Round the answer to 3 significant figures

Oct 13, 2025 by miodeya.com 44 views

Introduction

In chemistry, understanding the mass of atoms is crucial for various calculations and applications. One of the fundamental concepts in chemistry is the calculation of the mass of atoms based on their number of moles. In this article, we will focus on calculating the mass of 11.05 moles of carbon-12 atoms. We will use the atomic mass of carbon-12 and the Avogadro's number to determine the mass of the given number of moles.

Understanding Atomic Mass and Avogadro's Number

The atomic mass of an element is the average mass of a single atom of that element, expressed in atomic mass units (amu). The atomic mass of carbon-12 is 12.01 amu. Avogadro's number is a fundamental constant in chemistry that represents the number of particles (atoms or molecules) in one mole of a substance. It is equal to 6.022 x 10^23 particles per mole.

Calculating the Mass of Carbon-12 Atoms

To calculate the mass of 11.05 moles of carbon-12 atoms, we can use the following formula:

Mass (in grams) = Number of moles x Atomic mass (in amu) x Avogadro's number

We can rearrange the formula to solve for the mass:

Mass (in grams) = Number of moles x Atomic mass (in amu) x 6.022 x 10^23

Step-by-Step Calculation

Identify the given values: Number of moles = 11.05 moles, Atomic mass of carbon-12 = 12.01 amu, Avogadro's number = 6.022 x 10^23 particles per mole.
Plug in the values: Mass (in grams) = 11.05 moles x 12.01 amu x 6.022 x 10^23
Perform the calculation: Mass (in grams) = 11.05 x 12.01 x 6.022 x 10^23 = 8.305 x 10^25 grams
Round the answer to 3 significant figures: Mass (in grams) = 8.30 x 10^25 grams

Conclusion

In conclusion, the mass of 11.05 moles of carbon-12 atoms is 8.30 x 10^25 grams. This calculation demonstrates the importance of understanding the atomic mass and Avogadro's number in chemistry. By using these fundamental constants, we can calculate the mass of atoms and molecules with high accuracy.

Real-World Applications

The calculation of the mass of atoms has numerous real-world applications in various fields, including:

Chemical engineering: Understanding the mass of atoms is crucial for designing and optimizing chemical processes, such as the production of fuels and chemicals.
Materials science: The mass of atoms is essential for understanding the properties and behavior of materials, such as their strength, conductivity, and reactivity.
Biotechnology: The mass of atoms is important for understanding the behavior of biomolecules, such as proteins and DNA, and for designing new biotechnological applications.

Common Mistakes to Avoid

When calculating the mass of atoms, it is essential to avoid common mistakes, such as:

Incorrect units: Make sure to use the correct units for the atomic mass and Avogadro's number.
Rounding errors: Be careful when rounding numbers to avoid errors in the calculation.
Incorrect calculation: Double-check the calculation to ensure that it is correct.

Additional Resources

For further information on calculating the mass of atoms, refer to the following resources:

Textbooks: Chemistry textbooks, such as "Chemistry: The Central Science" by Theodore L. Brown, H. Eugene LeMay, and Bruce E. Bursten.
Online resources: Websites, such as Khan Academy and Chemistry LibreTexts, offer interactive tutorials and examples on calculating the mass of atoms.
Scientific articles: Research articles in scientific journals, such as the Journal of Chemical Education and the Journal of Physical Chemistry, provide in-depth information on the calculation of the mass of atoms.
Frequently Asked Questions: Calculating the Mass of Carbon-12 Atoms ====================================================================

Q: What is the atomic mass of carbon-12?

A: The atomic mass of carbon-12 is 12.01 amu (atomic mass units).

Q: What is Avogadro's number?

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

Q: How do I calculate the mass of carbon-12 atoms?

A: To calculate the mass of carbon-12 atoms, you can use the following formula:

Mass (in grams) = Number of moles x Atomic mass (in amu) x Avogadro's number

Q: What is the mass of 11.05 moles of carbon-12 atoms?

A: The mass of 11.05 moles of carbon-12 atoms is 8.30 x 10^25 grams.

Q: Why is it important to understand the mass of atoms?

A: Understanding the mass of atoms is crucial for various applications in chemistry, including chemical engineering, materials science, and biotechnology.

Q: What are some common mistakes to avoid when calculating the mass of atoms?

A: Some common mistakes to avoid when calculating the mass of atoms include:

Incorrect units
Rounding errors
Incorrect calculation

Q: Where can I find more information on calculating the mass of atoms?

A: You can find more information on calculating the mass of atoms in textbooks, online resources, and scientific articles.

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

A: Avogadro's number is a fundamental constant in chemistry that represents the number of particles (atoms or molecules) in one mole of a substance. It is essential for understanding the behavior of substances and for calculating the mass of atoms.

Q: How do I convert the mass of atoms from grams to other units?

A: To convert the mass of atoms from grams to other units, you can use conversion factors. For example, to convert grams to kilograms, you can divide the mass in grams by 1000.

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

A: Atomic mass refers to the average mass of a single atom of an element, while molecular mass refers to the average mass of a molecule of a substance.

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

A: To calculate the molecular mass of a substance, you can add the atomic masses of the individual atoms that make up the molecule.

Q: What is the significance of the mass of atoms in real-world applications?

A: The mass of atoms is essential for understanding the behavior of substances and for designing and optimizing chemical processes, materials, and biotechnological applications.

Q: Where can I find more resources on calculating the mass of atoms?

A: You can find more resources on calculating the mass of atoms in textbooks, online resources, and scientific articles. Some recommended resources include:

Khan Academy: Calculating the mass of atoms
Chemistry LibreTexts: Calculating the mass of atoms
Journal of Chemical Education: Articles on calculating the mass of atoms
Journal of Physical Chemistry: Articles on calculating the mass of atoms