Fe₂O₃ (s) + 3 H₂ (g) → 2 Fe (s) + 3 H₂O (g) is a redox reaction. What would be its Gibbs Free energy change under standard conditions? Is the reaction spontaneous at 25 °C?

• A. 513.6 kJ; No, the reaction is not spontaneous at 25 °C.
• B. 56.4 kJ; No, the reaction is not spontaneous at 25 °C.
• C. −513.6 kJ; Yes, the reaction is not spontaneous at 25 °C.
• D. 56.4 kJ; Yes, the reaction is spontaneous at 25 °C.

Answer: (B)

Verified step by step guidance

1. Identify the reaction and the standard Gibbs free energy of formation (G°f) values for each substance involved from the table: Fe2O3 (−742.2 kJ/mol), H2 (0 kJ/mol, elemental form), Fe (0 kJ/mol, elemental form), and H2O (−228.6 kJ/mol).
2. Write the balanced chemical equation: \(\mathrm{Fe_2O_3 (s) + 3 H_2 (g) \rightarrow 2 Fe (s) + 3 H_2O (g)}\).
3. Calculate the standard Gibbs free energy change for the reaction using the formula: \(\Delta G^\circ = \sum \nu G^\circ_f (\text{products}) - \sum \nu G^\circ_f (\text{reactants})\), where \(\nu\) are the stoichiometric coefficients.
4. Substitute the values: \(\Delta G^\circ = [2 \times G^\circ_f(Fe) + 3 \times G^\circ_f(H_2O)] - [1 \times G^\circ_f(Fe_2O_3) + 3 \times G^\circ_f(H_2)]\).
5. Evaluate the sign of \(\Delta G^\circ\) to determine spontaneity at 25 °C: if \(\Delta G^\circ < 0\), the reaction is spontaneous; if \(\Delta G^\circ > 0\), it is non-spontaneous.