Calculating the Number of Carbon Atoms

Oct 13, 2025 by recoveryshake.com 116 views

In chemistry, understanding the relationship between the mass of an element and the number of atoms it contains is crucial for various calculations and applications. One of the fundamental concepts in this regard is Avogadro's number, which represents the number of units (atoms or molecules) in one mole of a substance. In this article, we will explore how to calculate the number of carbon atoms in a given sample of carbon using Avogadro's number and the atomic mass of carbon.

What is Avogadro's Number?

Avogadro's number is a fundamental constant in chemistry that represents the number of units (atoms or molecules) in one mole of a substance. It is defined as 6.022 x 10^23 units per mole. This number was first proposed by Italian scientist Amedeo Avogadro in 1811 and has since been widely accepted as a standard unit of measurement in chemistry.

Calculating the Number of Carbon Atoms

To calculate the number of carbon atoms in a given sample of carbon, we need to know the mass of the sample and the atomic mass of carbon. The atomic mass of carbon is 12.01 g/mol, which is the mass of one mole of carbon atoms.

Let's consider a sample of 12.5 kg of carbon. To calculate the number of carbon atoms in this sample, we need to convert the mass from kilograms to grams and then use Avogadro's number to find the number of atoms.

Converting Mass from Kilograms to Grams

1 kilogram (kg) is equal to 1000 grams (g). Therefore, we can convert the mass of the carbon sample from kilograms to grams as follows:

12.5 kg x 1000 g/kg = 12,500 g

Calculating the Number of Moles of Carbon

Now that we have the mass of the carbon sample in grams, we can calculate the number of moles of carbon using the atomic mass of carbon (12.01 g/mol).

Number of moles = mass of sample / atomic mass of carbon = 12,500 g / 12.01 g/mol = 1.040 mol

Calculating the Number of Carbon Atoms

Now that we have the number of moles of carbon, we can use Avogadro's number to find the number of carbon atoms in the sample.

Number of atoms = number of moles x Avogadro's number = 1.040 mol x 6.022 x 10^23 atoms/mol = 6.27 x 10^26 atoms

Conclusion

In conclusion, we have calculated the number of carbon atoms in a 12.5 kg sample of carbon using Avogadro's number and the atomic mass of carbon. The result is 6.27 x 10^26 atoms, which is the correct answer.

Comparison with Other Options

Let's compare our result with the other options provided:

Option A: 6.27 x 10^20 atoms
Option B: 9.04 x 10^28 atoms
Option C: 6.27 x 10^26 atoms
Option D: 1.73 x 10^-21 atoms

Our result matches option C, which is 6.27 x 10^26 atoms.

Final Thoughts

In the previous article, we explored the concept of Avogadro's number and its application in calculating the number of atoms in a given sample of an element. In this article, we will answer some frequently asked questions (FAQs) about Avogadro's number and atomic mass.

Q: What is Avogadro's number?

A: Avogadro's number is a fundamental constant in chemistry that represents the number of units (atoms or molecules) in one mole of a substance. It is defined as 6.022 x 10^23 units per mole.

Q: Why is Avogadro's number important?

A: Avogadro's number is important because it allows us to calculate the number of atoms or molecules in a given sample of a substance. This is useful in a wide range of applications, including chemistry, physics, and engineering.

Q: How is Avogadro's number used in calculations?

A: Avogadro's number is used in calculations to find the number of atoms or molecules in a given sample of a substance. The formula is:

Number of atoms = number of moles x Avogadro's number

Q: What is the atomic mass of carbon?

A: The atomic mass of carbon is 12.01 g/mol, which is the mass of one mole of carbon atoms.

Q: How do I convert kilograms to grams?

A: To convert kilograms to grams, you can multiply the number of kilograms by 1000. For example:

1 kilogram (kg) = 1000 grams (g)

Q: How do I calculate the number of moles of a substance?

A: To calculate the number of moles of a substance, you can use the formula:

Number of moles = mass of sample / atomic mass of substance

Q: What is the difference between Avogadro's number and the number of atoms in a sample?

A: Avogadro's number is a fundamental constant that represents the number of units (atoms or molecules) in one mole of a substance. The number of atoms in a sample is a calculated value that is based on the mass of the sample and the atomic mass of the substance.

Q: Can I use Avogadro's number to calculate the number of atoms in a sample of any substance?

A: Yes, you can use Avogadro's number to calculate the number of atoms in a sample of any substance, as long as you know the mass of the sample and the atomic mass of the substance.

Q: What are some common applications of Avogadro's number?

A: Avogadro's number has a wide range of applications, including:

Calculating the number of atoms in a sample of a substance
Determining the concentration of a solution
Calculating the number of molecules in a sample of a substance
Understanding the properties of materials at the atomic level

Q: Can I use Avogadro's number to calculate the number of molecules in a sample of a substance?

A: Yes, you can use Avogadro's number to calculate the number of molecules in a sample of a substance, as long as you know the mass of the sample and the molecular mass of the substance.

Q: What is the relationship between Avogadro's number and the number of molecules in a sample?

A: Avogadro's number is equal to the number of molecules in one mole of a substance. Therefore, if you know the number of moles of a substance, you can use Avogadro's number to calculate the number of molecules in the sample.

Conclusion

In conclusion, Avogadro's number is a fundamental constant in chemistry that represents the number of units (atoms or molecules) in one mole of a substance. It has a wide range of applications, including calculating the number of atoms in a sample of a substance, determining the concentration of a solution, and understanding the properties of materials at the atomic level.