The balanced chemical equation for the reaction C + 2H2 → CH4 tells us that one mole of carbon produces one mole of methane. So, if 10.7 moles of methane are produced, then 10.7 moles of carbon are required to produce it.
To find the mass of carbon required to produce 10.7 moles of methane, we can use the molar mass of carbon (12 g/mol) and the following calculation:
Mass of carbon = Number of moles of carbon × Molar mass of carbon
Mass of carbon = 10.7 mol × 12 g/mol
Mass of carbon = 128.4 g
Therefore, 128.4 grams of carbon are required to produce 10.7 moles of methane, CH4.