Lattice Energy & Born-Haber Cycle - NEET Notes, Formula & Common Mistakes

What NEET Asks

• Typically 1-2 questions from Chemical Bonding, often involving calculations from Born-Haber Cycle or conceptual understanding of factors affecting lattice energy.
• Questions can be direct formula application or multi-step calculations requiring careful sign conventions.
• Understanding relative stability of ionic compounds based on lattice energy is frequently tested.

Key Points

• Lattice Energy (U): Energy released when one mole of an ionic compound is formed from its gaseous ions. It's always exothermic (negative value).
• Born-Haber Cycle: An indirect method to calculate lattice energy, based on Hess's Law of constant heat summation. It relates enthalpy of formation (ΔH_f) to other enthalpy changes.
• Factors Affecting Lattice Energy: Directly proportional to ionic charges (q1, q2) and inversely proportional to internuclear distance (r_cation + r_anion). U ∝ (q1 * q2) / (r_c + r_a).
• High Lattice Energy: Leads to greater stability and higher melting point for ionic compounds.
• Enthalpies Involved: Sublimation (S), Dissociation (D), Ionization Energy (IE), Electron Gain Enthalpy (ΔH_eg or EA), Enthalpy of Formation (ΔH_f).

Must-Know Formula / Reaction

Born-Haber Cycle for MX(s): ΔH_f = ΔH_sublimation(M) + ½ ΔH_dissociation(X2) + IE(M) + ΔH_eg(X) + U

• ΔH_f: Enthalpy of formation of ionic compound from its elements in standard states.
• ΔH_sublimation(M): Energy to convert solid metal to gaseous atoms (Endothermic, +).
• ½ ΔH_dissociation(X2): Energy to convert gaseous halogen molecule to gaseous atoms (Endothermic, +).
• IE(M): Ionization energy of gaseous metal atom (Endothermic, +).
• ΔH_eg(X): Electron gain enthalpy of gaseous non-metal atom (Exothermic/Endothermic, generally -ve for 1st EA, +ve for 2nd EA).
• U: Lattice energy (Exothermic, -ve).

Common Mistakes

• Students often forget to balance the stoichiometric coefficients for dissociation or electron gain enthalpy (e.g., ½ D for X, or 2EA for 2X).
• Don't confuse the sign conventions: Ionization energy and sublimation are always positive; lattice energy is always negative. Electron gain enthalpy can be positive or negative.
• Incorrectly using electron affinity (usually +ve value) instead of electron gain enthalpy (ΔH_eg, which can be -ve or +ve).

Rapid Revision

Born-Haber Cycle applies Hess's Law. High charges and small sizes lead to higher (more negative) lattice energy, implying greater stability. Remember the five energy terms and their correct signs for quick calculations. Lattice energy is energy RELEASED.