To determine the number of moles in [tex]\(3.61 \times 10^{24}\)[/tex] molecules of [tex]\(CH_3OH\)[/tex], we can use Avogadro's number, which is [tex]\(6.02 \times 10^{23}\)[/tex] molecules per mole. Here are the steps to solve the problem:
1. Understand the problem: We need to find the number of moles of [tex]\(CH_3OH\)[/tex] given a certain number of molecules. Given data:
- Number of molecules: [tex]\(3.61 \times 10^{24}\)[/tex]
- Avogadro's number: [tex]\(6.02 \times 10^{23}\)[/tex] molecules per mole
2. Use the conversion factor: Avogadro's number tells us how many molecules are in one mole. The formula to convert molecules to moles is:
[tex]\[
\text{moles} = \frac{\text{number of molecules}}{\text{Avogadro's number}}
\][/tex]
3. Plug in the given values:
[tex]\[
\text{moles} = \frac{3.61 \times 10^{24}}{6.02 \times 10^{23}}
\][/tex]
4. Calculate the result:
[tex]\[
\text{moles} = 5.996677740863787
\][/tex]
Therefore, there are approximately [tex]\(5.997\)[/tex] moles (rounded to three significant figures) in [tex]\(3.61 \times 10^{24}\)[/tex] molecules of [tex]\(CH_3OH\)[/tex].
