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I am writing an essay on the chemistry of rocket fuel, and I was wondering what, if any, would be a commonly accepted value for the actual yield of the reaction between hydrogen, $\ce{H2},$ and oxygen, $\ce{O2}.$ I would also love it if you could cite some sources so I can find more information on this exothermic reaction:
$$\ce{H2 + O2 -> H2O + heat}$$
The equilibrium constant for the reaction $\ce{2H2 + O2 <=> 2H2O}$ is colossal, equal to $\mathrm{2.4 \times 10^{47}}$ at $\mathrm{500\ K}$ (source). This would ensure virtually 100% yield for the combustion of a stoichiometric mixture of oxygen and hydrogen in equilibrium conditions. However, a rocket engine is a reaction vessel that is far from equilibrium, and therefore oxygen could remain unreacted. This is in fact a problem, as it could damage the engine at its operating temperature. This, among other reasons, is why oxygen/hydrogen mixtures for rocket engines are actually very hydrogen-rich, containing up to twice the stoichiometric amount of hydrogen required.
So in practice, taking everything into account, rocket engines running on oxyhydrogen fuel are designed to have a practically 100% combustion yield based on the limiting reagent, oxygen, while possessing a substantial excess of hydrogen fuel. There is a strong engineering pressure to maximise energy output by ensuring the oxygen is completely consumed; unreacted oxygen is a waste of lift capacity, storage space, materials, cost, etc.
