What Is The Mass Of $5.246 \times 10^{23}$ Atoms Of Xenon Gas, Xe? The Molar Mass Of Xenon Is $131.29 , G/mol$.A. $6.887 \times 10^{25} , G$ B. $ 4.148 × 10 49 G 4.148 \times 10^{49} \, G 4.148 × 1 0 49 G [/tex] C. 114.4 G D. 0.8711 G

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What is the Mass of $5.246 \times 10^{23}$ Atoms of Xenon Gas, Xe?

Understanding the Problem

To find the mass of $5.246 \times 10^{23}$ atoms of xenon gas, we need to use the concept of molar mass and Avogadro's number. The molar mass of xenon is given as $131.29 , g/mol$, and we are asked to find the mass of a specific number of atoms.

Recalling Avogadro's Number

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 defined as $6.022 \times 10^{23}$ particles per mole. This number is a conversion factor that allows us to convert between moles and particles.

Converting Moles to Particles

To find the mass of $5.246 \times 10^{23}$ atoms of xenon, we need to convert this number to moles using Avogadro's number. We can set up a conversion factor as follows:

6.022×1023 atoms1 mol=5.246×1023 atomsx mol\frac{6.022 \times 10^{23} \, \text{atoms}}{1 \, \text{mol}} = \frac{5.246 \times 10^{23} \, \text{atoms}}{x \, \text{mol}}

Solving for x, we get:

x=5.246×1023 atoms6.022×1023 atoms/mol≈0.8711 molx = \frac{5.246 \times 10^{23} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} \approx 0.8711 \, \text{mol}

Finding the Mass

Now that we have the number of moles, we can find the mass of xenon by multiplying the number of moles by the molar mass:

Mass=number of moles×molar mass\text{Mass} = \text{number of moles} \times \text{molar mass}

Mass=0.8711 mol×131.29 g/mol≈114.4 g\text{Mass} = 0.8711 \, \text{mol} \times 131.29 \, \text{g/mol} \approx 114.4 \, \text{g}

Conclusion

Therefore, the mass of $5.246 \times 10^{23}$ atoms of xenon gas is approximately 114.4 g.

Answer

The correct answer is C. 114.4 g.

Discussion

This problem requires a basic understanding of Avogadro's number and molar mass. It also requires the ability to convert between moles and particles, and to perform unit conversions. The correct answer can be obtained by following the steps outlined above.

Additional Information

  • Avogadro's number is a fundamental constant in chemistry that represents the number of particles (atoms or molecules) in one mole of a substance.
  • The molar mass of a substance is the mass of one mole of that substance.
  • To find the mass of a specific number of particles, we need to convert that number to moles using Avogadro's number, and then multiply the number of moles by the molar mass.

References

  • IUPAC. (2019). Avogadro's number. In IUPAC Compendium of Chemical Terminology (2nd ed., pp. 65-66).
  • IUPAC. (2019). Molar mass. In IUPAC Compendium of Chemical Terminology (2nd ed., pp. 65-66).
    Q&A: Understanding the Mass of Atoms and Molecules

Frequently Asked Questions

Q: What is the difference between the mass of an atom and the mass of a molecule?

A: The mass of an atom is the mass of a single atom, while the mass of a molecule is the mass of a group of atoms bonded together. The mass of a molecule is typically greater than the mass of a single atom.

Q: How do I convert between moles and particles?

A: To convert between moles and particles, you can use Avogadro's number, which is 6.022 x 10^23 particles per mole. For example, if you have 1 mole of a substance, you have 6.022 x 10^23 particles of that substance.

Q: What is the molar mass of a substance?

A: The molar mass of a substance is the mass of one mole of that substance. It is typically expressed in units of grams per mole (g/mol).

Q: How do I find the mass of a specific number of particles?

A: To find the mass of a specific number of particles, you need to convert that number to moles using Avogadro's number, and then multiply the number of moles by the molar mass.

Q: What is the relationship between the mass of an atom and the mass of a molecule?

A: The mass of a molecule is typically greater than the mass of a single atom because a molecule is a group of atoms bonded together. The mass of a molecule is the sum of the masses of the individual atoms that make up the molecule.

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

A: To calculate the mass of a molecule, you need to know the molar mass of the molecule and the number of moles of the molecule. You can then multiply the number of moles by the molar mass to find the mass of the molecule.

Q: What is the significance of 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 used to convert between moles and particles, and is a key concept in understanding the behavior of matter at the atomic and molecular level.

Q: How do I use Avogadro's number to convert between moles and particles?

A: To use Avogadro's number to convert between moles and particles, you can set up a conversion factor as follows:

6.022×1023 particles1 mol=x particlesy mol\frac{6.022 \times 10^{23} \, \text{particles}}{1 \, \text{mol}} = \frac{x \, \text{particles}}{y \, \text{mol}}

Solving for x, you can find the number of particles in a given number of moles.

Q: What is the relationship between the mass of an atom and the mass of a substance?

A: The mass of an atom is a fundamental property of the atom, while the mass of a substance is the sum of the masses of the individual atoms that make up the substance. The mass of a substance is typically expressed in units of grams or kilograms.

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

A: To calculate the mass of a substance, you need to know the molar mass of the substance and the number of moles of the substance. You can then multiply the number of moles by the molar mass to find the mass of the substance.

Q: What is the significance of molar mass?

A: Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It is used to convert between moles and mass, and is a key concept in understanding the behavior of matter at the atomic and molecular level.

Q: How do I use molar mass to convert between moles and mass?

A: To use molar mass to convert between moles and mass, you can set up a conversion factor as follows:

131.29 g/mol1 mol=x gy mol\frac{131.29 \, \text{g/mol}}{1 \, \text{mol}} = \frac{x \, \text{g}}{y \, \text{mol}}

Solving for x, you can find the mass of a substance in a given number of moles.

Conclusion

Understanding the mass of atoms and molecules is a fundamental concept in chemistry. By using Avogadro's number and molar mass, you can convert between moles and particles, and calculate the mass of a substance. These concepts are essential in understanding the behavior of matter at the atomic and molecular level.