Stoichiometric Air-Fuel Ratio (Octane Combustion)
Stoichiometric Air-Fuel Ratio (Octane Combustion)
The stoichiometric air-fuel ratio (AFR) is the exact mass of air needed to completely burn a given mass of fuel with no leftover fuel or oxygen, and for gasoline engines it is one of the most important numbers in the whole combustion system — it is the target the engine control unit constantly tries to hit by metering fuel injection against measured airflow. Running rich (more fuel than stoichiometric) wastes fuel and increases emissions of unburned hydrocarbons and carbon monoxide, while running lean risks higher combustion temperatures, NOx formation, and in extreme cases engine knock or misfire — so this ratio, derived here from the balanced combustion equation for octane (C8H18), anchors the whole fuel control strategy.
The stoichiometric air-fuel ratio is AFR = (n_O2·M_O2)/(x_O2·M_fuel), built from the balanced combustion equation and the oxygen content of air. where n_O2 is the moles of O2 required per mole of fuel from the balanced equation, M_O2 and M_fuel are the molar masses of oxygen and fuel, and x_O2 is the mass fraction of oxygen in air.
Inputs
n_o2 := 12.5=12.5
M_o2 := 0.032 kg/mol=0.03 kg/mol
M_fuel := 0.114 kg/mol=0.11 kg/mol
x_o2 := 0.232=0.23
Converting the mole-based stoichiometry into a mass basis, and then dividing by the fraction of air that is actually oxygen, gives the total mass of air (not just the oxygen in it) needed to completely burn one unit mass of fuel.
AFR := (n_o2·M_o2)/(x_o2·M_fuel)=15.12
Results
The result, close to 15.1 kg of air per kg of fuel, lines up well with the widely quoted stoichiometric AFR of about 14.7 for gasoline (the small difference reflects gasoline being a blend rather than pure octane). This is the number a fuel injection system targets at "lambda = 1" operation, and modern engines use an oxygen sensor in the exhaust to trim fuel delivery in real time to hold AFR at this value for the catalytic converter to work efficiently. Deviating from this stoichiometric AFR is done deliberately in some conditions — rich for cold start or full power, lean for fuel economy in some engines — but always as a controlled offset from this reference value.
Assumptions & limitations
- Complete combustion to CO2 and H2O assumed (no dissociation or incomplete burning).
- Fuel treated as pure octane (C8H18); real gasoline is a blend with a slightly different AFR.
- Air composition assumed standard dry air (23.2% O2 by mass).
- Does not account for exhaust gas recirculation or humidity in the intake air.