In a crystal, at 827 °C, one out of 10^10 lattice site is found to be vacant but at 927 °C, one out of 2 × 10^9 lattice sites is found to be vacant. The enthalpy of vacancy formation, in kJ/mol, is

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Prashant Kotian · Accepted Answer

Correct answer: B. The fraction of vacant lattice sites is given by: n/N = exp(-ΔH / RT). Taking logs: ln((n2/N) / (n1/N)) = (ΔH / R) × (1/T1 - 1/T2). Given T1 = 1100 K, n1/N = 10^-10 and T2 = 1200 K, n2/N = 5 × 10^-10. ln(5) ≈ 1.6094. Thus, 1.6094 = (ΔH / 8.314) × (1/1100 - 1/1200) => 1.6094 = ΔH × 100 / (8.314 × 1100 × 1200) => ΔH ≈ 176.8 kJ/mol.

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