Final answer:
The change in energy (ΔErxn) for the combustion of hexane in a bomb calorimeter, with a temperature increase of 12.35 °C and heat capacity of 5.75 kJ/°C, is approximately 3945 kJ/mol.
Step-by-step explanation:
To find the change in energy (ΔErxn) for the combustion of hexane (C6H14), we first need to calculate the heat absorbed by the bomb calorimeter, then adjust it to a per mole basis. The temperature increase observed is from 26.32 °C to 38.67 °C, giving a change in temperature (ΔT) of 12.35 °C. The heat capacity of the bomb calorimeter (Ccal) is given as 5.75 kJ/°C.
The total heat (q) absorbed by the calorimeter is calculated as:
q = Ccal × ΔT
q = 5.75 kJ/°C × 12.35 °C
q = 71.0125 kJ
Next, we calculate the number of moles of hexane combusted. The molar mass of hexane is approximately 86.18 g/mol. Thus:
Moles of hexane = mass of hexane / molar mass of hexane
Moles of hexane = 1.552 g / 86.18 g/mol
Moles of hexane = 0.018 mol
Finally, to find the ΔErxn per mole of hexane:
ΔErxn = q / moles of hexane
ΔErxn = 71.0125 kJ / 0.018 mol
ΔErxn ≈ 3945 kJ/mol
This is the change in energy for the combustion of hexane per mole.