Consider the stepwise reduction of iron oxides via carbon monoxide: 1) has . 2) has . Utilizing Hess — Thermodynamics and Thermochemistry Chemistry Question
Question
Consider the stepwise reduction of iron oxides via carbon monoxide: 1) $Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)$ has $\Delta H_1 = -26.8 \text{ kJ}$. 2) $FeO(s) + CO(g) \rightarrow Fe(s) + CO_2(g)$ has $\Delta H_2 = -16.5 \text{ kJ}$. Utilizing Hess's Law, calculate the enthalpy change ($\Delta H$) in kJ for the intermediate reduction step: $Fe_2O_3(s) + CO(g) \rightarrow 2FeO(s) + CO_2(g)$.
💡 Solution & Explanation
To formulate the target equation, we apply Hess's Law by algebraically manipulating the known reactions. We leave Equation 1 untouched: $Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2 \quad (\Delta H_1 = -26.8 \text{ kJ})$. We must reverse Equation 2 and multiply it by a factor of 2 to cancel out the elemental iron: $2Fe + 2CO_2 \rightarrow 2FeO + 2CO \quad (\Delta H = -2 \times -16.5 = +33.0 \text{ kJ})$. Adding the two adjusted equations yields the target: $Fe_2O_3 + CO \rightarrow 2FeO + CO_2$. Thus, $\Delta H_{target} = -26.8 + 33.0 = +6.2 \text{ kJ}$.