Final answer:
The calculated molar heat of combustion for the compound is 1340.29 kJ/mol, which does not match any of the provided answer options. This suggests there may be a discrepancy in the question or the provided answer choices.
Step-by-step explanation:
To determine the molar heat of combustion of the compound, we need to calculate the heat absorbed by the water in the calorimeter and then use that information to find the heat released per mole of the compound.
Firstly, calculate the heat absorbed by the water using the formula q = mcΔT, where m is the mass of water in grams, c is the specific heat capacity, and ΔT is the change in temperature:
q = (3000 g)(4.184 J/g°C)(31.0°C) = 388,584 J or 388.584 kJ
Since 0.290 moles of the compound were burned to release this amount of heat, we then divide the total heat by the number of moles to find the heat of combustion per mole:
Molar heat of combustion = 388.584 kJ / 0.290 moles = 1340.29 kJ/mol
The values provided in the answer options do not match the calculated value, which means there might have been a mistake in the question, or the provided answer choices do not include the calculated value.