This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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Here is the Born-Haber cycle for sodium chloride, the calculation of its lattice dissociation energy, and the relevant law. Step 1: List the known and assumed enthalpy values. From the previous question and general chemical data: Heat of formation of NaCl, H_f = -410 kJ/mol Sublimation energy of Na, H_sub = +108 kJ/mol Atomization energy of Cl, H_atom = +121 kJ/mol Ionization energy of Na, H_IE = +496 kJ/mol (Assumed standard value) Electron affinity of Cl, H_EA = -349 kJ/mol (Assumed standard value) Step 2: Born-Haber Cycle Representation. The Born-Haber cycle for NaCl can be represented by the following series of reactions and their enthalpy changes: 1. Overall formation: Na_(s) + (1)/(2)Cl_2(g) → NaCl_(s) H_f = -410 kJ/mol 2. Sublimation of sodium: Na_(s) → Na_(g) H_sub = +108 kJ/mol 3. Atomization of chlorine: (1)/(2)Cl_2(g) → Cl_(g) H_atom = +121 kJ/mol 4. Ionization of gaseous sodium: Na_(g) → Na^+_(g) + e^- H_IE = +496 kJ/mol 5. Electron affinity of gaseous chlorine: Cl_(g) + e^- → Cl^-_(g) H_EA = -349 kJ/mol 6. Lattice formation of sodium chloride: Na^+_(g) + Cl^-_(g) → NaCl_(s) H_lattice, formation = ? Step 3: Calculate the lattice formation energy of sodium chloride. According to Hess's Law, the overall enthalpy change for the formation of NaCl is equal to the sum of the enthalpy changes of the individual steps: H_f = H_sub + H_atom + H_IE + H_EA + H_lattice, formation Substitute the known values: -410 kJ/mol = (+108 kJ/mol) + (+121 kJ/mol) + (+496 kJ/mol) + (-349 kJ/mol) + H_lattice, formation -410 kJ/mol = (108 + 121 + 496 - 349) kJ/mol + H_lattice, formation -410 kJ/mol = 376 kJ/mol + H_lattice, formation H_lattice, formation = -410 kJ/mol - 376 kJ/mol H_lattice, formation = -786 kJ/mol Step 4: Calculate the lattice dissociation energy of sodium chloride. Lattice dissociation energy is the energy required to break one mole of an ionic solid into its constituent gaseous ions. It is the negative of the lattice formation energy. H_lattice, dissociation = - H_lattice, formation H_lattice, dissociation = - (-786 kJ/mol) H_lattice, dissociation = +786 kJ/mol Step 5: Name and state the law applied. The law applied is Hess's Law. Hess's Law states that the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken, as long as the initial and final conditions are the same. Last free one today — make it count tomorrow, or type /upgrade for unlimited.