Lattice Enthalpy — Born-Haber cycle
Thermodynamics & Thermochemistry
9
JEE Qs
8%
Hard
75
min
Always draw out the Born-Haber cycle diagram and systematically list all enthalpy terms with their correct signs and stoichiometric coefficients before summing them up to avoid calculation errors.
🧮 Key Formulas
✅ Key Points for JEE
- 1The Born-Haber cycle is a direct application of Hess's Law to calculate the lattice enthalpy (or any other unknown enthalpy term) of an ionic compound.
- 2Lattice enthalpy (U or ΔH_lattice) is the enthalpy change when one mole of an ionic compound is formed from its constituent gaseous ions (e.g., Na⁺(g) + Cl⁻(g) → NaCl(s)). It is always exothermic (negative).
- 3Carefully identify and use the correct stoichiometry (e.g., 0.5 for dissociation of X₂ if only one X atom is needed, or multiplication by 'n' for 'n' moles of a specific ion).
- 4Pay close attention to the sign convention for each enthalpy term: ionization energies are positive, electron affinities can be negative (first) or positive (successive), sublimation and dissociation enthalpies are positive, and formation enthalpy can be positive or negative.
- 5The factors affecting lattice enthalpy are primarily ionic charge (higher charge = more negative lattice enthalpy) and ionic radius (smaller radius = more negative lattice enthalpy). U ∝ (q₊q₋) / (r₊ + r₋).
⚠️ Common Mistakes
- ✕Incorrectly assigning the signs of the enthalpy terms (e.g., treating ionization energy as negative or lattice enthalpy as positive in the cycle).
- ✕Failing to apply the correct stoichiometric coefficients for dissociation enthalpy (e.g., using ΔH_diss for X₂ instead of 0.5 * ΔH_diss for X) or for multiple ionization energies/electron affinities.
- ✕Confusing lattice formation enthalpy (from gaseous ions) with lattice dissociation enthalpy (to gaseous ions), which have opposite signs.
📝 Practice Questions
See allQ32.Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ( ρ ) are intensive variables. (C) Volume (V), temperature (T) and density ( ρ ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below : (1) (B) and (C) Only (2) (C) and (D) Only (3) (D) and (A) Only (4) (A) and (B) Only
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Q53.A liquid when kept inside a thermally insulated closed vessel at 25∘C was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ? (1) ΔU < 0, q = 0, w > 0 (2) ΔU = 0, q = 0, w = 0 (3) ΔU > 0, q = 0, w > 0 (4) ΔU = 0, q < 0, w > 0
Q31.Water of mass m gram is slowly heated to increase the temperature from T1 to Tz The change in entropy of the water, given specific heat of water is 1Jkg−1 K−1 , is : (1) m ln ( T2T1 ) (2) zero (3) m ln ( T1T2 ) (4) m (T2 −T1)
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NCERT Chapters
- Class 11 Chemistry Ch 6: Thermodynamics
- Class 11 Chemistry Ch 3: Classification of Elements and Periodicity in Properties
- Class 11 Chemistry Ch 4: Chemical Bonding and Molecular Structure