Calculating the Number of Atoms in a Given Mass

Oct 13, 2025 by miodeya.com 59 views

Introduction

Magnesium (Mg) is a chemical element with a molar mass of $24.30 \, \text{g/mol}$ . The Avogadro's number, which is $6.02 \times 10^{23}$ atoms per mole, is a fundamental constant in chemistry that relates the amount of a substance in moles to the number of atoms or molecules present. In this article, we will explore how to calculate the number of atoms present in a given mass of magnesium.

Understanding Molar Mass and Avogadro's Number

The molar mass of an element is the mass of one mole of that element, expressed in grams per mole (g/mol). For magnesium, the molar mass is $24.30 \, \text{g/mol}$ . This means that one mole of magnesium weighs $24.30 \, \text{g}$ . Avogadro's number, on the other hand, is a constant that relates the amount of a substance in moles to the number of atoms or molecules present. It is defined as $6.02 \times 10^{23}$ atoms per mole.

Calculating the Number of Atoms in a Given Mass

To calculate the number of atoms present in a given mass of magnesium, we need to follow these steps:

Determine the number of moles: First, we need to determine the number of moles of magnesium present in the given mass. We can do this by dividing the given mass by the molar mass of magnesium.
Calculate the number of atoms: Once we have the number of moles, we can calculate the number of atoms present by multiplying the number of moles by Avogadro's number.

Step-by-Step Calculation

Let's calculate the number of atoms present in 48.60 g of magnesium.

Step 1: Determine the number of moles

To determine the number of moles, we divide the given mass by the molar mass of magnesium:

\text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}}

\text{Number of moles} = \frac{48.60 \, \text{g}}{24.30 \, \text{g/mol}}

\text{Number of moles} = 2.00 \, \text{mol}

Step 2: Calculate the number of atoms

Now that we have the number of moles, we can calculate the number of atoms present by multiplying the number of moles by Avogadro's number:

\text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number}

\text{Number of atoms} = 2.00 \, \text{mol} \times 6.02 \times 10^{23} \, \text{atoms/mol}

\text{Number of atoms} = 1.20 \times 10^{24} \, \text{atoms}

Conclusion

In this article, we have explored how to calculate the number of atoms present in a given mass of magnesium. By following the steps outlined above, we can determine the number of moles and then calculate the number of atoms present. This is a fundamental concept in chemistry that has numerous applications in various fields.

Answer

The correct answer is B. $1.20 \times 10^{24}$ atoms.

Discussion

This problem requires a basic understanding of molar mass and Avogadro's number. The student should be able to apply these concepts to calculate the number of atoms present in a given mass of magnesium. This problem is relevant to chemistry and has numerous applications in various fields.

Additional Resources

For further reading and practice, the following resources are recommended:

Practice Problems

Calculate the number of atoms present in 25.00 g of magnesium.
Determine the number of moles of magnesium present in 50.00 g of magnesium.
Calculate the number of atoms present in 10.00 g of magnesium.

Answer Key

$1.00 \times 10^{24}$ atoms
2.07 mol
$6.02 \times 10^{22}$ atoms
The Molar Mass of Magnesium: Understanding Atomic Count in a Given Mass ====================================================================================

Q&A: Frequently Asked Questions

Q: What is the molar mass of magnesium?

A: The molar mass of magnesium is $24.30 \, \text{g/mol}$ .

Q: What is Avogadro's number?

A: Avogadro's number is a constant that relates the amount of a substance in moles to the number of atoms or molecules present. It is defined as $6.02 \times 10^{23}$ atoms per mole.

Q: How do I calculate the number of atoms present in a given mass of magnesium?

A: To calculate the number of atoms present in a given mass of magnesium, follow these steps:

Determine the number of moles: Divide the given mass by the molar mass of magnesium.
Calculate the number of atoms: Multiply the number of moles by Avogadro's number.

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

A: Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). Atomic mass, on the other hand, is the mass of a single atom of an element, expressed in atomic mass units (amu).

Q: Can I use the atomic mass of magnesium to calculate the number of atoms present in a given mass?

A: No, you cannot use the atomic mass of magnesium to calculate the number of atoms present in a given mass. The atomic mass is the mass of a single atom, while the molar mass is the mass of one mole of atoms.

Q: How do I determine the number of moles of magnesium present in a given mass?

A: To determine the number of moles of magnesium present in a given mass, divide the given mass by the molar mass of magnesium.

Q: Can I use a calculator to calculate the number of atoms present in a given mass of magnesium?

A: Yes, you can use a calculator to calculate the number of atoms present in a given mass of magnesium. Simply enter the given mass, the molar mass of magnesium, and Avogadro's number into the calculator, and it will give you the number of atoms.

Q: What is the significance of Avogadro's number?

A: Avogadro's number is a fundamental constant in chemistry that relates the amount of a substance in moles to the number of atoms or molecules present. It is used to calculate the number of atoms or molecules present in a given mass of a substance.

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

A: Yes, you can use Avogadro's number to calculate the number of molecules present in a given mass of a substance. Simply multiply the number of moles by Avogadro's number.

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

A: Avogadro's number has numerous applications in various fields, including chemistry, physics, and engineering. Some common applications include:

Calculating the number of atoms or molecules present in a given mass of a substance
Determining the amount of a substance present in a given volume
Calculating the number of moles of a substance present in a given mass
Determining the concentration of a solution

Conclusion

In this article, we have explored the concept of molar mass and Avogadro's number, and how to calculate the number of atoms present in a given mass of magnesium. We have also answered some frequently asked questions related to this topic. By understanding these concepts, you can apply them to various fields and make informed decisions.