Propane Combustion: Calculating Enthalpy Change & Heat Release

Hey there, chemistry enthusiasts! Let's dive into a fun problem involving thermodynamics, specifically focusing on the combustion of propane (C₃H₈). We're going to calculate the enthalpy change (ΔH) for the combustion reaction and then figure out how much heat is released when a certain amount of propane burns. So, grab your calculators and let's get started. This is a common type of problem you might encounter in a high school or introductory college chemistry course, so paying attention can really help you understand the concepts of enthalpy, heat of formation, and stoichiometry. It's all about applying Hess's Law and understanding how energy changes during chemical reactions.

Understanding the Basics: Enthalpy and Combustion

First, let's make sure we're on the same page about the key concepts. Enthalpy (H) is a measure of the total heat content of a system at constant pressure. Changes in enthalpy (ΔH) tell us whether a reaction releases heat (exothermic, ΔH < 0) or absorbs heat (endothermic, ΔH > 0). Combustion is a chemical process that involves rapid reaction between a substance with an oxidant, usually oxygen, to produce heat and light. In the case of propane, it reacts with oxygen to form carbon dioxide and water. The standard enthalpy of formation (ΔHᶠ) is the enthalpy change when one mole of a compound is formed from its elements in their standard states. We’ll be using these values to calculate the overall enthalpy change of the combustion reaction. Understanding these fundamentals is crucial for tackling this problem. Remember that energy is neither created nor destroyed, it just changes forms, which is the heart of Hess’s Law. The law tells us that the total enthalpy change for a reaction is independent of the pathway taken. This means we can use the standard enthalpies of formation to calculate the enthalpy change for a reaction, even if the reaction occurs in multiple steps.

Now, let's break down the given information and what we need to do. We're given the standard enthalpies of formation (ΔHᶠ) for water (H₂O(l)), carbon dioxide (CO₂(g)), and propane (C₃H₈(g)). Our goal is to calculate the enthalpy change for the combustion of propane, and then find the heat released when a specific mass of propane is burned. This involves writing the balanced chemical equation, applying Hess’s Law, and using the molar mass to convert between grams and moles. It might seem daunting at first, but let’s go through it step by step, and it will be as easy as pie. Think of it like a puzzle. Each piece of information is a puzzle piece, and we need to assemble them to find the answer. The more practice you get, the easier it becomes. Let's start with the first part of the problem – calculating the enthalpy change for the combustion of propane.

Calculating the Enthalpy Change (ΔH) for Propane Combustion

Alright, let’s get into the nitty-gritty of the calculation! The combustion of propane (C₃H₈) involves the reaction with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O). The balanced chemical equation for this reaction is:

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(l)

Now, let's talk about the key to unlocking this problem: Hess's Law. It states that the enthalpy change for a reaction is the same whether it occurs in one step or in a series of steps. This allows us to use the standard enthalpies of formation (ΔHᶠ) to calculate the enthalpy change (ΔH) for the reaction. The formula we’ll use is:

ΔH = ΣnΔHᶠ(products) - ΣnΔHᶠ(reactants)

Where 'n' is the stoichiometric coefficient from the balanced chemical equation, and ΔHᶠ represents the standard enthalpy of formation. This formula essentially tells us to subtract the total enthalpy of formation of the reactants from the total enthalpy of formation of the products. Let's look at the given values:

• ΔHᶠ H₂O(l) = -285.5 kJ/mol
• ΔHᶠ CO₂(g) = -393.5 kJ/mol
• ΔHᶠ C₃H₈(g) = -103 kJ/mol
• ΔHᶠ O₂(g) = 0 kJ/mol (because it's an element in its standard state)

Now, let’s plug these values into our equation:

ΔH = [3 × ΔHᶠ(CO₂) + 4 × ΔHᶠ(H₂O)] - [1 × ΔHᶠ(C₃H₈) + 5 × ΔHᶠ(O₂)]

ΔH = [3 × (-393.5 kJ/mol) + 4 × (-285.5 kJ/mol)] - [1 × (-103 kJ/mol) + 5 × (0 kJ/mol)]

ΔH = [-1180.5 kJ/mol - 1142 kJ/mol] - [-103 kJ/mol]

ΔH = -2322.5 kJ/mol + 103 kJ/mol

ΔH = -2219.5 kJ/mol

So, the enthalpy change (ΔH) for the combustion of propane is -2219.5 kJ/mol. The negative sign indicates that the reaction is exothermic, meaning it releases heat. This is a very important result, guys! Remember to always include the units (kJ/mol) and the correct sign (+ or -) in your answer. Also, make sure that you use the balanced chemical equation to correctly apply the stoichiometric coefficients. Double-check your calculations to avoid any silly mistakes.

Calculating the Heat Released from 10 Grams of Propane

Now that we’ve calculated the enthalpy change for the combustion of propane per mole, let's find out how much heat is released when 10 grams of propane is burned. We need to convert the mass of propane (10 grams) into moles, and then use the enthalpy change we calculated to find the heat released.

First, we need the molar mass of propane (C₃H₈). We are given the atomic masses of carbon (C = 12 g/mol) and hydrogen (H = 1 g/mol). So, the molar mass of propane is:

Molar mass of C₃H₈ = (3 × 12 g/mol) + (8 × 1 g/mol) = 36 g/mol + 8 g/mol = 44 g/mol

Now, we convert 10 grams of propane to moles:

Moles of C₃H₈ = (mass of C₃H₈) / (molar mass of C₃H₈) = 10 g / 44 g/mol ≈ 0.227 mol

Finally, we can calculate the heat released (q) using the enthalpy change (ΔH) and the number of moles of propane:

q = ΔH × moles of C₃H₈

q = -2219.5 kJ/mol × 0.227 mol ≈ -504.1 kJ

Therefore, approximately 504.1 kJ of heat is released when 10 grams of propane undergoes complete combustion. The negative sign confirms that the reaction releases heat, and the answer is consistent with our expectation since the combustion reaction is exothermic. Remember that the amount of heat released is directly proportional to the amount of propane burned. The more propane you burn, the more heat is released.

Summary and Key Takeaways

Awesome work, everyone! We've successfully calculated the enthalpy change for the combustion of propane and determined the heat released by burning a specific amount of propane. Here’s a quick recap of the important steps:

1. Write the balanced chemical equation: This is the foundation of our calculations.
2. Use Hess's Law: Apply the formula ΔH = ΣnΔHᶠ(products) - ΣnΔHᶠ(reactants).
3. Convert grams to moles: Use the molar mass to convert the mass of the substance to moles.
4. Calculate the heat released: Multiply the enthalpy change by the number of moles.

Key takeaways from this exercise:

• Enthalpy change (ΔH) is crucial: It tells us whether a reaction releases or absorbs heat.
• Hess's Law is a powerful tool: It allows us to calculate enthalpy changes using standard enthalpies of formation.
• Stoichiometry matters: Always pay attention to the coefficients in the balanced chemical equation.

Understanding these concepts is vital in chemistry, and it forms the basis of many practical applications, from designing more efficient fuels to understanding environmental issues. Keep practicing these types of problems, and you'll become a pro in no time! Keep in mind that combustion reactions are essential in many applications. They provide energy for heating, transportation, and electricity generation. Understanding how to calculate the heat released from these reactions is therefore important in engineering, environmental science, and other related fields. Mastering the calculation of enthalpy change and the heat released in combustion reactions builds a solid foundation for further study in chemistry and related fields. Keep up the great work, and keep exploring the amazing world of chemistry!