To determine the number of atoms in a sample containing 2 moles of carbon, we need to use Avogadro's number, which is the number of atoms in one mole of any substance. Avogadro's number is approximately [tex]\( 6.022 \times 10^{23} \)[/tex].
Here’s a detailed step-by-step solution:
1. Identify the given quantity: The sample contains 2 moles of carbon.
2. Recall Avogadro's number: Avogadro's number, [tex]\( N_A \)[/tex], is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms/mole.
3. Calculate the total number of atoms: Multiply the number of moles by Avogadro's number to get the total number of atoms.
[tex]\[
\text{Total number of atoms} = (\text{number of moles}) \times (N_A)
\][/tex]
Substituting the values:
[tex]\[
\text{Total number of atoms} = 2 \times 6.022 \times 10^{23}
\][/tex]
4. Perform the multiplication:
[tex]\[
2 \times 6.022 = 12.044
\][/tex]
Therefore,
[tex]\[
2 \times 6.022 \times 10^{23} = 12.044 \times 10^{23}
\][/tex]
5. Express in scientific notation: Convert [tex]\( 12.044 \times 10^{23} \)[/tex] to [tex]\( 1.204 \times 10^{24} \)[/tex] by adjusting the coefficient to be a number between 1 and 10.
So,
[tex]\[
12.044 \times 10^{23} = 1.204 \times 10^{24}
\][/tex]
Therefore, the correct answer is:
C. [tex]\( 1.204 \times 10^{24} \)[/tex] atoms.
