What is the mass of 4.51×1022 Pb atoms?

Verified step by step guidance

1. Determine the molar mass of lead (Pb) from the periodic table. The molar mass of Pb is approximately 207.2 g/mol.
2. Use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol, to find the number of moles of Pb atoms. Set up the conversion: \(\text{moles of Pb} = \frac{4.51 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}}\).
3. Calculate the number of moles of Pb using the conversion factor from the previous step.
4. Use the number of moles calculated to find the mass of Pb. Set up the conversion: \(\text{mass of Pb} = \text{moles of Pb} \times 207.2 \text{ g/mol}\).
5. Calculate the mass of Pb using the conversion factor from the previous step.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For lead (Pb), the molar mass is approximately 207.2 g/mol. This value is essential for converting between the number of atoms and the mass of the substance, as it allows us to relate the atomic scale to macroscopic quantities.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10²³, is the number of atoms, molecules, or particles in one mole of a substance. This constant is crucial for converting between the number of individual atoms and moles, enabling calculations involving quantities of substances in chemical reactions and stoichiometry.

Conversion of Atoms to Mass

To find the mass of a specific number of atoms, one must first convert the number of atoms to moles using Avogadro's number, and then multiply the number of moles by the molar mass of the element. This process allows for the determination of the mass of a given number of atoms, linking atomic scale measurements to macroscopic mass.