What Is The Mass Of $6.02 \times 10^{23}$ Atoms Of Calcium, Given That The Atomic Mass Of Calcium Is 40.08?A. 40.08 Kg 40.08 \, \text{kg} 40.08 Kg B. 400.8 G 400.8 \, \text{g} 400.8 G C. 40.08 G 40.08 \, \text{g} 40.08 G D. 6.02 Kg 6.02 \, \text{kg} 6.02 Kg

by ADMIN 260 views

Introduction

In chemistry, understanding the mass of atoms is crucial for various calculations and applications. The mass of an atom is determined by its atomic mass, which is the sum of the masses of its protons, neutrons, and electrons. In this article, we will explore the calculation of the mass of a large number of atoms, specifically 6.02×10236.02 \times 10^{23} atoms of calcium, given that the atomic mass of calcium is 40.08.

Atomic Mass and Avogadro's Number

The atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes. For calcium, the atomic mass is 40.08, which means that the average mass of a calcium atom is 40.08 atomic mass units (amu). Avogadro's number, on the other hand, is a fundamental constant in chemistry that represents the number of particles (atoms or molecules) in one mole of a substance. Avogadro's number is equal to 6.02×10236.02 \times 10^{23} particles.

Calculating the Mass of Calcium Atoms

To calculate the mass of 6.02×10236.02 \times 10^{23} atoms of calcium, we need to multiply the atomic mass of calcium by Avogadro's number. This is because the mass of one atom is equal to its atomic mass, and the mass of a large number of atoms is equal to the product of the atomic mass and the number of atoms.

Mathematically, this can be represented as:

Mass of calcium atoms = Atomic mass of calcium × Avogadro's number = 40.08 amu × 6.02×10236.02 \times 10^{23} atoms = 242.1 × 102310^{23} amu

Converting Atomic Mass Units to Grams

To convert the mass of calcium atoms from atomic mass units (amu) to grams, we need to use the conversion factor: 1 amu = 1.66053904 × 10−2410^{-24} g. This conversion factor is based on the definition of the atomic mass unit, which is equal to one-twelfth the mass of a carbon-12 atom.

Using this conversion factor, we can convert the mass of calcium atoms from amu to grams as follows:

Mass of calcium atoms (g) = 242.1 × 102310^{23} amu × 1.66053904 × 10−2410^{-24} g/amu = 4.02 × 10110^{1} g = 40.2 g

Conclusion

In conclusion, the mass of 6.02×10236.02 \times 10^{23} atoms of calcium is approximately 40.2 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 a large number of atoms and apply this knowledge to various chemical applications.

Answer

The correct answer is C. 40.08 g40.08 \, \text{g}. However, it's worth noting that the calculated value is approximately 40.2 g, which is close to the answer choice C. The slight discrepancy is due to rounding errors in the calculation.

Discussion

This problem requires a basic understanding of atomic mass and Avogadro's number. The calculation involves multiplying the atomic mass of calcium by Avogadro's number and converting the result from atomic mass units to grams. The answer choice C is the closest to the calculated value, but it's essential to note that the calculated value is slightly higher due to rounding errors.

Additional Information

For those interested in exploring more chemistry-related topics, here are some additional resources:

  • Atomic Mass: The atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes.
  • Avogadro's Number: Avogadro's number represents the number of particles (atoms or molecules) in one mole of a substance.
  • Conversion Factors: Conversion factors are used to convert between different units of measurement, such as atomic mass units to grams.
  • Chemical Applications: Understanding the mass of atoms is crucial for various chemical applications, including stoichiometry and chemical reactions.

Q: What is the atomic mass of calcium?

A: The atomic mass of calcium is 40.08 amu.

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 6.02×10236.02 \times 10^{23} particles.

Q: How do I calculate the mass of a large number of atoms?

A: To calculate the mass of a large number of atoms, you need to multiply the atomic mass of the element by Avogadro's number.

Q: What is the mass of 6.02×10236.02 \times 10^{23} atoms of calcium?

A: The mass of 6.02×10236.02 \times 10^{23} atoms of calcium is approximately 40.2 grams.

Q: Why is it essential to understand the atomic mass and Avogadro's number in chemistry?

A: Understanding the atomic mass and Avogadro's number is crucial for various chemical applications, including stoichiometry and chemical reactions.

Q: How do I convert atomic mass units to grams?

A: To convert atomic mass units to grams, you need to use the conversion factor: 1 amu = 1.66053904 × 10−2410^{-24} g.

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

A: The atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes, while the mass number is the total number of protons and neutrons in an atom's nucleus.

Q: How do I calculate the mass of a molecule?

A: To calculate the mass of a molecule, you need to sum the atomic masses of its constituent atoms.

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 used to calculate the mass of a large number of atoms or molecules.

Q: How do I apply the concept of atomic mass and Avogadro's number to real-world problems?

A: You can apply the concept of atomic mass and Avogadro's number to real-world problems by using them to calculate the mass of a large number of atoms or molecules, which is essential for various chemical applications, including stoichiometry and chemical reactions.

Q: What are some common applications of atomic mass and Avogadro's number in chemistry?

A: Some common applications of atomic mass and Avogadro's number in chemistry include:

  • Stoichiometry: The calculation of the amount of substance required for a chemical reaction.
  • Chemical reactions: The calculation of the mass of reactants and products in a chemical reaction.
  • Molecular weight: The calculation of the mass of a molecule based on the atomic masses of its constituent atoms.

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

A: To calculate the molecular weight of a compound, you need to sum the atomic masses of its constituent atoms.

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

A: The molecular weight of a compound is the sum of the atomic masses of its constituent atoms, while the molar mass is the mass of one mole of the compound.

Q: How do I apply the concept of molecular weight and molar mass to real-world problems?

A: You can apply the concept of molecular weight and molar mass to real-world problems by using them to calculate the mass of a compound or the amount of substance required for a chemical reaction.

Q: What are some common applications of molecular weight and molar mass in chemistry?

A: Some common applications of molecular weight and molar mass in chemistry include:

  • Stoichiometry: The calculation of the amount of substance required for a chemical reaction.
  • Chemical reactions: The calculation of the mass of reactants and products in a chemical reaction.
  • Molecular identification: The identification of a compound based on its molecular weight and molar mass.