Calculating Heat Released In Methane Combustion

Hey there, chemistry enthusiasts! Let's dive into a classic thermochemistry problem: figuring out the heat released when methane ($CH_4$) undergoes combustion. Combustion reactions are super important – they're how we generate energy in many applications, from powering our homes to running our vehicles. In this case, we're going to use the given enthalpy change, the balanced chemical equation, and a bit of stoichiometry to nail down the answer. So, grab your lab coats (metaphorically, of course!) and let's get started!

Understanding the Basics: Combustion and Enthalpy

First things first, let's break down the fundamentals. Combustion is a chemical process that involves the rapid reaction between a substance with an oxidant, usually oxygen, to produce heat and light. Methane, the primary component of natural gas, is an excellent fuel because it reacts vigorously with oxygen. The balanced chemical equation for the combustion of methane is: $CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g)$. This equation tells us exactly what's happening at the molecular level: one molecule of methane reacts with two molecules of oxygen to produce one molecule of carbon dioxide and two molecules of water (in the gaseous state). The $\Delta H^{\circ}$ value gives us the enthalpy change of the reaction, which is the amount of heat absorbed or released during the reaction at constant pressure. A negative $\Delta H^{\circ}$ value (like the -802 kJ/mol in our problem) means the reaction is exothermic – it releases heat into the surroundings. This is what we want to find, the amount of heat released when a specific amount of methane is burned.

Now, let's look at the given information, $\Delta H^{\circ} = -802 kJ/mol$. This means that when one mole of methane burns, 802 kJ of heat is released. This value is crucial because it acts as our conversion factor between moles of methane and the heat released. The negative sign is a reminder that the heat is released (exothermic process). Keep this value in mind, since we will use this to find the amount of heat released when 4.19 moles of $CH_4$ are burned. This problem utilizes Hess's law, which states that the total enthalpy change for a reaction is independent of the pathway taken. This allows us to calculate the enthalpy change for a reaction using the standard enthalpy of formation for the reactants and products. This is a very useful law in chemistry that helps us calculate heat released or absorbed during a chemical reaction.

Step-by-Step Calculation: Finding the Heat Released

Alright, let's get down to the nitty-gritty and calculate the heat released when 4.19 moles of methane are burned. We know that for every 1 mole of $CH_4$ burned, 802 kJ of heat is released. So, we'll use this as a conversion factor. We start with the given number of moles of methane and then multiply by the enthalpy change to find the heat released. Here’s how we do it step-by-step:

1. Start with the given quantity: We are given 4.19 moles of $CH_4$.
2. Use the enthalpy change as a conversion factor: We know that for every 1 mole of $CH_4$, 802 kJ of heat is released. This can be written as -802 kJ/1 mol $CH_4$.
3. Set up the calculation: To calculate the total heat released, we multiply the number of moles of $CH_4$ by the enthalpy change: Heat Released = (moles of $CH_4$) x ($\Delta H^{\circ}$)
4. Perform the calculation: Heat Released = (4.19 mol $CH_4$) x (-802 kJ/1 mol $CH_4$) = -3360.38 kJ

Notice that the