A student evaluates the industrial extraction of iron metal from iron(III) oxide using carbon monoxide gas at \(298 \text{ K}\). The thermochemical equations for the individual processes are shown below:

\(\text{Fe}_2\text{O}_3(s) \rightarrow 2\,\text{Fe}(s) + \frac{3}{2}\,\text{O}_2(g) \quad \Delta G^\circ = +740 \text{ kJ/mol}_{rxn}\)

\(\text{CO}(g) + \frac{1}{2}\,\text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta G^\circ = -280 \text{ kJ/mol}_{rxn}\)

Based on the information above, what is the standard Gibbs free energy change, \(\Delta G^\circ\), for the net coupled reaction shown below?

\(\text{Fe}_2\text{O}_3(s) + 3\,\text{CO}(g) \rightarrow 2\,\text{Fe}(s) + 3\,\text{CO}_2(g)\)