More Atoms: SO₂ Vs. NH₃ Calculation!
Hey guys! Ever wondered how to figure out which sample has more atoms when you're dealing with different compounds? This is a classic chemistry problem, and we're going to break it down step by step. We'll look at two test tubes: one with sulfur dioxide (SO₂) and another with ammonia (NH₃). The question is simple: which one has more atoms? But the answer isn't as straightforward as just looking at the mass. We need to dive into some calculations. Let's get started!
Understanding the Problem: Mass vs. Number of Atoms
So, you've got two test tubes. Test tube A contains 2 grams of sulfur dioxide (SO₂), and test tube B contains 2 grams of ammonia (NH₃). At first glance, you might think they have the same number of atoms since they have the same mass. But hold on! That's where molar mass and Avogadro's number come into play. Remember, atoms have different masses, and molecules are made up of different combinations of atoms. So, 2 grams of one substance can contain a very different number of atoms compared to 2 grams of another. To really understand this, we need to convert grams into moles, and then moles into the number of atoms. This involves a bit of stoichiometry, which is basically the math of chemical reactions. Think of it like this: you can't compare apples and oranges directly. You need a common unit, like “pieces of fruit,” to make a fair comparison. In chemistry, the “mole” is that common unit for counting atoms and molecules. And Avogadro's number is the magic key that unlocks the door between moles and actual numbers of particles. So, let's grab our calculators and dive into the math. We'll figure out exactly how many atoms are chilling in each test tube, and then we'll know for sure which one wins the atom-counting contest!
Step 1: Calculate the Molar Mass of Each Compound
First things first, we need to calculate the molar mass of both sulfur dioxide (SO₂) and ammonia (NH₃). Molar mass is the mass of one mole of a substance, and it's expressed in grams per mole (g/mol). You can find the atomic masses of each element on the periodic table. For sulfur (S), it's approximately 32.06 g/mol, for oxygen (O) it's about 16.00 g/mol, and for nitrogen (N) it's around 14.01 g/mol, and for hydrogen (H) it's about 1.01 g/mol. Let’s break it down:
Sulfur Dioxide (SO₂)
SO₂ has one sulfur atom and two oxygen atoms. So, to calculate its molar mass, we add up the atomic masses:
- Molar mass of SO₂ = (1 × atomic mass of S) + (2 × atomic mass of O)
- Molar mass of SO₂ = (1 × 32.06 g/mol) + (2 × 16.00 g/mol)
- Molar mass of SO₂ = 32.06 g/mol + 32.00 g/mol
- Molar mass of SO₂ = 64.06 g/mol
Ammonia (NH₃)
NH₃ has one nitrogen atom and three hydrogen atoms. The calculation is similar:
- Molar mass of NH₃ = (1 × atomic mass of N) + (3 × atomic mass of H)
- Molar mass of NH₃ = (1 × 14.01 g/mol) + (3 × 1.01 g/mol)
- Molar mass of NH₃ = 14.01 g/mol + 3.03 g/mol
- Molar mass of NH₃ = 17.04 g/mol
Now we know that one mole of SO₂ weighs 64.06 grams, and one mole of NH₃ weighs 17.04 grams. This difference in molar mass is a crucial piece of the puzzle. It means that for the same mass (2 grams in our case), we'll have a different number of moles of each compound. And that difference in the number of moles will directly affect the number of atoms. Next, we'll use these molar masses to figure out exactly how many moles of each compound we have in our test tubes.
Step 2: Convert Grams to Moles
Okay, now that we know the molar masses of SO₂ and NH₃, we can convert the given mass (2 grams) of each compound into moles. This is a super important step because moles are the key to counting atoms! The formula we'll use is:
- Moles = Mass / Molar mass
Let's apply this to both compounds:
Sulfur Dioxide (SO₂)
- Moles of SO₂ = 2 grams / 64.06 g/mol
- Moles of SO₂ ≈ 0.0312 moles
Ammonia (NH₃)
- Moles of NH₃ = 2 grams / 17.04 g/mol
- Moles of NH₃ ≈ 0.1174 moles
See the difference? Even though we started with the same mass (2 grams), we have significantly more moles of NH₃ than SO₂. This is because NH₃ has a much smaller molar mass. Think of it like this: if you have a bag that can hold a certain weight, you can fit more ping pong balls (lightweight) than bowling balls (heavyweight) in that bag. Moles are like counting the number of “balls” (molecules) we have. Now that we know the number of moles, we're one step closer to finding the number of atoms. But we're not quite there yet. We need to remember that each molecule contains multiple atoms. So, the next step is to consider the number of atoms per molecule.
Step 3: Determine Atoms per Molecule
Before we can calculate the total number of atoms, we need to figure out how many atoms are in each molecule of SO₂ and NH₃. This is pretty straightforward—we just need to look at the chemical formulas. For sulfur dioxide (SO₂), there's one sulfur (S) atom and two oxygen (O) atoms, making a total of 3 atoms per molecule. For ammonia (NH₃), there's one nitrogen (N) atom and three hydrogen (H) atoms, adding up to 4 atoms per molecule. Let's summarize:
- SO₂: 3 atoms per molecule (1 S + 2 O)
- NH₃: 4 atoms per molecule (1 N + 3 H)
This is a crucial piece of information! It tells us that even if we had the same number of molecules of SO₂ and NH₃, the NH₃ would still have more atoms simply because each molecule is “richer” in atoms. But we don't have the same number of molecules; we have a different number of moles (which we calculated in the previous step). So, we need to combine this information with the number of moles to get the total number of atoms. This brings us to our final step: using Avogadro's number to bridge the gap between moles and actual atom counts.
Step 4: Calculate the Total Number of Atoms Using Avogadro's Number
Alright, we're in the home stretch! We've got the moles of each compound and the number of atoms per molecule. Now, we need to use Avogadro's number to find the total number of atoms. Avogadro's number (approximately 6.022 × 10²³) is a fundamental constant in chemistry. It tells us how many entities (atoms, molecules, ions, etc.) are in one mole of a substance. Think of it as a chemical “dozen,” but on a much grander scale. So, to calculate the total number of molecules, we multiply the number of moles by Avogadro's number. And then, we multiply that result by the number of atoms per molecule (which we figured out in the last step). The formula looks like this:
- Total atoms = Moles × Avogadro's number × Atoms per molecule
Let's apply this formula to both SO₂ and NH₃:
Sulfur Dioxide (SO₂)
- Total atoms in SO₂ = 0.0312 moles × 6.022 × 10²³ atoms/mole × 3 atoms/molecule
- Total atoms in SO₂ ≈ 5.63 × 10²² atoms
Ammonia (NH₃)
- Total atoms in NH₃ = 0.1174 moles × 6.022 × 10²³ atoms/mole × 4 atoms/molecule
- Total atoms in NH₃ ≈ 2.83 × 10²³ atoms
Look at those numbers! We've got our answer. Let’s break down what they mean.
Conclusion: Which Test Tube Wins the Atom Count?
After all those calculations, it's clear: test tube B, containing ammonia (NH₃), has significantly more atoms than test tube A, containing sulfur dioxide (SO₂). We calculated that 2 grams of SO₂ contains approximately 5.63 × 10²² atoms, while 2 grams of NH₃ contains roughly 2.83 × 10²³ atoms. That's a huge difference! So, even though the masses were the same, the number of atoms was not. This highlights the importance of considering molar mass and the composition of molecules when comparing quantities of substances at the atomic level. Remember, guys, chemistry isn't just about memorizing formulas; it's about understanding the relationships between different concepts. In this case, we saw how mass, moles, molar mass, Avogadro's number, and the number of atoms per molecule all come together to give us the answer. Next time you're faced with a similar problem, remember these steps, and you'll be able to tackle it like a pro! And if you ever need a refresher, just come back to this guide. Happy calculating!