Convert 1 gallon to liters to mL, then use density to convert to grams and divide by molar mass to convert to moles.
Then moles x 5.48E3 kJ/mol = ??
Then moles x 5.48E3 kJ/mol = ??
1. Start by calculating the mass of octane in grams:
- Density of octane = 0.703 g/mL
- 1 gallon = 3.785 L
- Therefore, the mass of octane in one gallon = 3.785 L * 0.703 g/mL = 2.66 g/gal
2. Convert the mass of octane in grams to moles, using the molar mass of octane:
- Molar mass of octane (C8H18) = (12.01 g/mol x 8) + (1.01 g/mol x 18) = 114.23 g/mol
- Moles of octane in one gallon = 2.66 g/gal / 114.23 g/mol = 0.0233 mol
3. Finally, calculate the heat liberated per gallon by multiplying the moles of octane by the enthalpy change:
- Heat liberated per mole = -5.48 x 10^3 kJ/mol
- Heat liberated per gallon = (0.0233 mol) * (-5.48 x 10^3 kJ/mol) = -127.64 kJ/gal
Therefore, approximately 127.64 kilojoules of heat are liberated per gallon of octane burned.