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 \(4.00\) moles of iron are reacted with excess \(\mathrm{O}_{2}\) ? b. How much heat is released when \(1.00\) mole of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) 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

The short answers for each part of the question are: a. -1652 kJ of heat is released when 4.00 moles of iron are reacted with excess O₂. b. -826 kJ of heat is released when 1.00 mole of Fe₂O₃ is produced. c. -7.38 kJ of heat is released when 1.00 g iron is reacted with excess O₂. d. -34.4 kJ of heat is released when 10.0 g Fe and 2.00 g O₂ are reacted.

Step-by-step solution

We are given 4.00 moles of iron, with excess O₂. The enthalpy change for the reaction, ΔH, is -1652 kJ. #Step 2: Use stoichiometry to determine the amount of heat released#

According to the balanced equation, 4 moles of Fe react with 3 moles of O₂ to produce 2 moles of Fe₂O₃ and release -1652 kJ of heat. Since the moles of iron given in the problem are equal to the moles in the balanced equation, the heat released remains the same as the ΔH value given. Therefore, the heat released is -1652 kJ. b. How much heat is released when 1.00 mole of Fe₂O₃ is produced? #Step 1: Identify the given information#

We are given the production of 1.00 mole of Fe₂O₃. The enthalpy change for the reaction, ΔH, is -1652 kJ. #Step 2: Use stoichiometry to determine the amount of heat released#

According to the balanced equation, 2 moles of Fe₂O₃ are produced with -1652 kJ heat release. To determine the heat released when only 1 mole is produced, divide ΔH by 2: Heat released = (-1652 kJ) / 2 = -826 kJ c. How much heat is released when 1.00 g iron is reacted with excess O₂? #Step 1: Convert grams of iron to moles of iron#

Use the molar mass of iron (Fe) to convert grams to moles: Moles of Fe = (1.00 g) / (55.85 g/mol) ≈ 0.0179 mol #Step 2: Use stoichiometry to determine the amount of heat released per mole of iron#

Since 4 moles of iron react to release -1652 kJ of heat, determine the heat per mole of iron: Heat per mole of iron = (-1652 kJ) / 4 = -413 kJ/mol #Step 3: Calculate the heat released for 1.00 g of iron#

Multiply the moles of iron by the heat released per mole of iron. Heat released = 0.0179 mol × -413 kJ/mol ≈ -7.38 kJ d. How much heat is released when 10.0 g Fe and 2.00 g O₂ are reacted? #Step 1: Determine the limiting reactant#

Convert the given mass of each reactant to moles using their respective molar masses (Fe: 55.85 g/mol, O₂: 32.00 g/mol): 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 In the balanced equation, the stoichiometric ratio between Fe and O₂ is 4:3. Divide the moles of each reactant by the stoichiometric coefficients: Fe: 0.179 / 4 ≈ 0.0447 O₂: 0.0625 / 3 ≈ 0.0208 Since the quotient for O₂ is smaller than the quotient for Fe, O₂ is the limiting reactant. #Step 2: Calculate the heat released based on the limiting reactant#

Based on the enthalpy change, -1652 kJ is released for every 3 moles of O₂ reacted. Find the heat released per mole of O₂, so divide ΔH by 3: Heat per mole of O₂ = (-1652 kJ) / 3 = -550.67 kJ/mol #Step 3: Calculate the heat released for the given amount of O₂#

Multiply the moles of O₂ by the heat released per mole of O₂: Heat released = 0.0625 mol × -550.67 kJ/mol ≈ -34.4 kJ

Key concepts

Stoichiometry

Stoichiometry is a fundamental aspect of chemistry that refers to calculating the quantities of reactants and products involved in a chemical reaction. It uses balanced chemical equations to find relationships between different substances involved in the reaction.
In a balanced equation like the one given in the problem, coefficients indicate the number of moles of each substance that react or are produced. For example, in the reaction \(4 \mathrm{Fe}(s) + 3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{Fe}_{2}\mathrm{O}_{3}(s)\), the coefficients show that four moles of iron react with three moles of oxygen to produce two moles of iron(III) oxide.
Using these stoichiometric relationships, we can determine the amount of heat released or absorbed in a chemical reaction by relating the quantities of reactants and products to the enthalpy change, \( \Delta H \). This approach helps calculate how much heat a certain amount of reactant will release when it undergoes a chemical change, as we see in the exercises.

Limiting Reactant

The concept of the limiting reactant is vital to understanding chemical reactions. In many chemical processes, not all reactants are used up completely. The limiting reactant is the substance that is consumed first and thus determines the amount of product formed.
To find the limiting reactant, we convert the mass of each reactant to moles and use the stoichiometric ratios from the balanced equation to see which reactant will run out first. In the problem, converting 10.0 g Fe and 2.00 g \(\mathrm{O}_{2}\) to moles revealed that oxygen is the limiting reactant. Since we have more moles of iron than needed for the available oxygen, oxygen limits the reaction.

• The limiting reactant concept helps determine the exact amount of product and heat produced, ensuring that theoretical calculations align more closely with practical outcomes.

Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, involved in chemical reactions. It focuses on understanding the energy aspects of chemical transformations by using enthalpy changes (\(\Delta H\)).
The given reaction is exothermic, meaning it releases heat, indicated by a negative \(\Delta H\) of -1652 kJ. This tells us that when the reaction proceeds as written, it releases that specific amount of energy.
In problems involving heat packs or similar reactions, the goal is often to calculate the amount of heat released based on given quantities of reactants. Thermochemistry and stoichiometry are interconnected in these calculations, as a precise stoichiometric understanding aids in correctly calculating energy changes.

Reaction Stoichiometry

Reaction stoichiometry not only involves understanding the proportions of reactants and products but also linking these to energy changes. In chemical equations, stoichiometry dictates how much product forms based on the initial amount of reactants and the reaction's enthalpy change.
In the heat pack reaction, the stoichiometric coefficients from the balanced chemical equation help us determine the heat released for different scenarios, such as when different amounts of iron or iron oxide are involved.
This calculated proportion of energy release or absorption in a chemical reaction helps scientists and engineers design processes and products that require specific energy outputs, such as heat packs, where accurate energy release is crucial for effective temperature management.