To determine the number of carbon atoms in Rachel's sample containing 2 moles of carbon, we need to use Avogadro's number. Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], tells us the number of atoms or molecules in one mole of a substance.
Step-by-step solution:
1. Understand Avogadro's number:
Avogadro's number [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole signifies the number of atoms in one mole of any substance.
2. Given information:
- Number of moles of carbon: [tex]\(2\)[/tex] moles
- Avogadro's number: [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole
3. Calculate the total number of atoms:
To find the total number of atoms in 2 moles of carbon, multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of atoms} = (\text{Number of moles}) \times (\text{Avogadro's number})
\][/tex]
[tex]\[
\text{Number of atoms} = 2 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole}
\][/tex]
4. Perform the multiplication:
[tex]\[
2 \times 6.022 \times 10^{23} = 12.044 \times 10^{23}
\][/tex]
5. Express the result in scientific notation:
[tex]\[
12.044 \times 10^{23} = 1.2044 \times 10^{24}
\][/tex]
Given this, we can round off the result to a reasonable number of significant figures:
[tex]\[
1.204 \times 10^{24}
\][/tex]
So, the total number of carbon atoms in Rachel's sample is [tex]\(1.204 \times 10^{24}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(1.204 \times 10^{24}\)[/tex] atoms
