Question

How much heat in kilojoules is evolved or absorbed in the reaction of \(2.50 \mathrm{~g}\) of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) with enough carbon monoxide to produce iron metal? Is the process exothermic or endothermic? $$\begin{aligned}\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{CO}(g) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}_{2}(g) \\ \Delta H^{\circ}=-24.8 \mathrm{~kJ}\end{aligned}$$

Short answer

The heat evolved is approximately -0.39 kJ. The process is exothermic.

Step-by-step solution

Calculate moles of \(\mathrm{Fe}_2\mathrm{O}_3\)

Determine the number of moles of \( \mathrm{Fe}_2\mathrm{O}_3 \) using its molar mass. The molar mass of \( \mathrm{Fe}_2\mathrm{O}_3 \) is approximately 159.7 g/mol. Use the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]\[ \text{moles of } \mathrm{Fe}_2\mathrm{O}_3 = \frac{2.50 \, \text{g}}{159.7 \, \text{g/mol}} \approx 0.0157 \, \text{mol} \]

Use Stoichiometry to Find Heat Change

Given that the reaction enthalpy change \( \Delta H^\circ \) is \(-24.8 \, \text{kJ}\) per mole of \( \mathrm{Fe}_2\mathrm{O}_3 \) reacted, multiply the moles of \( \mathrm{Fe}_2\mathrm{O}_3 \) by \( \Delta H^\circ \):\[ \text{Heat evolved} = 0.0157 \, \text{mol} \times (-24.8 \, \text{kJ/mol}) \approx -0.39 \, \text{kJ} \]

Determine Process Type

Since the enthalpy change \( \Delta H^\circ \) is negative, it indicates that the process is exothermic. This means heat is evolved or released during the reaction.

Key concepts

Stoichiometry

Stoichiometry is a central concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It helps us understand the proportional relationships between different substances in a chemical equation. In this particular exercise, we are examining a reaction between iron(III) oxide (\( \mathrm{Fe}_2\mathrm{O}_3 \)) and carbon monoxide (\( \mathrm{CO} \)) to form iron and carbon dioxide. The stoichiometric coefficients in the balanced equation:

• 1 mole of \( \mathrm{Fe}_2\mathrm{O}_3 \)
• 3 moles of \( \mathrm{CO} \)
• 2 moles of \( \mathrm{Fe} \)
• 3 moles of \( \mathrm{CO}_2 \)

show the proportions in which the substances react and are formed.
To find out how much heat is involved in this reaction, we first need to determine the number of moles of \( \mathrm{Fe}_2\mathrm{O}_3 \) being used. We do this by dividing the mass of \( \mathrm{Fe}_2\mathrm{O}_3 \) by its molar mass. Knowing the moles helps us track the energy changes through stoichiometric calculations. This method, known as proportional reasoning, is crucial for finding the heat change, also referred to as the enthalpy change.

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), reflects the heat absorbed or evolved during a reaction at constant pressure. It's an essential concept to understand the energy dynamics of chemical processes. In this exercise, we focus on an enthalpy change of \( -24.8 \, \text{kJ/mol} \) for the reaction of one mole of \( \mathrm{Fe}_2\mathrm{O}_3 \) with carbon monoxide.
Using the enthalpy change, we calculate the heat evolved when a specific amount of reactant, in this case, 2.50 grams of \( \mathrm{Fe}_2\mathrm{O}_3 \), undergoes reaction. With the stoichiometry, we convert grams to moles and multiply by the enthalpy change per mole to get the total heat evolved: \(0.0157 \, \text{mol} \times (-24.8 \, \text{kJ/mol}) \approx -0.39 \, \text{kJ} \).
This value gives us the energy change associated with the reaction. The negative sign indicates that the reaction releases heat, which links directly to the concept of exothermic reactions.

Exothermic Reaction

Exothermic reactions are characterized by the release of heat. They have a negative \( \Delta H \) value, signifying that energy is transferred from the system to the surroundings. This is because the energy required to break the bonds in the reactants is less than the energy released when new bonds are formed in the products.
In the given reaction, the negative enthalpy change of \(-24.8 \, \text{kJ/mol}\) confirms that it is exothermic. Consequently, when \( \mathrm{Fe}_2\mathrm{O}_3 \) reacts with carbon monoxide, heat is evolved. This kind of reaction increases the temperature of the surroundings, making them feel warmer. Understanding exothermic reactions can help in contexts like designing heat engines or understanding biological processes where energy release is crucial to function.
It's important to consider safety implications, as exothermic reactions can lead to significant temperature rises if not controlled properly.