Final answer:
To find the mass of a silver sample with 1.97 × 1022 atoms, calculate the moles of silver using Avogadro's number, then convert the moles to grams using the atomic mass of silver, resulting in approximately 3.53 grams.
Step-by-step explanation:
Calculating the Mass of a Silver Sample
To calculate the mass in grams of a silver sample containing 1.97 × 1022 atoms, we need to use Avogadro's number and the atomic mass of silver. Avogadro's number (6.022 × 1023 atoms/mol) is the number of atoms in one mole of a substance. The atomic mass of silver (Ag) is approximately 107.87 grams per mole.
First, we calculate the number of moles of silver using the given number of atoms:
moles Ag = atoms Ag / Avogadro's number
moles Ag = 1.97 × 1022 atoms / 6.022 × 1023 atoms/mol
moles Ag ≈ 0.0327 moles
Next, we convert moles to grams using the atomic mass of silver:
mass Ag = moles Ag × atomic mass of Ag
mass Ag = 0.0327 moles × 107.87 g/mol
mass Ag ≈ 3.53 grams
Therefore, the mass of the silver sample is approximately 3.53 grams.