Final answer:
When 4.000 mol of methane is burned, it produces 3212 kJ of energy, following the stoichiometric proportionality to the amount of methane combusted.
Step-by-step explanation:
The question relates to stoichiometry and enthalpy changes in chemical reactions, specifically the combustion of methane. The amount of energy produced by the combustion of methane is proportional to the amount of methane burned. According to the provided information, burning 1.000 mol of methane produces 803 kJ of energy. Therefore, burning 4.000 mol of methane would produce 4 times that amount. The calculation is as follows:
4.000 mol methane × 803 kJ/mol = 3212 kJ
Thus, when 4.000 mol of methane is burned, 3212 kJ of energy is produced.