A stoichiometric mixture is that THEORETICAL perfect balance of air and fuel such that every carbon atom in the fuel burns to CO2, and every hydrogen atom in the fuel burns to H2O, and furthermore there is not one single oxygen molecule in the original air fuel mix left over. This is complete combustion, and extracts all the potential energy available in the fuel. Call this Emax. You simply cannot get any more energy out of the fuel...the first law of thermodynamics says in simple non-technical terms....you can't get something for nothing. The second law says worse than that....you can't break even. In the real world, you will never extract the Emax.
if we introduce a stoichiometrically perfect mixture into a cylinder, compress, and spark it, then peek into the exhaust port right behind the exhaust valve, we will find carbon monoxide, CO. This is incomplete combustion as the energy released by the reaction of carbon to CO is LESS than that of carbon burning to CO2. Therefore, if CO is present in the exhaust, the extraction of energy from the fuel is less than Emax. We will find in the exhaust port NOx's. These form by the combination of oxygen with nitrogen at the high temperatures found in the cylinder. NOx's do not contribute to the energy extracted from the fuel, they suck it off, reducing the power output. We will also find in the exhaust port, unburned or raw fuel, representing potential energy lost. Remember the first law of thermo? If we want power, we have to burn fuel...can't get something from nothing. Unburned fuel is potential power wasted. Unburned fuel results because some fuel molecules did not "meet up" with oxygen molecules in the maelstrom of combustion in the cylinder.
There will be free oxygen in the exhaust stream as well...any oxygen that did not completely react with carbon, and did not react with the unburned fuel, must be accounted for, less whatever combined with nitrogen.
Most persons on this site want power...what to do?
Richen the mixture. This introduces relatively more fuel molecules than oxygen in the cylinder, and statistically, there is a higher probability that some of these fuel molecules will meet up with the oxygen molecules that escaped in the preceeding example. Some of this fuel will burn, producing more energy that before, but alas, less than Emax. Remember the second law... can't break even nohow. Call this energy E rich. A rich mixture also has the following effects. Fuel droplets vaporizing suck up heat, cooling the cylinder and lowering the combustion temperature. Less NOx's are formed at lower temperatures, reducing the loss of energy due NOx formation. A look in the exhaust port will find higher unburned fuel, less free oxygen, lower NOx, and who knows what the CO will do, and who cares?
For completeness, let's look at the case of leaning the mixture.
By leaning the mixture, we reduce the fuel and introduce relatively more oxygen molecules than fuel molecules in the cylinder. Statistically, there is a higher probability that an oxygen molecule will find one of those fuel molecules that escaped in the stoichiometric example. Then a higher percentage, but not higher quantity, of fuel molecules will be burned relative to stoichiometric, producing a cleaner exhaust. Energy extracted from the fuel is less than Emax, or Erich, because we deliberately introduced less fuel into the cylinder. Remember the first law? Can't get more power by burning less fuel.
A stoichiometric fuel air ratio depends on the proportion of carbon and hydrogen in the fuel. Different fuel composition, such as methanol blends will change stoichiometry. It should be noted that 10% methanol will require a different stoichiometric ratio than, let's say...20%.
In this treatise, I emphacized placing the exhaust gas analyzer right behind the exhaust valve. This is because exhaust products can react in the exhaust pipe and mufflers, so what comes out of the mufflers is not necessarily what comes out of the cylinder. Unburned fuel, burning in the exhaust system, produces the "crackles" we hear.
The third law of thermodynamics states in simple non-technical terms, ... that's the way things are, you might as well get used to it.