Problem#9: Consider the fuel octane (the main component of gasoline) and its combustion reaction
2C8H18(l) + 25O2(g) → 16CO2(g) + 18H2O(l)
ΔHo = -10,942 kJ
The “fuel value” of a fuel (unit kJ/g) is defined as the energy released when 1 g of the fuel undergoes combustion. Calculate the fuel value of octane. (MM of C8H18 = 114 g/mol)
Convert 1 g of octane to moles. Then multiply that by (1/2)*10,942 kJ, becasuse the reaction as written consumes 2 moles of octane.
To calculate the fuel value of octane, we need to first determine the amount of octane in moles that is required for the combustion reaction. Then, we can use the given enthalpy change to calculate the energy released.
Step 1: Convert the mass of octane to moles.
Given the molar mass of octane (C8H18) = 114 g/mol.
Since we want to determine the fuel value for 1 g of octane, divide the molar mass by the mass:
1 g / 114 g/mol = 0.00877 mol.
Step 2: Use the balanced combustion equation to calculate the energy released.
Looking at the balanced combustion equation:
2C8H18(l) + 25O2(g) → 16CO2(g) + 18H2O(l)
We can see that for every 2 moles of octane that undergo combustion, 16 moles of CO2 and 18 moles of H2O are produced. Therefore, for the 0.00877 mol of octane we calculated earlier, the moles of CO2 and H2O produced will be proportional.
Moles of CO2 = (16/2) × 0.00877 mol = 0.07016 mol
Moles of H2O = (18/2) × 0.00877 mol = 0.098985 mol
Step 3: Calculate the energy released.
The enthalpy change, ΔHo, for the combustion reaction of octane is given as -10,942 kJ.
The energy released per mole of octane combusted can be calculated by dividing the given enthalpy change by the moles of octane:
Energy released per mole = ΔHo / moles of octane combusted
Energy released per mole = -10,942 kJ / 0.00877 mol
Finally, to calculate the fuel value (energy released per gram of octane), we divide the energy released per mole by the mass of octane which is 1 gram:
Fuel value = (ΔHo / moles of octane combusted) / mass of octane
Fuel value = (-10,942 kJ / 0.00877 mol) / 1 g
Calculating this value will give you the fuel value of octane in kJ/g.