How many silver atoms are there in 9.55 g of silver?

Verified step by step guidance

1. Determine the molar mass of silver (Ag) from the periodic table. The molar mass of silver is approximately 107.87 g/mol.
2. Convert the mass of silver from grams to moles using the formula: \( \text{moles of Ag} = \frac{\text{mass of Ag in grams}}{\text{molar mass of Ag}} \).
3. Substitute the given mass of silver (9.55 g) and the molar mass of silver (107.87 g/mol) into the formula to find the number of moles of silver.
4. Use Avogadro's number, which is \( 6.022 \times 10^{23} \) atoms/mol, to convert the moles of silver to the number of atoms. The formula is: \( \text{number of atoms} = \text{moles of Ag} \times 6.022 \times 10^{23} \).
5. Substitute the calculated moles of silver into the formula to find the number of silver atoms.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For silver (Ag), the molar mass is approximately 107.87 g/mol. This value is essential for converting between grams of a substance and the number of moles, which is a fundamental step in determining the number of atoms present in a given mass.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances (grams) to the microscopic scale (individual atoms or molecules). It is crucial for calculating the number of atoms in a sample once the number of moles is known.

Conversion from Grams to Moles

To find the number of moles from a given mass, the formula used is: moles = mass (g) / molar mass (g/mol). This conversion is necessary to determine how many moles of silver are present in 9.55 g, which can then be multiplied by Avogadro's number to find the total number of silver atoms in that mass.