To solve this problem, let's break it down step-by-step:
1. Determine the molar mass of methane (CH₄):
- Carbon (C) has a molar mass of 12 g/mol.
- Hydrogen (H) has a molar mass of 1 g/mol.
- Since methane (CH₄) has one carbon atom and four hydrogen atoms, its molar mass is:
\(\[
\text{Molar mass of CH₄} = 12 + 4 \times 1 = 16 \, \text{g/mol}
\]\)
2. Calculate the number of moles of methane in 80 grams:
\(\[
\text{Moles of CH₄} = \frac{\text{mass}}{\text{molar mass}} = \frac{80 \, \text{g}}{16 \, \text{g/mol}} = 5 \, \text{moles}
\]\)
3. Determine the number of hydrogen atoms in the methane:
- Each CH₄ molecule contains 4 hydrogen atoms.
- Therefore, the number of moles of hydrogen atoms in 5 moles of CH₄ is:
\(\[
\text{Moles of H atoms} = 5 \, \text{moles of CH₄} \times 4 \, \text{H atoms/CH₄ molecule} = 20 \, \text{moles of H atoms}
\]\)
4. Determine the molar mass of ethane (C₂H₆):
- Ethane (C₂H₆) has two carbon atoms and six hydrogen atoms.
- The molar mass of ethane is:
\(\[
\text{Molar mass of C₂H₆} = 2 \times 12 + 6 \times 1 = 24 + 6 = 30 \, \text{g/mol}
\]\)
5. Calculate the number of moles of ethane (C₂H₆) that contain the same number of hydrogen atoms (20 moles of H atoms):
- Each C₂H₆ molecule has 6 hydrogen atoms.
- Therefore, to find the moles of ethane that provide 20 moles of hydrogen atoms:
\(\[
\text{Moles of C₂H₆} = \frac{20 \, \text{moles of H atoms}}{6 \, \text{H atoms/C₂H₆ molecule}} = \frac{20}{6} \approx 3.33 \, \text{moles}
\]\)
6. Calculate the mass of ethane (C₂H₆) that corresponds to this number of moles:
\(\[
\text{Mass of C₂H₆} = \text{moles} \times \text{molar mass} = 3.33 \, \text{moles} \times 30 \, \text{g/mol} = 100 \, \text{g}
\]\)
Thus, the mass of ethane that has the same number of hydrogen atoms as present in 80 grams of methane is:
Answer: B) 100 g
