​​​​​- _____(2)

The net amount of energy required to form Ba+ and O​​​​​​-

5.19 + 1.5= 6.69 eV

The potential energy at equilibrium ------

-e​​​​​2​​​​/4π€oro

[1.6×10-19]2/4×3.14×8.85×10-12×2.76×10-10×1.6×10-19 = -5.21 eV

The energy released in the formation BaCl of molecule from atoms at infinite separation is equal to 6.69 - 5.21= 1.48 eV this energy is equal to cohesive energy or binding energy of BacCl molecule  

For crystal Ba+2O-2

Total total ionization energy for the formation of Ba+2= 5.19 + 9.96 =15.15 eV

Total electron affinity for the formation of O​​​​​​-2= 1.5 - 9.0= -7.5 eV

Potential energy = z+z​​​-​​​​​​​​​​ -5.21 eV

Cohesive energy 15.15 -7.5 - (5.21×4)= -13.19 eV

The later one crystal energy have negative sign hence the formation of crystal from divalent ions is feasible