Why do engineers deliberately run most chemical rocket engines fuel-rich instead of stoichiometrically balanced?

Answer

Lighter exhaust molecules ($ ext{CO}$ and $ ext{H}_2$) resulting from the fuel-rich burn yield a larger efficiency gain via higher exhaust velocity.

Running fuel-rich results in lighter combustion products like carbon monoxide and diatomic hydrogen. The efficiency gain from having this lighter exhaust stream outweighs the penalty of ejecting some unburned fuel.

Why do engineers deliberately run most chemical rocket engines fuel-rich instead of stoichiometrically balanced?

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