Calculating Carbon Atoms In An Organic Compound: A Step-by-Step Guide

Hey guys! Let's dive into a chemistry problem that's super common: figuring out the number of carbon atoms in an organic compound. This is the kind of stuff you might encounter in your chemistry class or even in some real-world applications. We'll break down the problem step-by-step, making it easy to understand, even if you're not a chemistry whiz. The scenario: we've got an organic compound where carbon makes up 80% of the mass. We also know Avogadro's number (6 x 10^23), and we need to find out how many carbon atoms are in 18 grams of this compound. Ready? Let's get started!

Understanding the Problem: Carbon Composition and Molecular Calculations

Alright, so the core of the problem lies in understanding the percentage composition of the carbon within the organic compound. What does that mean, exactly? It means that out of the total mass of the compound, 80% of it is made up of carbon atoms. The rest, we assume, is made up of other elements like hydrogen, oxygen, or nitrogen. We're given that we have 18 grams of this compound, and our goal is to figure out how many individual carbon atoms are present within that mass. We'll need to use some fundamental chemistry principles to get to the answer.

First things first, it's essential to realize that we're dealing with molecules. Organic compounds are made up of molecules, and these molecules are, in turn, composed of atoms – in this case, carbon atoms and atoms of other elements. To find the number of carbon atoms, we'll need to convert the mass of the compound into the mass of carbon, then convert that mass into moles, and finally, convert the moles into the number of atoms. It sounds like a lot, but trust me, it's not as complex as it might seem. We'll be using the concept of molar mass, which is the mass of one mole of a substance. And of course, we'll be using Avogadro's number, which tells us the number of entities (atoms, molecules, etc.) in one mole of a substance. So, essentially, we're going to break down the compound into its carbon components and then use the given information to find the number of atoms.

To make it even clearer, let's put it into a visual format that summarizes the process: We start with the total mass of the compound and its carbon percentage -> calculate the mass of carbon -> convert the mass of carbon into moles using the molar mass of carbon -> calculate the number of carbon atoms using Avogadro's number. This step-by-step approach will ensure we understand each step of the calculation and that we don't miss any critical details. Let's move onto the calculations!

Step-by-Step Calculation: Finding the Number of Carbon Atoms

Okay, buckle up, because here comes the fun part: the actual calculations! We'll start with the information we know and systematically move towards our goal. Remember, the goal is to determine the number of carbon atoms present in 18 grams of the organic compound. This section breaks down each step in detail to help you understand every aspect of the process.

Step 1: Calculate the mass of carbon in the compound.

We know that the compound is 80% carbon. So, to find the mass of carbon in 18 grams of the compound, we need to multiply the total mass by the percentage of carbon. The calculation is as follows:

Mass of carbon = 18 grams × 80% = 18 grams × 0.80 = 14.4 grams

This means that in 18 grams of the organic compound, there are 14.4 grams of carbon.

Step 2: Convert the mass of carbon to moles.

To convert grams of carbon to moles, we need to use the molar mass of carbon, which is approximately 12 grams/mole (g/mol). We can find this value on the periodic table. The formula is:

Moles of carbon = Mass of carbon / Molar mass of carbon

Moles of carbon = 14.4 g / 12 g/mol = 1.2 moles

Therefore, 14.4 grams of carbon is equal to 1.2 moles.

Step 3: Calculate the number of carbon atoms.

We now have the number of moles of carbon. We can convert moles to the number of atoms using Avogadro's number (6 x 10^23 atoms/mol). The formula is:

Number of carbon atoms = Moles of carbon × Avogadro's number

Number of carbon atoms = 1.2 moles × 6 × 10^23 atoms/mol = 7.2 × 10^23 atoms

Thus, the number of carbon atoms in 18 grams of the organic compound is 7.2 × 10^23. However, this is not an option in your question. Let's analyze the question once more! We can observe that we have made a small mistake: the question states the options in a form that is not entirely correct! So, let's adjust it a little bit. We will continue calculating it and adjust to the correct solution.

Analyzing and Adjusting the Final Answer

Now, let's step back and carefully review what we've done and make sure everything aligns with the available answer options. This is a crucial step to avoid simple mistakes and ensure we select the right answer. We will examine the results we achieved in the previous section.

Looking back at our calculations, we found that:

• The mass of carbon is 14.4 grams.
• The number of moles of carbon is 1.2 moles.
• The number of carbon atoms is 7.2 × 10^23 atoms.

However, it's evident that 7.2 × 10^23 is not one of the choices provided. Therefore, let's reconsider the calculations. Our initial steps seem correct, but let’s review to make sure we didn’t miss anything. We can re-check the calculation using a different approach to ensure it’s accurate. Another way to do this is as follows: We know the compound is 80% carbon and we have 18 grams. This tells us 14.4 grams is the carbon content. The molar mass of carbon is approximately 12 g/mol. This is constant, so we can convert the mass of carbon to moles by dividing its mass by the molar mass: 14.4 g / 12 g/mol = 1.2 moles. We have the moles of carbon, now we multiply that number of moles by Avogadro's number (6 × 10^23) to find the number of atoms. Therefore, 1.2 * (6 × 10^23) = 7.2 × 10^23 atoms. Hmm… We have confirmed our calculation. This means, the options are incorrect. Nevertheless, the main goal is to fully understand the question. Therefore, if we assume there is a small typo, and the question is: "If Avogadro's constant = 6 × 10^23, the number of carbon atoms in 14.4 grams of carbon" is the question, then:

Number of carbon atoms = (14.4 g / 12 g/mol) * (6 × 10^23) = 1.2 * (6 × 10^23) = 7.2 × 10^23.

None of the options provided is correct. However, let us review the given options. The closest one is a. $3,6 \times 10^{23}$.

In conclusion, we have carefully worked through the calculations, reviewed them, and made sure we understood every detail. While the answer wasn’t in the given choices, the process of finding out the solution has been very comprehensive. Remember that precision and understanding are vital in chemistry, and always double-check your calculations, especially when dealing with complex problems. This should give you a good grasp of the whole process!