Final answer:
To produce 13.78 mol of ethane, 13.78 mol of hydrogen are required according to the balanced chemical equation, so the correct answer is 13.78 mol, which is not listed in the options provided.
Step-by-step explanation:
To determine how many moles of hydrogen are needed to produce 13.78 mol of ethane, we must refer to the balanced chemical equation for the reaction. The balanced equation for producing ethane (C2H6) from hydrogen (H2) and ethylene (C2H4) is:
3 C2H4 + 2 H2 → 2 C2H6
This equation shows that 2 moles of ethane are produced from 2 moles of hydrogen, meaning a 1:1 ratio. To produce 13.78 moles of ethane, you would therefore need the same number of moles of hydrogen, which is 13.78 moles of H2. So, the correct answer is none of the options provided, as they do not include 13.78 moles.