Given the following standard Gibbs free energy changes (): (i) ; . (ii) ; . Determine the standard f — Thermodynamics and Thermochemistry Chemistry Question
Question
Given the following standard Gibbs free energy changes ($\Delta_r G^\circ$): (i) $2Fe_2O_3(s) \rightarrow 4Fe(s) + 3O_2(g)$; $\Delta_r G^\circ = +1487.0 \text{ kJ mol}^{-1}$. (ii) $2CO(g) + O_2(g) \rightarrow 2CO_2(g)$; $\Delta_r G^\circ = -514.4 \text{ kJ mol}^{-1}$. Determine the standard free energy change ($\Delta_r G^\circ$) for the overall reduction reaction: $2Fe_2O_3(s) + 6CO(g) \rightarrow 4Fe(s) + 6CO_2(g)$.
💡 Solution & Explanation
The target reaction is $2Fe_2O_3(s) + 6CO(g) \rightarrow 4Fe(s) + 6CO_2(g)$. This can be obtained by adding reaction (i) to three times reaction (ii). We multiply equation (ii) by 3: $6CO(g) + 3O_2(g) \rightarrow 6CO_2(g)$; $\Delta_r G^\circ = 3 \times (-514.4) = -1543.2 \text{ kJ mol}^{-1}$. Adding this to equation (i): $\Delta_r G^\circ_{total} = +1487.0 + (-1543.2) = -56.2 \text{ kJ mol}^{-1}$.