1.578 g of an unknown hydrocarbon (110.7 g/mol) burns in bomb calorimeter in excess oxygen. The heat capacity of the calorimeter,Cv, = 5.709 kJ/ºC and ΔT =7.995 ºC. Find ΔE for this hydrocarbon in kJ/mol.
dE = Ccal*dT and that is kJ (if you use Ccal in kJ) for 1.578/110.7 mol xample. Convert that to kJ/1 mol.
To find ΔE (change in energy) for the hydrocarbon, we need to use the equation:
ΔE = q + w
Where q is the heat absorbed or released during the reaction, and w is the work done.
In this case, the hydrocarbon is combusting in a bomb calorimeter, which means the volume is constant, and no work is done (w = 0). Therefore, we can simplify the equation to:
ΔE = q
Now we need to calculate q using the equation:
q = Cₖ × ΔT
Where Cₖ is the heat capacity of the calorimeter, and ΔT is the change in temperature.
Given:
Cₖ (heat capacity of the calorimeter) = 5.709 kJ/ºC
ΔT (change in temperature) = 7.995 ºC
Substituting these values into the equation, we can find q:
q = 5.709 kJ/ºC × 7.995 ºC
q = 45.65 kJ
Now, to find ΔE per mole of the hydrocarbon, we need to convert the mass of the hydrocarbon (1.578 g) into moles. We can do this by dividing the mass by the molar mass:
moles = mass / molar mass
moles = 1.578 g / 110.7 g/mol
moles = 0.01424 mol
Finally, to find ΔE per mole, we divide q by the number of moles:
ΔE/mol = q / moles
ΔE/mol = 45.65 kJ / 0.01424 mol
ΔE/mol ≈ 3204.84 kJ/mol
Therefore, the ΔE for this hydrocarbon is approximately 3204.84 kJ/mol.