MgO has a lattice energy of approximately −3791 kJ/mol, much larger than NaCl's −787 kJ/mol. What is the primary reason for this difference?
AMgO has a higher molar mass, so more energy is released when the crystal forms
BMgO adopts a different crystal structure that packs ions more efficiently
CMg²⁺ and O²⁻ carry higher charges and have smaller ionic radii than Na⁺ and Cl⁻, producing much stronger electrostatic attraction
DThe enthalpy of formation of MgO is larger, so its lattice energy must be larger too
Lattice energy is fundamentally an electrostatic phenomenon governed by Coulomb's law: it increases with higher ionic charges and decreases with larger ionic radii. MgO has doubly charged ions (2+/2−) while NaCl has singly charged ions (1+/1−). The charge factor alone increases lattice energy by roughly a factor of four (2×2 vs 1×1). Additionally, Mg²⁺ and O²⁻ are smaller than Na⁺ and Cl⁻, bringing charges closer together. The combination of higher charge and smaller size explains the nearly five-fold difference in lattice energy. Note that option D confuses cause and effect: lattice energy is a component of the formation enthalpy calculation, not derived from it.
Question 2 Multiple Choice
Why can lattice energy not be measured directly by calorimetry, unlike most other enthalpies in the Born-Haber cycle?
ALattice energies are too small to detect with standard calorimetric equipment
BThere is no practical way to combine a mole of gaseous cations with a mole of gaseous anions under controlled conditions to directly measure the heat released
CCalorimetry only measures bond energies in molecular compounds, not ionic solids
DThe lattice energy and enthalpy of formation are the same quantity, so measuring one measures the other
Lattice energy is defined as the energy change when gaseous ions condense into a crystal: Na⁺(g) + Cl⁻(g) → NaCl(s). Performing this reaction in a calorimeter would require starting with isolated gaseous ions — an experimentally impractical starting state. You cannot easily generate and bottle a mole of gaseous Na⁺ and Cl⁻ ions. This is why the Born-Haber cycle is necessary: it provides an indirect route using measurable quantities (ionization energy, electron affinity, sublimation enthalpy, dissociation enthalpy, and formation enthalpy) to calculate lattice energy as the unknown term via Hess's law.
Question 3 True / False
The lattice energy of an ionic compound equals its standard enthalpy of formation.
TTrue
FFalse
Answer: False
This is one of the most common misconceptions about the Born-Haber cycle. Lattice energy is only one step in the formation process. The standard enthalpy of formation (e.g., Na(s) + ½Cl₂(g) → NaCl(s)) also includes sublimation of the metal, dissociation of the halogen molecule, ionization of the metal, and electron affinity of the nonmetal. The lattice energy is the last step: gaseous ions → solid crystal. It is typically the largest single term, but it is not equal to ΔH_f. The Born-Haber cycle's entire purpose is to relate these distinct quantities through Hess's law.
Question 4 True / False
The Born-Haber cycle is an application of Hess's law: because enthalpy is a state function, the sum of all steps in the cycle must equal the directly measurable enthalpy of formation.
TTrue
FFalse
Answer: True
This is the core principle. Hess's law states that the total enthalpy change is path-independent — only the initial and final states matter. The Born-Haber cycle constructs a multi-step path (sublimation + ionization + dissociation + electron affinity + lattice formation) from the same reactants to the same product as the direct formation reaction. All steps must sum to ΔH_f. Because every step except lattice energy is independently measurable, lattice energy can be solved as the one unknown term.
Question 5 Short Answer
Using the Born-Haber framework, explain why the hypothetical compound NaCl₂ does not form as a stable ionic solid.
Think about your answer, then reveal below.
Model answer: Forming NaCl₂ would require removing two electrons from sodium — the first ionization energy (removing the outer 3s electron, ~496 kJ/mol) plus the enormous second ionization energy (removing an electron from sodium's stable neon-like core, ~4562 kJ/mol). The total ionization cost for Na²⁺ is roughly 5058 kJ/mol. No feasible lattice energy for a Na²⁺/Cl⁻ compound (only singly charged Cl⁻ ions) could compensate for this enormous energetic input. The Born-Haber cycle makes this explicit: summing all steps for the hypothetical NaCl₂ gives a strongly positive ΔH_f, meaning the compound is thermodynamically unstable relative to the elements.
This question requires using the Born-Haber logic as an explanatory tool, not just a calculation procedure. The key insight is that lattice energy scales with charge, but going from NaCl to NaCl₂ only doubles the charge on the cation while the second ionization energy increases by roughly an order of magnitude. The energetic accounting shows why real ionic compounds form with the specific charges they do — not because of convention, but because of thermodynamic necessity.