To find the number of molecules of menthol ([tex]\(C_{10}H_{20}O\)[/tex]) in a sample that has [tex]\(2.25 \times 10^{-6}\)[/tex] moles of hydrogen ([tex]\(H\)[/tex]), we can follow these steps:
1. Determine the moles of menthol:
- Menthol ([tex]\(C_{10}H_{20}O\)[/tex]) has 20 hydrogen atoms for every molecule of menthol.
- Thus, to find the moles of menthol, we divide the moles of hydrogen by the number of hydrogen atoms in one molecule of menthol.
[tex]\[
\text{Moles of menthol} = \frac{2.25 \times 10^{-6} \, \text{moles of H}}{20}
\][/tex]
- This simplifies to:
[tex]\[
\text{Moles of menthol} = 1.125 \times 10^{-7} \, \text{moles}
\][/tex]
2. Calculate the number of molecules of menthol:
- Using Avogadro's number, [tex]\(6.022 \times 10^{23}\)[/tex], we convert moles of menthol to molecules.
[tex]\[
\text{Number of molecules} = 1.125 \times 10^{-7} \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole}
\][/tex]
- This gives:
[tex]\[
\text{Number of molecules} = 6.77475 \times 10^{16}
\][/tex]
3. Express the result in the form [tex]\( \text{coefficient} \times 10^{\text{exponent}} \)[/tex]:
- The number of molecules of menthol can be expressed as:
[tex]\[
\boxed{6.774750000000001 \times 10^{16}}
\][/tex]
Thus, the number of molecules of menthol ([tex]\(C_{10}H_{20}O\)[/tex]) in the sample is approximately [tex]\(6.77475 \times 10^{16}\)[/tex] molecules.
