Determine ΔG° for the reaction: Fe₂O₃(s) + 3 CO(g) → 2 Fe(s) + 3 CO₂(g) Use the following reactions with known ΔG°_rxn values:
2 Fe(s) + 3/2 O₂(g) → Fe₂O₃(s) ΔG°_rxn = -742.2 kJ
CO(g) + 12 O₂( g) → CO₂(g) ΔG°_rxn = -257.2 kJ

Verified step by step guidance

1. Identify the target reaction: Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g).
2. Write the given reactions with their ΔG° values: (1) 2 Fe(s) + \(\frac{3}{2}\) O2(g) → Fe2O3(s), ΔG° = -742.2 kJ; (2) CO(g) + \(\frac{1}{2}\) O2(g) → CO2(g), ΔG° = -257.2 kJ.
3. Reverse reaction (1) to match the target reaction's direction: Fe2O3(s) → 2 Fe(s) + \(\frac{3}{2}\) O2(g), change sign of ΔG° to +742.2 kJ.
4. Multiply reaction (2) by 3 to match the target reaction's stoichiometry: 3 CO(g) + \(\frac{3}{2}\) O2(g) → 3 CO2(g), multiply ΔG° by 3 to get -771.6 kJ.
5. Add the modified reactions to obtain the target reaction and sum their ΔG° values: Fe2O3(s) + 3 CO(g) → 2 Fe(s) + 3 CO2(g), ΔG° = 742.2 kJ + (-771.6 kJ).

Key Concepts

Gibbs Free Energy (ΔG°)

Gibbs Free Energy (ΔG°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. A negative ΔG° indicates that a reaction is spontaneous, while a positive ΔG° suggests non-spontaneity. Understanding ΔG° is crucial for predicting the favorability of chemical reactions.

Standard Reaction Gibbs Free Energy (ΔG°rxn)

Standard Reaction Gibbs Free Energy (ΔG°rxn) refers to the change in Gibbs Free Energy for a reaction under standard conditions (1 bar pressure, 298 K temperature). It is calculated using the Gibbs Free Energy values of the reactants and products. This concept is essential for determining the spontaneity and equilibrium of reactions, as seen in the provided reactions.

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps, regardless of the pathway taken. This principle can be applied to Gibbs Free Energy calculations, allowing us to combine known ΔG°rxn values from multiple reactions to find the ΔG° for a target reaction. It is a powerful tool in thermodynamics for deriving reaction energetics.