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Chemistry · THERMODYNAMICS

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For the reaction \( \text{Fe}_2\text{O}_3(s) + 3\text{H}_2(g) \rightarrow 2\text{Fe}(s) + 3\text{H}_2\text{O}(l) \), the standard enthalpy change is \( \Delta_r H_1^\ominus = -33.3\text{ kJ mol}^{-1} \). What is the standard enthalpy change \( \Delta_r H_2^\ominus \) for the reaction: \( \frac{1}{2}\text{Fe}_2\text{O}_3(s) + \frac{3}{2}\text{H}_2(g) \rightarrow \text{Fe}(s) + \frac{3}{2}\text{H}_2\text{O}(l) \)?

  1. -33.3 kJ mol⁻¹
  2. -16.65 kJ mol⁻¹
  3. +16.65 kJ mol⁻¹
  4. -66.6 kJ mol⁻¹

Correct answer · Option 2

-16.65 kJ mol⁻¹

Explanation

Enthalpy is an extensive property; halving all stoichiometric coefficients halves the reaction enthalpy: \( \Delta_r H_2^\ominus = \frac{1}{2} \Delta_r H_1^\ominus = \frac{-33.3}{2} = -16.65\text{ kJ mol}^{-1} \).
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