Question

Sodium chloride has a lattice energy of - 787 kJ/mol. Computational analysis of a hypothetical salt...

Sodium chloride has a lattice energy of - 787 kJ/mol. Computational analysis of a hypothetical salt XY indicates that X^3+ has the same radius as the sodium ion and Y^3- has the same radius as the chloride ion. Estimate the lattice energy of XY.

Born and Lande presented the following model for lattice energy:

E=−NAMz+ze2/4πϵoro (1−1/n)

In this equation, NA is Avogadro's constant; M is the Madelung constant, which depends on the crystal geometry; z+ is the charge number of the cation; z- is the charge number of the anion; e is the elementary charge of the electron; n is the Born exponent, a characteristic of the compressibility of the solid; ϵo is the permittivity of free space; and r0 is the distance to the closest ion.

This model emphasizes two main factors that contribute to the lattice energy of an ionic solid: the charge on the ions, and the radius, or size, of the ions. The effect of those factors is:

• as the charge of the ions increases, the lattice energy increases
• as the size of the ions increases, the lattice energy decreases
• Therefore, the lattice energy for the hypothetical salt XY may be nearly 9 times to that of NaCl assuming all others factors in the above equation are same as NaCl
• -787x3x3 = 7083 KJ/mol