Question

Using the Born-Haber cycle outlined in section 9.3 for LiF, calculate the lattice energy of NaCl. [The heat of sublimation of Na is 108 kJ/mol, and δHf° (NaCl) = −411 kJ/mol. The energy needed to dissociate 1/2 mole of Cl₂ into Cl atoms is 121.4 kJ.]

Answer 1

The lattice energy of NaCl is calculated to be 640.4 kJ/mol using the Born-Haber cycle, taking into account the heat of sublimation of Na.

Step-by-step explanation:

We apply Hess's Law, which states that the total change in enthalpy (ΔH) is the same regardless of the route taken. The known values include the heat of sublimation of Na (ΔHsub = 108 kJ/mol), dissociation of 1/2 mole of Cl2 into Cl atoms (ΔHd = 121.4 kJ), and standard enthalpy of formation for NaCl (ΔHf° = −411 kJ/mol).

Knowing that the lattice energy of NaCl (ΔHlattice) is an endothermic process, we need to add the heat of sublimation and dissociation energy and then subtract the standard enthalpy of formation of NaCl to find the lattice energy. The lattice energy calculation is as follows:

ΔHlattice = ΔHsub + ΔHd − ΔHf°. ΔHlattice = 108 kJ/mol + 121.4 kJ/mol − (−411 kJ/mol) = 640.4 kJ/mol. The lattice energy of NaCl is 640.4 kJ/mol when considering it as an endothermic process based on these values and the Born-Haber cycle.