Moles Of CO2: Calculation With 1.0836 X 10^24 Atoms

Hey guys! Let's dive into a fun chemistry problem today. We're going to figure out how many moles of carbon dioxide (CO2) we have when there are $1.0836 imes 10^{24}$ atoms involved. It sounds a bit complicated, but trust me, we'll break it down step by step so it's super easy to understand. So, buckle up and let's get started!

Understanding Moles and Avogadro's Number

First things first, let's talk about moles. In chemistry, a mole is a unit that represents a specific number of particles, like atoms or molecules. Think of it like a 'dozen' but on a much, much larger scale. Instead of 12, a mole represents $6.022 imes 10^{23}$ particles. This magical number is called Avogadro's number, and it's super important for converting between the number of particles and moles.

Avogadro's number ($6.022 imes 10^{23}$) is your best friend in these kinds of calculations. It tells us how many atoms, molecules, ions, or other particles are in one mole of a substance. So, if we know how many atoms we have, we can use Avogadro's number to find out how many moles that represents. It's like having a secret key to unlock the mystery of moles!

Why is this important? Well, in chemistry, we often deal with incredibly tiny particles like atoms and molecules. It's much easier to talk about moles instead of dealing with huge numbers of individual particles. It's like saying you have a dozen eggs instead of saying you have 12 eggs – it’s just more convenient. This concept is fundamental in stoichiometry, which is basically the math of chemical reactions. Understanding moles allows chemists to accurately measure and predict the amounts of reactants and products in chemical reactions. This is crucial for everything from designing new drugs to manufacturing materials.

Breaking Down the CO2 Molecule

Now, let's think about carbon dioxide (CO2). Each molecule of CO2 is made up of one carbon atom (C) and two oxygen atoms (O). This is a crucial piece of information because it tells us the atomic composition of the molecule, which we'll need for our calculation. Essentially, every CO2 molecule is a tiny team of one carbon and two oxygens working together. This team structure is important because it means we need to consider the total number of atoms, not just the number of molecules directly. When we talk about $1.0836 imes 10^{24}$ atoms, we are talking about the sum of all the carbon and oxygen atoms present in our sample of CO2.

The fact that CO2 is a triatomic molecule (meaning it has three atoms) is vital. For every one molecule of CO2, there are three atoms in total (one carbon and two oxygen). This 1:3 molecule-to-atom ratio is the key to unlocking our problem. If we know the total number of atoms, we can work backward to find out how many CO2 molecules we have. It's like knowing how many triplets there are at a party by counting all the people and dividing by three – we're using the ratio to convert between different units.

This understanding of molecular composition is not just specific to CO2. It applies to any chemical compound. Whether it’s water (H2O), which has three atoms per molecule, or methane (CH4), which has five, knowing the atomic makeup helps us convert between moles, molecules, and atoms. It’s a fundamental aspect of chemistry that allows us to quantify and understand the world at a molecular level. So, let's keep this idea in our toolkit as we move forward with the problem.

Steps to Calculate Moles of CO2

Okay, let's get down to business and calculate the moles of CO2. We have $1.0836 imes 10^{24}$ atoms, and we need to find out how many moles of CO2 that corresponds to. We'll use a step-by-step approach to make it crystal clear.

Step 1: Find the Number of CO2 Molecules

Since each CO2 molecule has three atoms (one carbon and two oxygen), we need to figure out how many CO2 molecules are in our sample. To do this, we'll divide the total number of atoms by 3. This step is crucial because we are transitioning from individual atoms to whole molecules, which is a key part of solving the puzzle.

So, the number of CO2 molecules = Total number of atoms / 3

Number of CO2 molecules = $(1.0836 imes 10^{24}) / 3$

Number of CO2 molecules = $3.612 imes 10^{23}$ molecules

This calculation gives us the number of individual CO2 molecules present. Remember, we started with the total count of atoms, but now we've converted that into the number of molecules, which brings us closer to our goal of finding moles. It's like converting inches to feet – we're just changing the unit of measurement while still describing the same quantity.

Step 2: Convert Molecules to Moles

Now that we know the number of CO2 molecules, we can convert this to moles using Avogadro's number. Remember, one mole contains $6.022 imes 10^{23}$ molecules. This is where Avogadro's number comes into play, acting as our conversion factor between the microscopic world of molecules and the macroscopic world of moles.

Moles of CO2 = Number of CO2 molecules / Avogadro's number

Moles of CO2 = $(3.612 imes 10^{23}) / (6.022 imes 10^{23})$

Moles of CO2 ≈ 0.6 moles

And there we have it! We've successfully converted the number of molecules into moles. This step is the heart of the problem, where we use a fundamental constant (Avogadro's number) to bridge the gap between counting individual particles and measuring amounts in moles. It’s a powerful conversion that allows us to work with manageable numbers in chemical calculations.

Final Answer and Discussion

So, if there are $1.0836 imes 10^{24}$ atoms, then we have approximately 0.6 moles of CO2. That means the correct answer is D) 0.6. Congrats, guys, if you followed along and got the same answer!

Let's recap the main steps we took to solve this:

1. We used the fact that each CO2 molecule has three atoms to find the number of CO2 molecules.
2. We then used Avogadro's number to convert the number of molecules into moles.

This problem highlights a key concept in chemistry: the mole. Understanding moles is essential for all sorts of chemical calculations. It’s not just about plugging numbers into a formula; it’s about understanding the relationship between the number of particles and the amount of substance. This allows chemists to accurately measure, predict, and control chemical reactions, which has huge implications in fields like medicine, materials science, and environmental science.

The beauty of chemistry lies in these kinds of conversions. We can move from the scale of individual atoms and molecules to macroscopic quantities that we can measure in the lab. This is what makes chemistry so powerful – it connects the invisible world of particles to the tangible world we experience every day. So, keep practicing these conversions, and you'll become a mole master in no time!

Practice Problems

To really nail this concept, let's try a couple of practice problems. These will help you solidify your understanding of how to convert between atoms, molecules, and moles.

Problem 1: How many moles are there in $3.011 imes 10^{23}$ molecules of water (H2O)?

Hint: You don't need the number of atoms per molecule this time, just Avogadro's number!

Problem 2: If you have 2 moles of methane (CH4), how many hydrogen atoms do you have?

Hint: Remember that each CH4 molecule has 4 hydrogen atoms.

Working through these problems will help you build confidence and see how these concepts apply in different situations. Chemistry is like a puzzle, and each problem you solve is another piece falling into place. So, give these a try, and let’s keep learning together!

Solving these kinds of problems might seem tricky at first, but with a bit of practice, you'll become a pro at converting between atoms, molecules, and moles. Keep up the great work, and remember that every challenge is just a step towards becoming a chemistry whiz! Cheers, guys, and happy calculating!