How many grams are present in a sample of calcium (Ca) that contains 2.71 × 10^{20} atoms?

• A. 0.0450 g
• B. 0.0027 g
• C. 1.50 g
• D. 0.0180 g

Answer: (D)

Verified step by step guidance

1. Identify the given information: the number of calcium atoms is \$2.71 \times 10^{20}$ atoms.
2. Recall that to find the mass of a sample from the number of atoms, you need to convert atoms to moles using Avogadro's number, which is \$6.022 \times 10^{23}$ atoms per mole.
3. Calculate the number of moles of calcium by dividing the number of atoms by Avogadro's number: \(\text{moles} = \frac{2.71 \times 10^{20}}{6.022 \times 10^{23}}\).
4. Use the molar mass of calcium (Ca), which is approximately 40.08 g/mol, to convert moles to grams: \(\text{mass} = \text{moles} \times 40.08 \, \text{g/mol}\).
5. Perform the multiplication to find the mass in grams, which will give you the mass of the calcium sample containing \$2.71 \times 10^{20}$ atoms.