Sure, let's solve this step by step.
1. Understanding the Concept:
- One mole of any substance contains [tex]\(6.02 \times 10^{23}\)[/tex] atoms (this number is known as Avogadro's number).
2. Identify the Given Data:
- Number of moles of carbon: [tex]\(2.654\)[/tex]
- Avogadro's number: [tex]\(6.02 \times 10^{23}\)[/tex] atoms/mole
3. Setup the Calculation:
- To find the number of carbon atoms in [tex]\(2.654\)[/tex] moles, we multiply the number of moles by Avogadro's number.
- This can be expressed as:
[tex]\[
\text{Number of carbon atoms} = \text{Number of moles} \times \text{Avogadro's number}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Number of carbon atoms} = 2.654 \times 6.02 \times 10^{23}
\][/tex]
4. Calculate the Result:
- Perform the multiplication:
[tex]\[
2.654 \times 6.02 \times 10^{23} = 1.5977079999999998 \times 10^{24}
\][/tex]
5. Final Answer:
- The number of carbon atoms in [tex]\(2.654\)[/tex] moles of carbon is:
[tex]\[
1.5977079999999998 \times 10^{24}
\][/tex]
So, by using the concept of moles and Avogadro's number, we determine that [tex]\(2.654\)[/tex] moles of carbon contains [tex]\(1.5977079999999998 \times 10^{24}\)[/tex] carbon atoms.
