Analyzing Molecular Composition: Decoding C₂H₆ And Mole Calculations

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Analyzing Molecular Composition: Decoding C₂H₆ and Mole Calculations

Hey everyone, let's dive into a chemistry problem that's all about molecules, atoms, and calculations. We've got a scenario involving 0.2 moles of the compound C₂H₆ (ethane), and we need to figure out which statements about it are true. This kind of problem is super common in chemistry, so understanding it is key. We'll break down the statements one by one, using our knowledge of moles, Avogadro's number, and molecular formulas. Ready to get started, guys?

Decoding the Molecule: Atoms and Moles

Alright, let's start with the basics. The compound C₂H₆, which is ethane, is a simple organic molecule. It's made up of carbon (C) and hydrogen (H) atoms. The formula tells us that each molecule of ethane has two carbon atoms and six hydrogen atoms. Now, when we talk about moles, we're referring to a specific amount of a substance – think of it like a dozen, but for atoms and molecules. One mole of any substance contains Avogadro's number (NA) of particles (atoms, molecules, etc.).

Statement I: 0.2 Moles of C₂H₆ contains 0.8 mol of Atoms

Let's analyze the first statement, which says that 0.2 moles of C₂H₆ contains 0.8 moles of atoms. To check this, we need to calculate the total number of atoms in one mole of C₂H₆. Remember, one molecule of C₂H₆ has 2 carbon atoms + 6 hydrogen atoms = 8 atoms in total. Therefore, one mole of C₂H₆ contains 8 moles of atoms. Now, we have 0.2 moles of C₂H₆. Multiply the number of moles of C₂H₆ (0.2) by the number of atoms per mole of C₂H₆ (8): 0.2 mol C₂H₆ * 8 atoms/mol C₂H₆ = 1.6 moles of atoms. So, the first statement is incorrect because it claims there are only 0.8 moles of atoms. The correct value is 1.6 moles of atoms. This is where it's important to keep track of every step and not get lost in the numbers. This demonstrates how crucial it is to understand the relationship between moles, molecules, and atoms for solving such problems.

Now, let's move on to the second part of the statement. We have already determined that one molecule of C₂H₆ has a total of 8 atoms, 2 carbon atoms and 6 hydrogen atoms. One mole of C₂H₆ contains 2 moles of carbon atoms, and 6 moles of hydrogen atoms. So, if we have 0.2 moles of C₂H₆, we can calculate the moles of carbon atoms and hydrogen atoms separately. For the carbon atoms, we have 0.2 mol C₂H₆ * 2 mol C / mol C₂H₆ = 0.4 mol C. As for the hydrogen atoms, we have 0.2 mol C₂H₆ * 6 mol H / mol C₂H₆ = 1.2 mol H. If we add the moles of the carbon atoms and hydrogen atoms, we get a total number of atoms of 1.6 mol, which is consistent with the result in the above calculation. In summary, the first statement is not correct, as 0.2 moles of C₂H₆ actually contain 1.6 moles of atoms, instead of 0.8 moles.

Statement II: 0.2 Moles of C₂H₆ Contains 0.4 moles of Carbon Atoms

Next, let's look at the second statement, which says that 0.2 moles of C₂H₆ contains 0.4 moles of carbon atoms. We know that each molecule of C₂H₆ has two carbon atoms. Therefore, one mole of C₂H₆ will have two moles of carbon atoms. So, if we have 0.2 moles of C₂H₆, we can calculate the moles of carbon atoms by multiplying: 0.2 mol C₂H₆ * 2 mol C / mol C₂H₆ = 0.4 mol C. This statement is correct! It's crucial to understand that the subscript in the chemical formula (C₂H₆) tells us the ratio of atoms within the molecule. This helps us to convert between moles of the compound and moles of the individual elements within it. Therefore, this is the first correct statement we have come across.

Here’s a simple way to remember it: The number of carbon atoms in the formula (2 in C₂H₆) multiplied by the number of moles of the compound (0.2 moles) gives you the moles of carbon atoms (0.4 moles). This process is an application of stoichiometry, which allows us to find the quantitative relationships between the reactants and products in a chemical reaction. In this case, we have a single compound and are analyzing the quantities of the atoms. Understanding stoichiometry is one of the pillars of chemistry, and it's essential for solving numerous types of problems.

Statement III: 0.2 Moles of C₂H₆ is NA mol Molecules

Lastly, the third statement states that 0.2 moles of C₂H₆ is NA mol molecules. The term NA represents Avogadro's number, which is approximately 6.022 x 10²³ . As mentioned earlier, one mole of any substance contains Avogadro's number of particles. This means that 1 mole of molecules is equivalent to NA molecules. However, the statement suggests that 0.2 moles of C₂H₆ is equivalent to NA mol molecules, which is incorrect. A correct statement would be that 0.2 moles of C₂H₆ is equivalent to 0.2 * NA molecules. Therefore, the third statement is incorrect.

Therefore, understanding Avogadro's number is critical. You can't just slap an NA in there without considering the amount you're working with. Always remember that 1 mole = NA entities (atoms, molecules, etc.). So, if you have 0.2 moles, you'd have 0.2 * NA molecules. Simple, right?

Conclusion: Putting it All Together

So, after analyzing each statement, we found that:

  • Statement I is incorrect: 0.2 moles of C₂H₆ contains 1.6 moles of atoms, not 0.8 moles.
  • Statement II is correct: 0.2 moles of C₂H₆ contains 0.4 moles of carbon atoms.
  • Statement III is incorrect: 0.2 moles of C₂H₆ is not NA mol molecules; it's 0.2 * NA molecules.

Therefore, only statement II is correct, and the correct option is the one that includes only statement II. This kind of question helps you reinforce your ability to interpret chemical formulas, relate moles to atoms/molecules, and perform basic calculations. Keep practicing, and you'll get the hang of it! You see, with a little bit of practice, even complex-looking chemistry problems become manageable. Remember, the key is to break down the problem into smaller, more understandable parts. Happy studying, everyone!

I hope this helps! If you have any more questions, feel free to ask!