When a 3.10g sample of liquid octane (C8H18) is burned in a bomb calorimeter, the temperature of the calorimeter rises by 26.8∘C. The heat capacity of the calorimeter, measured in a separate experiment, is 6.30kJ/∘C . Determine ΔErxn for the combustion of octane in units of kJ/mol octane.
http://www.chem.hope.edu/~polik/Chem345-2000/bombcalorimetry.htm
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dE = -CvdT
dE = -(6.30)(26.8) = kJ for (3.10/molar mass C8H18). Convert that to kJ/mol.
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To determine ΔErxn for the combustion of octane (C8H18), we can use the equation:
ΔErxn = qrxn
where qrxn is the heat absorbed or released during the reaction.
First, we need to calculate the heat absorbed by the calorimeter (qcal) using the equation:
qcal = Ccal * ΔT
where Ccal is the heat capacity of the calorimeter and ΔT is the change in temperature.
Given:
Ccal = 6.30 kJ/∘C
ΔT = 26.8∘C
Calculating qcal:
qcal = 6.30 kJ/∘C * 26.8∘C
qcal = 168.84 kJ
Next, we can calculate the heat released during the combustion of octane (qrxn). Since the entire sample of liquid octane (3.10 g) is burned, we need to convert it to moles. To do this, we'll use the molar mass of octane (C8H18), which is:
Molar mass of octane = (8 * atomic mass of carbon) + (18 * atomic mass of hydrogen)
The atomic masses of carbon and hydrogen can be found on the periodic table.
Calculating the molar mass of octane:
Molar mass of octane = (8 * 12.01 g/mol) + (18 * 1.01 g/mol)
Molar mass of octane = 114.23 g/mol
Now we can convert the 3.10 g of octane to moles:
moles of octane = 3.10 g / 114.23 g/mol
moles of octane = 0.0271 mol
Using the equation qrxn = qcal, we can determine ΔErxn:
qrxn = qcal = 168.84 kJ
Finally, to calculate ΔErxn per mole of octane, we divide qrxn by the number of moles:
ΔErxn = qrxn / moles of octane
ΔErxn = 168.84 kJ / 0.0271 mol
ΔErxn ≈ 6229.52 kJ/mol octane
Therefore, ΔErxn for the combustion of octane is approximately 6229.52 kJ/mol octane.
To find ΔErxn for the combustion of octane (C8H18), we need to calculate the heat released by the combustion reaction.
First, we need to determine the heat transferred to the calorimeter (qcalorimeter) using the formula:
qcalorimeter = Ccalorimeter * ΔT
where Ccalorimeter is the heat capacity of the calorimeter and ΔT is the change in temperature.
Given:
Ccalorimeter = 6.30 kJ/∘C
ΔT = 26.8 ∘C
Substituting these values into the formula, we get:
qcalorimeter = 6.30 kJ/∘C * 26.8 ∘C
qcalorimeter = 168.84 kJ
Next, we need to convert the mass of octane (3.10g) to moles.
The molar mass of octane (C8H18) can be calculated by summing the atomic masses of its constituent elements:
Molar Mass of octane = (8 * atomic mass of C) + (18 * atomic mass of H)
= (8 * 12.01 g/mol) + (18 * 1.01 g/mol)
= 114.23 g/mol
Using the molar mass, we can calculate the number of moles of octane:
moles of octane = mass of octane / molar mass of octane
= 3.10g / 114.23 g/mol
moles of octane = 0.027 mol
Finally, to find ΔErxn in units of kJ/mol, we divide the heat transferred to the calorimeter (qcalorimeter) by the number of moles of octane:
ΔErxn = qcalorimeter / moles of octane
= 168.84 kJ / 0.027 mol
ΔErxn ≈ 6257.78 kJ/mol octane
Therefore, ΔErxn for the combustion of octane is approximately 6257.78 kJ/mol octane.