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Could there be some kind of process, a kind of "retrograde electrolysis" where hydrogen gas (or in some other form) and oxygen gas (or in some there form) are mixed with required energy to combine to form water as a byproduct?

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Indeed, it's called combustion! When you burn hydrogen and oxygen gas, the reaction is:

$$\ce{2H2_{(g)} + O2_{(g)} -> 2H2O_{(g)} + energy}$$

Basically, you could see the former U.S. space shuttle as a large machine that turns hydrogen and oxygen into water. (Note: the space shuttle used liquid hydrogen and oxygen, but otherwise the principle and formula is exactly the same)

Since the Gibbs free energy of the forward reaction is negative ($-242\textrm{ kJ/mol}$), you don't need to add energy to the system, the reaction is spontaneous (mind you, you generally need a spark to ignite the combustion because there's a kinetic barrier to the reaction called the energy of activation).

The reverse reaction, water to hydrogen and oxygen, has a positive Gibbs free energy, so you need to add energy in the form of electricity to the system to make the reaction happen.

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  • $\begingroup$ Does a fuel cell have a similar process? $\endgroup$
    – user128932
    Commented Jul 15, 2014 at 2:03
  • $\begingroup$ The overall equation is the same but the mechanism is different. A platinum catalyst splits H2 into 2H+ (protons) and 2e- (electrons). A polymer membrane allows only the protons to pass through, forcing the electrons to take another route, creating an electric circuit. When the protons and electrons meet again they combine with oxygen from the air, giving water. $\endgroup$ Commented Jul 15, 2014 at 17:33
  • $\begingroup$ Could liquid hydrogen and liquid oxygen SOMEHOW be combined in some energetic reaction so that one byproduct is water? Or is this science fiction? $\endgroup$
    – user128932
    Commented Aug 9, 2014 at 3:36
  • $\begingroup$ It sure can, the U.S. Space Shuttle's rockets used liquid hydrogen and liquid oxygen as fuel. I realize I implied the shuttle used gaseous fuel, I've corrected my answer above, sorry about that. $\endgroup$ Commented Aug 9, 2014 at 13:01
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While the combustion is a correct answer, if you are looking for "retrograde electrolysis" than you best check out hydrogen fuel cells where are real electrochemical reaction, opposite of water splitting, takes place and produce directly electricity: http://en.wikipedia.org/wiki/Fuel_cell

There are different types, even different fuels, but the basic idea is the same: the oxidation and reduction process is separated by a membrane and the two reactions takes place on separate electrodes.

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