Final answer:
The molar ΔU for the combustion of glucose in a bomb calorimeter is -2369.0 kJ/mol, calculated by dividing the heat absorbed by the calorimeter (6.87×10⁵ J) by the number of moles of glucose (0.29 mol).
Step-by-step explanation:
To determine the molar ΔU for the combustion of glucose in a bomb calorimeter, we can use the heat absorbed by the calorimeter to calculate the change in internal energy (ΔU) of the reaction per mole of glucose. Since the calorimeter absorbs the heat released by the reaction, the heat absorbed by the calorimeter is equal in magnitude but opposite in sign to the heat of the reaction (ΔU). We have 0.29 mol of glucose combusting and releasing 6.87×10⁵ J of heat.
The molar ΔU, in kJ/mol, is calculated by dividing the total heat (in Joules) by the number of moles of glucose. First, we convert the energy into kilojoules:
ΔU (in kJ) = 6.87×10⁵ J × (1 kJ / 1000 J) = 687 kJ
Next, we divide by the number of moles to obtain the molar ΔU:
Molar ΔU = ΔU / number of moles = 687 kJ / 0.29 mol = 2369.0 kJ/mol
Therefore, the molar ΔU for the combustion of glucose in the bomb calorimeter is -2369.0 kJ/mol, indicating an exothermic reaction where energy is released.