Two possible ways of producing iron from iron ore are (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\frac{3}{2} \mathrm{C}(s) \longrightarrow 2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{CO}_{2}(g)\) (b) \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{H}_{2} \mathrm{O}(g)\) Which of these reactions proceeds spontaneously at the lower temperature?

To determine which reaction proceeds spontaneously at a lower temperature, follow these steps: 1. Calculate the enthalpy change (\(\Delta H\)) for both reactions using the enthalpy of formation values found in a standard enthalpy table. 2. Calculate the entropy change (\(\Delta S\)) for both reactions using the entropy values found in a standard entropy table. 3. Calculate the Gibbs free energy change (\(\Delta G\)) for both reactions using the formula \(\Delta G = \Delta H - T\Delta S\) and a certain temperature in Kelvin. 4. Compare the \(\Delta G\) values between reactions. The reaction with the lower \(\Delta G\) value at the desired temperature will proceed spontaneously at a lower temperature.