Calculating the Number of Moles of Gold Atoms

Oct 13, 2025 by leolavanderia.com.br 57 views

Understanding the Problem

Calculating the mass of gold(III) chloride that contains a trillion gold atoms requires a step-by-step approach. We need to determine the molar mass of gold(III) chloride, calculate the number of moles of gold atoms, and then find the mass of gold(III) chloride that contains that many gold atoms.

Molar Mass of Gold(III) Chloride

The molar mass of gold(III) chloride is the sum of the atomic masses of its constituent elements: gold (Au) and chlorine (Cl). The atomic mass of gold is 196.9665 g/mol, and the atomic mass of chlorine is 35.453 g/mol. Since gold(III) chloride has two gold atoms and six chlorine atoms, its molar mass can be calculated as follows:

Molar Mass of Gold(III) Chloride = 2 x Atomic Mass of Gold + 6 x Atomic Mass of Chlorine

Molar Mass of Gold(III) Chloride = 2 x 196.9665 g/mol + 6 x 35.453 g/mol
Molar Mass of Gold(III) Chloride = 393.933 g/mol + 212.718 g/mol
Molar Mass of Gold(III) Chloride = 606.651 g/mol

Calculating the Number of Moles of Gold Atoms

We are given that there are 1.00 x 10^12 gold atoms. To find the number of moles of gold atoms, we need to divide the number of gold atoms by Avogadro's number (6.022 x 10^23 atoms/mol).

Number of Moles of Gold Atoms = Number of Gold Atoms / Avogadro's Number

Number of Moles of Gold Atoms = 1.00 x 10^12 atoms / 6.022 x 10^23 atoms/mol
Number of Moles of Gold Atoms = 1.66 x 10^-12 mol

Calculating the Mass of Gold(III) Chloride

Now that we have the number of moles of gold atoms, we can find the mass of gold(III) chloride that contains that many gold atoms. We can use the molar mass of gold(III) chloride and the number of moles of gold atoms to calculate the mass of gold(III) chloride.

Mass of Gold(III) Chloride = Molar Mass of Gold(III) Chloride x Number of Moles of Gold Atoms

Mass of Gold(III) Chloride = 606.651 g/mol x 1.66 x 10^-12 mol
Mass of Gold(III) Chloride = 1.00 x 10^-9 g

Rounding the Answer to 3 Significant Figures

The mass of gold(III) chloride is 1.00 x 10^-9 g. Rounding this answer to 3 significant figures gives us 1.00 x 10^-9 g.

Conclusion

In conclusion, the mass of gold(III) chloride that contains a trillion gold atoms is 1.00 x 10^-9 g. This answer has a unit symbol (g) and has been rounded to 3 significant figures.

References

Atomic masses of elements: Atomic Masses of Elements
Avogadro's number: Avogadro's Number
Molar mass of gold(III) chloride: Molar Mass of Gold(III) Chloride

Discussion

This problem requires a step-by-step approach to calculate the mass of gold(III) chloride that contains a trillion gold atoms. We need to determine the molar mass of gold(III) chloride, calculate the number of moles of gold atoms, and then find the mass of gold(III) chloride that contains that many gold atoms. The answer has a unit symbol (g) and has been rounded to 3 significant figures.

Keywords

Gold(III) chloride
Molar mass
Number of moles
Mass of gold(III) chloride
Avogadro's number
Atomic masses of elements
Q&A: Calculating the Mass of Gold(III) Chloride =====================================================

Frequently Asked Questions

Q: What is the molar mass of gold(III) chloride?

A: The molar mass of gold(III) chloride is 606.651 g/mol.

Q: How do I calculate the number of moles of gold atoms?

A: To calculate the number of moles of gold atoms, you need to divide the number of gold atoms by Avogadro's number (6.022 x 10^23 atoms/mol).

Q: What is Avogadro's number?

A: Avogadro's number is 6.022 x 10^23 atoms/mol, which is the number of atoms in one mole of a substance.

Q: How do I calculate the mass of gold(III) chloride that contains a certain number of gold atoms?

A: To calculate the mass of gold(III) chloride that contains a certain number of gold atoms, you need to multiply the molar mass of gold(III) chloride by the number of moles of gold atoms.

Q: What is the mass of gold(III) chloride that contains a trillion gold atoms?

A: The mass of gold(III) chloride that contains a trillion gold atoms is 1.00 x 10^-9 g.

Q: Why do I need to round the answer to 3 significant figures?

A: You need to round the answer to 3 significant figures to ensure that the answer is accurate and easy to read.

Q: What are some related problems that I can try?

A: Some related problems that you can try include calculating the mass of a substance that contains a certain number of atoms, determining the molar mass of a compound, and calculating the number of moles of a substance.

Q: What are some keywords that I can use to search for more information?

A: Some keywords that you can use to search for more information include gold(III) chloride, molar mass, number of moles, mass of gold(III) chloride, Avogadro's number, and atomic masses of elements.

Additional Resources

Conclusion

In conclusion, calculating the mass of gold(III) chloride that contains a trillion gold atoms requires a step-by-step approach. We need to determine the molar mass of gold(III) chloride, calculate the number of moles of gold atoms, and then find the mass of gold(III) chloride that contains that many gold atoms. The answer has a unit symbol (g) and has been rounded to 3 significant figures.

Discussion

Keywords

Gold(III) chloride
Molar mass
Number of moles
Mass of gold(III) chloride
Avogadro's number
Atomic masses of elements