To determine the number of carbon atoms in a sample containing 2 moles of carbon, we first need to understand the relationship between moles and the number of atoms. This relationship is defined by Avogadro's number, which tells us the number of atoms in one mole of a substance.
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole. Therefore, we can calculate the total number of carbon atoms in Rachel's sample by multiplying the number of moles by Avogadro's number.
Here's the step-by-step solution:
1. Identify the number of moles of carbon:
Rachel has a sample containing [tex]\(2\)[/tex] moles of carbon.
2. Use Avogadro's number to find the number of atoms in one mole:
Avogadro's number is [tex]\(6.022 \times 10^{23}\)[/tex] atoms/mole.
3. Multiply the number of moles by Avogadro's number to find the total number of atoms:
[tex]\[
\text{Number of atoms} = \text{moles of carbon} \times \text{Avogadro's number}
\][/tex]
[tex]\[
\text{Number of atoms} = 2 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole}
\][/tex]
4. Perform the calculation:
[tex]\[
\text{Number of atoms} = 2 \times 6.022 \times 10^{23}
\][/tex]
[tex]\[
\text{Number of atoms} = 12.044 \times 10^{23}
\][/tex]
Convert this to scientific notation:
[tex]\[
\text{Number of atoms} = 1.2044 \times 10^{24}
\][/tex]
Therefore, the number of carbon atoms in Rachel's sample is [tex]\(1.2044 \times 10^{24}\)[/tex] atoms.
The correct answer is:
C. [tex]\(1.204 \times 10^{24}\)[/tex] atoms
