Question

how many zinc atoms are contained in 4.6 moles of zinc?
○6.02 × 10²³ zinc atoms
○2.8 × 10²³ zinc atoms
○1.3 × 10²³ zinc atoms
○1.3 × 10⁻²⁴ zinc atoms
○2.8 × 10²⁴ zinc atoms

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \( 6.02\times 10^{23} \) atoms per mole. This means that 1 mole of any substance contains \( 6.02\times 10^{23} \) particles (in this case, zinc atoms).

Step2: Calculate the number of zinc atoms

To find the number of zinc atoms in 4.6 moles, we use the formula: Number of atoms = Moles \(\times\) Avogadro's number.
So, we multiply 4.6 moles by \( 6.02\times 10^{23} \) atoms/mole.
\[
4.6\times(6.02\times 10^{23}) = (4.6\times 6.02)\times 10^{23}
\]
First, calculate \( 4.6\times 6.02 \approx 27.692 \)
Then, \( 27.692\times 10^{23}=2.7692\times 10^{24}\approx 2.8\times 10^{24} \)? Wait, no, wait. Wait, 4.6 6.02 = let's recalculate: 4 6.02 = 24.08, 0.6 6.02 = 3.612, so total is 24.08 + 3.612 = 27.692. Then 27.692 × 10²³ = 2.7692 × 10²⁴? But the options have 2.8 × 10²⁴? Wait, no, wait the options: the last option is 2.8 × 10²⁴ zinc atoms. Wait, maybe I miscalculated. Wait 4.6 moles 6.02e23 atoms/mole. Let's do 4.6 6.02: 4.6 6 = 27.6, 4.6 * 0.02 = 0.092, so total 27.6 + 0.092 = 27.692. Then 27.692e23 = 2.7692e24 ≈ 2.8e24. So the correct option is the last one: \( 2.8\times 10^{24} \) zinc atoms. Wait, but let's check the options again. The options are:

• \( 6.02\times 10^{23} \) (1 mole)
• \( 2.8\times 10^{23} \) (too small)
• \( 1.3\times 10^{23} \) (too small)
• \( 1.3\times 10^{-24} \) (way too small)
• \( 2.8\times 10^{24} \) (this is the result)

So the correct calculation is 4.6 * 6.02e23 = 2.7692e24 ≈ 2.8e24.

Answer:

\( 2.8\times 10^{24} \) zinc atoms (the last option: \( 2.8\times 10^{24} \) zinc atoms)