Final answer:
The mass of a sample of Ag containing 1.97 x 10²² atoms is calculated by first determining the number of moles of silver from the given number of atoms and then multiplying by the molar mass of silver (107.87 g/mol) to find the mass in grams, which is approximately 3.53 grams.
Step-by-step explanation:
The student has asked to calculate the mass in grams of a sample of Ag containing 1.97 x 10²² atoms. To do this, we must first find the number of moles of Ag that corresponds to this number of atoms using Avogadro's number (6.022 x 10²³ atoms/mol) as a conversion factor. Then, we use the molar mass of silver (Ag), which is 107.87 g/mol, to find the mass in grams.
First, we calculate the moles of Ag:
- Moles of Ag = number of atoms / Avogadro's number
- Moles of Ag = 1.97 x 10²² atoms / 6.022 x 10²³ atoms/mol
- Moles of Ag ≈ 0.0327 mol
Next, we calculate the mass in grams:
- Mass of Ag = moles of Ag x molar mass of Ag
- Mass of Ag = 0.0327 mol x 107.87 g/mol
- Mass of Ag ≈ 3.53 g
Therefore, the mass of the Ag sample containing 1.97 x 10²² atoms is approximately 3.53 grams.