Ionic Bonding And Lattice Energy

The Born-Haber cycle applies Hess's law to ionic compound formation by summing all the enthalpy steps needed to go from elements in their standard states to the ionic lattice. For MgCl_2, the steps are: (1) Sublimation of Mg(s) to Mg(g): +148 kJ/mol. (2) First ionisation energy of Mg(g) to Mg^+(g): +738 kJ/mol. (3) Second ionisation energy of Mg^+(g) to Mg^{2+}(g): +1451 kJ/mol. (4) Dissociation of Cl_2(g) to 2 Cl(g): +244 kJ/mol (for one mole of Cl_2, producing 2 Cl atoms needed for 2 Cl^- ions). (5) Electron affinity for 2 Cl(g) to 2 Cl^-(g): 2 × (-349) = -698 kJ/mol. (6) Lattice energy for Mg^{2+}(g) + 2 Cl^-(g) to MgCl_2(s): -2526 kJ/mol. Enthalpy of formation = 148 + 738 + 1451 + 244 + (-698) + (-2526) = 148 + 738 + 1451 + 244 - 698 - 2526. Step by step: 148 + 738 = 886; 886 + 1451 = 2337; 2337 + 244 = 2581; 2581 - 698 = 1883; 1883 - 2526 = -643 kJ/mol ≈ -642 kJ/mol. Option +642 kJ/mol has the correct magnitude but wrong sign; formation of ionic compounds from elements is exothermic. Option -1263 kJ/mol doubles the lattice energy contribution incorrectly. Option +286 kJ/mol is not derivable from the given data. This is a standard NCERT Born-Haber calculation. Plausibility: the experimental enthalpy of formation of MgCl_2 is approximately -641 kJ/mol, matching the calculated value.