Question

The overall reaction in a commercial heat pack can be represented as $$ 4 \mathrm{Fe}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad \Delta H=-1652 \mathrm{~kJ} $$ a. How much heat is released when \(4.00 \mathrm{~mol}\) iron is reacted with excess \(\mathrm{O}_{2}\) ? b. How much heat is released when \(1.00 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) is produced? c. How much heat is released when \(1.00 \mathrm{~g}\) iron is reacted with excess \(\mathrm{O}_{2} ?\) d. How much heat is released when \(10.0 \mathrm{~g} \mathrm{Fe}\) and \(2.00 \mathrm{~g} \mathrm{O}_{2}\) are reacted?

Short answer

a. Heat released = -1652 kJ b. Heat released = -826 kJ c. Heat released = -7.40 kJ d. Heat released = -34.5 kJ

Step-by-step solution

a. Heat released with 4.00 mol Fe and excess O₂

We are given that 4.00 mol of Fe are reacted with excess O₂, and we need to determine the amount of heat released for this reaction. Since the stoichiometry of the reaction indicates that 4 moles of Fe react with 3 moles of O₂ to produce 2 moles of Fe₂O₃, we can directly relate the given quantity of Fe to the ΔH value: ΔH = -1652 kJ (for 4 moles of Fe) Since we have exactly 4.00 moles of Fe, the heat released in this case will be equal to the given ΔH. Heat released = -1652 kJ

b. Heat released with 1.00 mol Fe₂O₃ produced

Now we are given that 1.00 mol of Fe₂O₃ is produced in the reaction, and we need to determine the amount of heat released for this scenario. First, we need to find the relationship between moles of Fe₂O₃ and the heat released. For the balanced chemical equation, we have: 4 Fe + 3 O₂ → 2 Fe₂O₃ ΔH = -1652 kJ Dividing the reaction by 2, we get: 2 Fe + \(\frac{3}{2}\) O₂ → 1 Fe₂O₃ In this case, the heat released would also be divided by 2: ΔH = -1652 kJ / 2 = -826 kJ Since we have 1 mol of Fe₂O₃ produced, the heat released in this case will be equal to the new ΔH. Heat released = -826 kJ

c. Heat released with 1.00 g Fe and excess O₂

Now we are given 1.00 g of Fe is reacted with excess O₂, and we need to determine the amount of heat released for this scenario. First, we need to convert the mass of Fe to moles: Moles of Fe = mass / molar mass Molar mass of Fe = 55.85 g/mol Moles of Fe = 1.00 g / 55.85 g/mol = 0.0179 mol Now, we use the stoichiometry and the ΔH value for 1 mol of Fe₂O₃ to find the heat released: Heat released = moles of Fe × (ΔH for 1 mol of Fe₂O₃) / 2 Heat released = 0.0179 mol × (-826 kJ/mol) / 2 = -7.40 kJ

d. Heat released with 10.0 g Fe and 2.00 g O₂ reacted

We are given that 10.0 g of Fe and 2.00 g of O₂ are reacted together, and we need to determine the amount of heat released for this scenario. First, we need to convert the masses to moles: Moles of Fe = 10.0 g / 55.85 g/mol = 0.179 mol Moles of O₂ = 2.00 g / 32.00 g/mol = 0.0625 mol Now we need to determine if either Fe or O₂ is the limiting reactant: Mole ratio Fe/O₂ = 4/3 If 0.179 mol of Fe reacts completely, it would require: 0.179 mol × (3 moles O₂ / 4 moles Fe) = 0.134 mol O₂ Since we only have 0.0625 mol O₂ available, O₂ is the limiting reactant. Now we can find the moles of Fe₂O₃ that will be produced: Moles of Fe₂O₃ = 0.0625 mol × (2 moles Fe₂O₃ / 3 moles O₂) = 0.0417 mol Finally, we can determine the heat released by using the ΔH value for 1 mol of Fe₂O₃: Heat released = 0.0417 mol × (-826 kJ/mol) = -34.5 kJ

Key concepts

Enthalpy Change

Enthalpy change is a key aspect of thermochemistry. It refers to the heat exchanged at constant pressure during a chemical reaction. Generally denoted by \( \Delta H \), it indicates whether the reaction is exothermic or endothermic.
In the given exercise, \( \Delta H = -1652 \, ext{kJ} \) represents the enthalpy change for the combustion of iron in the presence of oxygen.
This negative value indicates that the reaction releases heat, making it exothermic.
Understanding enthalpy change helps us gauge how much energy is absorbed or released when substances react. A negative \( \Delta H \) implies energy is disposed to the surroundings, warming it up compared to others where energy is absorbed. This is fundamentally helpful in specific applications like commercial heat packs, where the goal is to release heat to increase temperature.

Limiting Reactant

A limiting reactant in a chemical reaction is the substance that is completely consumed first. It establishes the maximum amounts of products that can be formed. In the case of the exercise, we calculated both reactants to identify which is limiting.
To find the limiting reactant, we converted the masses of iron and oxygen into moles using their molar masses. It turned out that although we had 0.179 moles of iron, we only had 0.0625 moles of \( O_2\).
This amount of \( O_2\) could only completely react with fewer moles of iron, showing \( O_2\) as the limiting reactant.
Understanding the concept of limiting reactants is crucial for predicting the amounts of products formed in a reaction. It ensures that the calculations for heat released are accurate, as we need to consider only the feasible reaction that occurs before one reactant runs out.

Stoichiometry

Stoichiometry is like a guiding map for chemical reactions. It tells us how much of each substance is involved or produced in a chemical reaction based on their balanced equations. In this exercise, we worked with the equation: \( 4 \, ext{Fe} + 3 \, ext{O}_2 \rightarrow 2 \, ext{Fe}_2\text{O}_3 \).
This equation reveals that four moles of iron react with three moles of \( O_2 \) to produce two moles of iron(III) oxide. Understanding this ratio is vital to applying the correct proportions when calculating the heat release and figuring out the limiting reactant.
By using stoichiometric coefficients, we derived the heat released when different quantities of reactants were involved. Accurate stoichiometric calculations ensure that reactions can be conducted efficiently, minimizing waste and maximizing yield, which is essential for industrial and laboratory settings alike.

Exothermic Reaction

Exothermic reactions are those where heat is released as products form. Such reactions are opposite to endothermic reactions, which absorb heat. The exercise concerns an exothermic reaction, represented by the enthalpy change \( \Delta H = -1652 \, ext{kJ} \).
In real-world applications, these reactions prove beneficial when heat production is advantageous. For instance, commercial heat packs utilize exothermic reactions to generate warmth when needed, such as outdoor activities or muscle therapy.
Recognizing an exothermic reaction involves observing the temperature rise or noting a negative \( \Delta H \). These reactions often result in surroundings feeling warmer due to the heat released. Thus, can be observed in various scenarios, from natural processes to human-engineered systems designed to harness this energy release for beneficial use.