To find out how many moles of hydrogen are in 5.0 moles of [tex]\( CH_4 \)[/tex], we need to consider the molecular composition of methane ([tex]\( CH_4 \)[/tex]). Here are the steps to solve the problem:
1. Understand the composition of [tex]\( CH_4 \)[/tex]:
Methane ([tex]\( CH_4 \)[/tex]) is a molecule composed of one carbon atom and four hydrogen atoms. This means that each molecule of [tex]\( CH_4 \)[/tex] contains four hydrogen atoms.
2. Determine the relationship of moles:
Since each molecule of [tex]\( CH_4 \)[/tex] has four hydrogen atoms, each mole of [tex]\( CH_4 \)[/tex] will have four moles of hydrogen atoms. This is because the mole is a measure that counts entities (like atoms or molecules), and Avogadro's number applies uniformly. One mole of [tex]\( CH_4 \)[/tex] contains Avogadro's number of [tex]\( CH_4 \)[/tex] molecules, and since each molecule has four hydrogen atoms, one mole of [tex]\( CH_4 \)[/tex] equals four moles of hydrogen atoms.
3. Calculate the total moles of hydrogen:
To find the total moles of hydrogen in 5.0 moles of [tex]\( CH_4 \)[/tex], we multiply the number of moles of [tex]\( CH_4 \)[/tex] by the number of hydrogen atoms per [tex]\( CH_4 \)[/tex] molecule (which is 4).
So, we have:
[tex]\[
\text{Total moles of hydrogen} = 5.0 \text{ moles of } CH_4 \times 4 \text{ moles of } H \text{ per mole of } CH_4
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Total moles of hydrogen} = 5.0 \times 4 = 20.0 \text{ moles}
\][/tex]
Therefore, there are [tex]\( 20.0 \)[/tex] moles of hydrogen in [tex]\( 5.0 \)[/tex] moles of [tex]\( CH_4 \)[/tex].
