Calculate Delta H r x n for the following reaction: Fe2O3 (s) + 3CO (g)—–> 2Fe (s) + 3CO2 (g). Use the following reactions and given delta H’s. 2Fe (s) + 3/2O2 (g)—–>Fe2O3 (s), Delta H= -824.2 kJ CO (g) + 1/2O2 (g)—–>CO2 (g), Delta H=-282.7 K j
The Correct Answer and Explanation is :
To determine the enthalpy change ((\Delta H_{rxn})) for the reaction:
[
\text{Fe}_2\text{O}_3 (s) + 3CO (g) \rightarrow 2Fe (s) + 3CO_2 (g)
]
using the given reactions:
- Formation of Iron(III) Oxide
[
2Fe (s) + \frac{3}{2}O_2 (g) \rightarrow Fe_2O_3 (s) \quad \Delta H = -824.2 \text{ kJ}
] - Formation of Carbon Dioxide
[
CO (g) + \frac{1}{2}O_2 (g) \rightarrow CO_2 (g) \quad \Delta H = -282.7 \text{ kJ}
]
Step 1: Reverse the First Equation
The target reaction has Fe(_2)O(_3) as a reactant, but in the given equation, it appears as a product. So, we reverse the equation:
[
Fe_2O_3 (s) \rightarrow 2Fe (s) + \frac{3}{2}O_2 (g)
]
Since we reversed the reaction, we also reverse the sign of (\Delta H):
[
\Delta H = +824.2 \text{ kJ}
]
Step 2: Multiply the Second Equation
The given second reaction forms CO(_2) from CO. Since the target equation involves 3 CO molecules, we multiply the entire equation by 3:
[
3CO (g) + \frac{3}{2}O_2 (g) \rightarrow 3CO_2 (g)
]
Since we multiplied the reaction by 3, we also multiply (\Delta H) by 3:
[
\Delta H = 3 \times (-282.7) = -848.1 \text{ kJ}
]
Step 3: Add the Two Adjusted Equations
Now, summing both reactions:
[
Fe_2O_3 (s) + \frac{3}{2}O_2 (g) + 3CO (g) \rightarrow 2Fe (s) + \frac{3}{2}O_2 (g) + 3CO_2 (g)
]
The (\frac{3}{2}O_2 (g)) cancels from both sides, giving:
[
Fe_2O_3 (s) + 3CO (g) \rightarrow 2Fe (s) + 3CO_2 (g)
]
which matches the target reaction.
Step 4: Sum the Enthalpy Changes
[
\Delta H_{rxn} = 824.2 + (-848.1) = -23.9 \text{ kJ}
]
Conclusion
The enthalpy change for the reaction is (-23.9) kJ, meaning the reaction is exothermic, releasing a small amount of energy. This makes sense because iron oxide is being reduced while carbon monoxide is oxidized to carbon dioxide, a common thermodynamically favorable process in metallurgy.