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Chemistry · THERMODYNAMICS

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For the dissociation of crystal lattice: \( \text{NaCl}(s) \rightarrow \text{Na}^+(g) + \text{Cl}^-(g) \), the lattice enthalpy is \( \Delta_{\text{lattice}} H^\ominus = +788\text{ kJ mol}^{-1} \) at \( 298\text{ K} \). Assuming ideal gas behavior for ions, what is the change in internal energy (\( \Delta_{\text{lattice}} U^\ominus \))? (Take \( 2RT \approx 5\text{ kJ mol}^{-1} \))

  1. \( +793\text{ kJ mol}^{-1} \)
  2. \( +788\text{ kJ mol}^{-1} \)
  3. \( -783\text{ kJ mol}^{-1} \)
  4. \( +783\text{ kJ mol}^{-1} \)

Correct answer · Option 4

\( +783\text{ kJ mol}^{-1} \)

Explanation

\( \Delta H = \Delta U + \Delta n_g RT \). Here \( \Delta n_g = 2 - 0 = 2 \), so \( \Delta U = \Delta H - 2RT = 788 - 5 = +783\text{ kJ mol}^{-1} \).
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