I was thinking that a hybrid rocket could be made using hydrogen peroxide and activated charcoal or some other carbon source.
Step 1: Decompose hydrogen peroxide to steam and oxygen, as in a monopropellant H₂O₂ rocket. This step is exothermic.
2H₂O₂ → 2H₂O + O₂
Step 2: Have the superheated steam flow over the finely divided carbon, which is the "water gas" reaction and is endothermic:
H₂O + C → H₂ + CO
Step 3: The oxygen produced by the hydrogen peroxide incompletely burns the water gas, which should be exothermic.
2H₂ + 2CO + O₂ → x(H₂O + CO) + y(H₂ + CO₂), where x + y = 2
Total reaction: 2H₂O₂ + 2C → x(H₂O + CO) + y(H₂ + CO₂). This is certainly exothermic in total, and also favored entropically.
Depending on the kinetics, either reaction x or reaction y would dominate; I'm hoping y will, as having lots of diatomic hydrogen would be good for specific impulse.
According to the article on water gas, the carbon bed has to be heated red-hot. I'm hoping that having the steam be hot and the carbon be porous would be sufficient. I'm also wondering if the oxygen would react right there in the chamber, or if it'd flow out the back and need to be ignited. Small amounts of catalysts might be mixed in with the carbon as well. You might even be able to just coat the carbon with silver catalyst so the decomposition of hydrogen peroxide heats the coal bed, but replacing the catalyst every time would probably be expensive.
The primary advantage of such a rocket would be that the oxidizer is relatively nontoxic and nonreactive; the fuel is safe enough you could eat it like a biscuit; any fire caused by an oxidizer tank leak or rupture could be far more easily contained; and design of the rocket should be fairly simple, involving just placing a fuel biscuit in the exhaust of a H₂O₂ monoprop rocket; this could theoretically supercharge the peroxide-using USAF Astronaut Maneuvering Unit.
Has this idea been tried before by serious rocketers? What are the numbers (enthalpy, Gibbs free energy, calculated specific impulse, and so on)? How can I make sure the carbon biscuit is porous enough that it reacts easily and completely with the steam and oxygen, yet not so porous that it just gets shredded and blasted through the exhaust by the pressure?