Calculating the Molar Mass of Aluminum Oxide

Oct 13, 2025 by magicalceylontours.com 109 views

In this problem, we are asked to find the mass in grams of $4.2 \times 10^{37}$ molecules of aluminum oxide ( $Al_2O_3$ ). To solve this problem, we need to understand the concept of molar mass and how to calculate it.

What is Molar Mass?

Molar mass is the mass of one mole of a substance. It is a measure of the mass of a substance that contains 6.022 x 10^23 particles (atoms or molecules). The molar mass of a substance can be calculated by adding up the atomic masses of its constituent atoms.

Calculating the Molar Mass of Aluminum Oxide

To calculate the molar mass of aluminum oxide, we need to know the atomic masses of aluminum (Al) and oxygen (O). The atomic mass of aluminum is 26.98 g/mol, and the atomic mass of oxygen is 16.00 g/mol.

The formula for aluminum oxide is $Al_2O_3$ , which means it contains 2 aluminum atoms and 3 oxygen atoms. Therefore, the molar mass of aluminum oxide can be calculated as follows:

Molar mass of $Al_2O_3$ = (2 x 26.98 g/mol) + (3 x 16.00 g/mol) = 53.96 g/mol + 48.00 g/mol = 101.96 g/mol

Calculating the Mass of $4.2 \times 10^{37}$ Molecules of Aluminum Oxide

Now that we have the molar mass of aluminum oxide, we can calculate the mass of $4.2 \times 10^{37}$ molecules of aluminum oxide. To do this, we need to use the formula:

Mass = Number of molecules x Molar mass

We know the number of molecules is $4.2 \times 10^{37}$ , and the molar mass of aluminum oxide is 101.96 g/mol. Therefore, we can calculate the mass as follows:

Mass = $4.2 \times 10^{37}$ molecules x 101.96 g/mol = $4.2 \times 10^{37}$ x 101.96 g/mol = $4.28 \times 10^{40}$ g

Conclusion

In this problem, we calculated the mass of $4.2 \times 10^{37}$ molecules of aluminum oxide. We first calculated the molar mass of aluminum oxide, which is 101.96 g/mol. Then, we used the formula Mass = Number of molecules x Molar mass to calculate the mass of $4.2 \times 10^{37}$ molecules of aluminum oxide. The result is $4.28 \times 10^{40}$ g.

Answer

$The answer is: **$4.28 \times 10^{40}$**<br/> **Frequently Asked Questions (FAQs) About Molar Mass and Molecular Mass**$

In this article, we will answer some frequently asked questions about molar mass and molecular mass.

Q: What is the difference between molar mass and molecular mass?

A: Molar mass is the mass of one mole of a substance, while molecular mass is the mass of a single molecule of a substance. Molar mass is typically expressed in units of grams per mole (g/mol), while molecular mass is typically expressed in units of atomic mass units (amu).

Q: How do I calculate the molar mass of a compound?

A: To calculate the molar mass of a compound, you need to add up the atomic masses of its constituent atoms. You can find the atomic masses of elements in the periodic table. For example, the molar mass of water (H2O) is calculated as follows:

Molar mass of H2O = (2 x 1.01 g/mol) + (1 x 16.00 g/mol) = 2.02 g/mol + 16.00 g/mol = 18.02 g/mol

Q: What is the relationship between molar mass and molecular mass?

A: The relationship between molar mass and molecular mass is that the molar mass of a substance is equal to the molecular mass of its molecules multiplied by Avogadro's number (6.022 x 10^23). This means that the molar mass of a substance is a multiple of its molecular mass.

Q: How do I calculate the molecular mass of a compound?

A: To calculate the molecular mass of a compound, you need to add up the atomic masses of its constituent atoms. You can find the atomic masses of elements in the periodic table. For example, the molecular mass of water (H2O) is calculated as follows:

Molecular mass of H2O = (2 x 1.01 amu) + (1 x 16.00 amu) = 2.02 amu + 16.00 amu = 18.02 amu

Q: What is the significance of molar mass in chemistry?

A: Molar mass is a fundamental concept in chemistry that has many practical applications. It is used to calculate the mass of a substance, to determine the number of moles of a substance, and to calculate the concentration of a solution. Molar mass is also used to calculate the molecular mass of a substance, which is essential in understanding the properties and behavior of molecules.

Q: How do I convert between molar mass and molecular mass?

A: To convert between molar mass and molecular mass, you can use the following formula:

Molar mass = Molecular mass x Avogadro's number = Molecular mass x 6.022 x 10^23

For example, if the molecular mass of a substance is 18.02 amu, its molar mass would be:

Molar mass = 18.02 amu x 6.022 x 10^23 = 108.4 g/mol

Q: What are some common mistakes to avoid when calculating molar mass?

A: Some common mistakes to avoid when calculating molar mass include:

Forgetting to include the atomic masses of all the atoms in the compound
Using the wrong atomic masses for the elements
Not converting the atomic masses to the same units (e.g., g/mol or amu)
Not using the correct formula for calculating molar mass

By avoiding these common mistakes, you can ensure that your calculations are accurate and reliable.

Conclusion

In this article, we have answered some frequently asked questions about molar mass and molecular mass. We have discussed the difference between molar mass and molecular mass, how to calculate the molar mass of a compound, and how to convert between molar mass and molecular mass. We have also highlighted some common mistakes to avoid when calculating molar mass. By understanding these concepts and avoiding common mistakes, you can become proficient in calculating molar mass and molecular mass.