How Many Moles Are Present In $1.21 \times 10^{23}$ Atoms Of Ga?A. $7.29 \times 10^{46}$ Mol B. 0.201 Mol C. 0.402 Mol D. 2.01 Mol

by ADMIN 138 views

Understanding the Problem

To solve this problem, we need to recall the relationship between the number of atoms and the number of moles. The number of moles of a substance is defined as the number of atoms or molecules divided by Avogadro's number ($6.022 \times 10^{23}$). In this case, we are given the number of atoms of gallium (Ga) and we need to find the number of moles.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry that relates the number of atoms or molecules to the number of moles. It is defined as the number of atoms or molecules in one mole of a substance. Avogadro's number is equal to $6.022 \times 10^{23}$.

Calculating the Number of Moles

To calculate the number of moles, we need to divide the number of atoms by Avogadro's number. The formula for this calculation is:

Number of moles=Number of atomsAvogadro’s number\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}

In this case, the number of atoms is $1.21 \times 10^{23}$ and Avogadro's number is $6.022 \times 10^{23}$.

Performing the Calculation

Now, let's perform the calculation:

Number of moles=1.21×10236.022×1023\text{Number of moles} = \frac{1.21 \times 10^{23}}{6.022 \times 10^{23}}

Number of moles=1.216.022\text{Number of moles} = \frac{1.21}{6.022}

Number of moles=0.201\text{Number of moles} = 0.201

Conclusion

Therefore, the number of moles present in $1.21 \times 10^{23}$ atoms of Ga is 0.201 mol.

Answer

The correct answer is B. 0.201 mol.

Additional Information

To verify the answer, we can use the relationship between the number of moles and the number of atoms:

Number of moles=Number of atomsAvogadro’s number\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}

Number of moles=1.21×10236.022×1023\text{Number of moles} = \frac{1.21 \times 10^{23}}{6.022 \times 10^{23}}

Number of moles=1.216.022\text{Number of moles} = \frac{1.21}{6.022}

Number of moles=0.201\text{Number of moles} = 0.201

This calculation confirms that the number of moles present in $1.21 \times 10^{23}$ atoms of Ga is indeed 0.201 mol.

Real-World Applications

Understanding the relationship between the number of atoms and the number of moles is crucial in various fields such as chemistry, physics, and engineering. For example, in chemical reactions, the number of moles of reactants and products is essential to determine the stoichiometry of the reaction. In materials science, the number of moles of atoms in a material is used to determine its properties such as density and thermal conductivity.

Conclusion

In conclusion, the number of moles present in $1.21 \times 10^{23}$ atoms of Ga is 0.201 mol. This calculation is essential in various fields such as chemistry, physics, and engineering, and is used to determine the stoichiometry of chemical reactions and the properties of materials.

References

  • IUPAC, "Avogadro's Number", International Union of Pure and Applied Chemistry, 2019.
  • CRC Handbook of Chemistry and Physics, 100th Edition, CRC Press, 2020.
  • Atkins, P. W., and de Paula, J., "Physical Chemistry", 10th Edition, Oxford University Press, 2018.

Introduction

In our previous article, we discussed how to calculate the number of moles present in a given number of atoms. In this article, we will answer some frequently asked questions related to moles and Avogadro's number.

Q: What is Avogadro's number?

A: Avogadro's number is a fundamental constant in chemistry that relates the number of atoms or molecules to the number of moles. It is defined as the number of atoms or molecules in one mole of a substance. Avogadro's number is equal to $6.022 \times 10^{23}$.

Q: Why is Avogadro's number important?

A: Avogadro's number is essential in chemistry because it allows us to convert between the number of atoms or molecules and the number of moles. This is crucial in determining the stoichiometry of chemical reactions and the properties of materials.

Q: How do I calculate the number of moles?

A: To calculate the number of moles, you need to divide the number of atoms by Avogadro's number. The formula for this calculation is:

Number of moles=Number of atomsAvogadro’s number\text{Number of moles} = \frac{\text{Number of atoms}}{\text{Avogadro's number}}

Q: What is the relationship between the number of moles and the number of atoms?

A: The number of moles is equal to the number of atoms divided by Avogadro's number. This means that if you know the number of atoms, you can calculate the number of moles by dividing by Avogadro's number.

Q: Can I use Avogadro's number to calculate the number of atoms?

A: Yes, you can use Avogadro's number to calculate the number of atoms by multiplying the number of moles by Avogadro's number. The formula for this calculation is:

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

Q: What is the significance of Avogadro's number in real-world applications?

A: Avogadro's number is crucial in various fields such as chemistry, physics, and engineering. It is used to determine the stoichiometry of chemical reactions, the properties of materials, and the behavior of gases.

Q: How do I remember Avogadro's number?

A: You can remember Avogadro's number by using the following mnemonic: "Six point zero two two times ten to the twenty-third".

Q: Can I use a calculator to calculate the number of moles?

A: Yes, you can use a calculator to calculate the number of moles. Simply enter the number of atoms and Avogadro's number into the calculator and divide the number of atoms by Avogadro's number.

Q: What is the difference between moles and atoms?

A: Moles and atoms are related but distinct concepts. Moles are a unit of measurement that represents a large number of atoms or molecules, while atoms are the individual building blocks of matter.

Q: Can I use Avogadro's number to calculate the number of molecules?

A: Yes, you can use Avogadro's number to calculate the number of molecules by multiplying the number of moles by Avogadro's number. The formula for this calculation is:

Number of molecules=Number of moles×Avogadro’s number\text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number}

Conclusion

In conclusion, Avogadro's number is a fundamental constant in chemistry that relates the number of atoms or molecules to the number of moles. Understanding Avogadro's number is essential in various fields such as chemistry, physics, and engineering. By using the formulas and calculations outlined in this article, you can easily calculate the number of moles and atoms.

References

  • IUPAC, "Avogadro's Number", International Union of Pure and Applied Chemistry, 2019.
  • CRC Handbook of Chemistry and Physics, 100th Edition, CRC Press, 2020.
  • Atkins, P. W., and de Paula, J., "Physical Chemistry", 10th Edition, Oxford University Press, 2018.