34. Calculate the lattice energy for Al_{2}O_{3}. Estimate the Born exponent based on the electron configurations of the ions.

Answer

The quantities needed to be estimated to use the Born-Landé equation are the Madelung constant, the Born exponent, and the internuclear distance between the Al^{3+} and the O^{2–} ions.

The Madelung constant is found from Table 5.12 (DMA) to be 4.040.

The Born exponent is found from electron configurations: Al^{3+} and O^{2–} both have the [Ne] electron configuration so n = 7.

The internuclear distance is the sum of the cationic (DMA Table 5.8, CN = 6) and anionic radii (DMA Table 5.10) = 67.5 + 126 = 193.5 pm.

Using these values:

E_{lat} = 14910 kJ/mol