3.4 Strengths of ionic/covalent bonds: bond energy & Coulomb's law  (Page 3/8)

Ionic bond strength and lattice energy

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (Δ H _lattice )    of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:

Note that we are using the convention where the ionic solid is separated into ions, so our lattice energies will be endothermic (positive values). Some texts use the equivalent but opposite convention, defining lattice energy as the energy released when separate ions combine to form a lattice and giving negative (exothermic) values. Thus, if you are looking up lattice energies in another reference, be certain to check which definition is being used. In both cases, a larger magnitude for lattice energy indicates a more stable ionic compound. For sodium chloride, Δ H _lattice = 769 kJ. Thus, it requires 769 kJ to separate one mole of solid NaCl into gaseous Na ⁺ and Cl ^– ions. When one mole each of gaseous Na ⁺ and Cl ^– ions form solid NaCl, 769 kJ of heat is released.

The lattice energy Δ H _lattice of an ionic crystal can be expressed by the following equation (derived from Coulomb’s law, governing the forces between electric charges):

in which C is a constant that depends on the type of crystal structure; Z ⁺ and Z ^– are the charges on the ions; and R _o is the interionic distance (the sum of the radii of the positive and negative ions). Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. When all other parameters are kept constant, doubling the charge of both the cation and anion quadruples the lattice energy. For example, the lattice energy of LiF (Z ⁺ and Z ^– = 1) is 1023 kJ/mol, whereas that of MgO (Z ⁺ and Z ^– = 2) is 3900 kJ/mol (R _o is nearly the same—about 200 pm for both compounds).

Different interatomic distances produce different lattice energies. For example, we can compare the lattice energy of MgF ₂ (2957 kJ/mol) to that of MgI ₂ (2327 kJ/mol) to observe the effect on lattice energy of the smaller ionic size of F ^– as compared to I ^– .