Calculating Moles of Aluminum Oxide

Oct 13, 2025 by sorusgentrification.com 59 views

Understanding the Problem

Calculating the number of moles of a substance is a fundamental concept in chemistry. In this article, we will focus on calculating the number of moles of aluminum oxide ( $Al_2O_3$ ) present in a given mass of the substance. We will use the relative formula mass (M_r) of aluminum oxide, which is 102 g/mol.

What is Relative Formula Mass (M_r)?

The relative formula mass (M_r) of a compound is the sum of the atomic masses of its constituent elements, expressed in grams per mole (g/mol). In the case of aluminum oxide ( $Al_2O_3$ ), the M_r is calculated as follows:

Atomic mass of aluminum (Al) = 27 g/mol
Atomic mass of oxygen (O) = 16 g/mol
Since there are two aluminum atoms and three oxygen atoms in the formula unit of aluminum oxide, the M_r is calculated as: M_r = (2 x 27) + (3 x 16) = 54 + 48 = 102 g/mol

Calculating Moles of Aluminum Oxide

To calculate the number of moles of aluminum oxide present in a given mass, we can use the following formula:

moles = mass / M_r

In this case, we are given a mass of 25.5 g of aluminum oxide. We can plug this value into the formula along with the M_r of aluminum oxide (102 g/mol) to calculate the number of moles.

Step-by-Step Calculation

Identify the given values: mass of aluminum oxide = 25.5 g, M_r of aluminum oxide = 102 g/mol
Plug in the values into the formula: moles = 25.5 g / 102 g/mol
Perform the calculation: moles = 0.25 mol

Conclusion

In this article, we calculated the number of moles of aluminum oxide present in 25.5 g of aluminum oxide using the relative formula mass (M_r) of the substance. We used the formula moles = mass / M_r to perform the calculation, which resulted in a value of 0.25 mol.

Real-World Applications

Calculating the number of moles of a substance is a crucial concept in chemistry, with numerous real-world applications. For example, in the production of aluminum, the number of moles of aluminum oxide is used to determine the amount of aluminum that can be extracted from the oxide. Similarly, in the production of cement, the number of moles of aluminum oxide is used to determine the amount of cement that can be produced.

Common Mistakes to Avoid

When calculating the number of moles of a substance, it is essential to avoid common mistakes such as:

Using the atomic mass of an element instead of the relative formula mass (M_r) of the compound
Failing to account for the number of atoms of each element in the formula unit of the compound
Not using the correct units for the mass and M_r values

Conclusion

Q: What is the relative formula mass (M_r) of aluminum oxide ( $Al_2O_3$ )?

A: The relative formula mass (M_r) of aluminum oxide ( $Al_2O_3$ ) is 102 g/mol. This is calculated by summing the atomic masses of the constituent elements: 2 x 27 (aluminum) + 3 x 16 (oxygen) = 54 + 48 = 102 g/mol.

Q: How do I calculate the number of moles of aluminum oxide present in a given mass?

A: To calculate the number of moles of aluminum oxide present in a given mass, you can use the following formula:

moles = mass / M_r

Where mass is the given mass of aluminum oxide and M_r is the relative formula mass of aluminum oxide (102 g/mol).

Q: What is the difference between atomic mass and relative formula mass?

A: Atomic mass refers to the mass of a single atom of an element, while relative formula mass (M_r) refers to the sum of the atomic masses of the constituent elements in a compound. In the case of aluminum oxide ( $Al_2O_3$ ), the atomic mass of aluminum is 27 g/mol and the atomic mass of oxygen is 16 g/mol. However, the relative formula mass of aluminum oxide is 102 g/mol, which is the sum of the atomic masses of the constituent elements.

Q: How do I ensure that I am using the correct units for the mass and M_r values?

A: To ensure that you are using the correct units for the mass and M_r values, make sure to use the following units:

Mass: grams (g)
M_r: grams per mole (g/mol)

Q: What are some common mistakes to avoid when calculating the number of moles of aluminum oxide?

A: Some common mistakes to avoid when calculating the number of moles of aluminum oxide include:

Using the atomic mass of an element instead of the relative formula mass (M_r) of the compound
Failing to account for the number of atoms of each element in the formula unit of the compound
Not using the correct units for the mass and M_r values

Q: How do I apply the concept of calculating moles of aluminum oxide to real-world scenarios?

A: The concept of calculating moles of aluminum oxide can be applied to various real-world scenarios, such as:

Determining the amount of aluminum that can be extracted from aluminum oxide in the production of aluminum
Determining the amount of cement that can be produced from aluminum oxide in the production of cement

Q: Can I use the same formula to calculate the number of moles of other substances?

A: Yes, the formula moles = mass / M_r can be used to calculate the number of moles of other substances, as long as you have the relative formula mass (M_r) of the substance and the given mass.

Conclusion

Calculating the number of moles of aluminum oxide is a crucial concept in chemistry, with numerous real-world applications. By understanding the relative formula mass (M_r) of aluminum oxide and using the correct formula, you can accurately calculate the number of moles of aluminum oxide present in a given mass.