It is true that hydrogen is an explosive gas, and it also needs oxygen to burn. But the key point lies in this question: What is burning? The answer is that burning is the process of reacting with oxygen to produce energy. (Well, to be really pedantic, it may be possible to use other gases such a Fluorine, but oxygen is so readily available, we usually mean oxygen.)
The burning process in the case of oxygen and hydrogen is relatively simple. If you put together suitable volumes of hydrogen and oxygen and provide a spark to start the reaction, one oxygen atom will combine with two hydrogen atoms, and will release energy in the process. The energy gets released in the form of molecular kinetic energy, and since the motion is random, this is exactly what we call heat energy. The gases heat up, and as all expanding gases do, they expand. That fast expansion of hot gases is what we call "an explosion".
What is the result of this burning/explosion? The answer is simple, if the proportions were right (one volume of oxygen for two volumes of hydrogen gas) all you get is water! Thus, water is _already burnt_. It is the "ashes" of hydrogen after it has burned.
If you wish to burn it again, you have to separate oxygen and hydrogen. But, to do that, you need to supply as much energy as is released when the burning occurred. This is possible by electrolysis.
Answered by: Yasar Safkan, Ph.D., Software Engineer, GVZ., Istanbul, Turkey
You mention that H2 is explosive. What does this mean? It means that the H atoms have a lot of potential energy in their current state- they are not very stable. If those same atoms are attached to an oxygen atom, they are much more stable, and have much less potential energy. By the law of conservation of energy we know that when the hydrogen atoms switch from a high potential energy state to a low energy state, that energy has to go somewhere, and in fact this is the source of the light, heat, sound, etc. of the explosion you mention. A chemist would say this chemical change is exothermic (heat out).
Now picture those hydrogen atoms in a water molecule. They are already in a stable state, and do not posess the potential energy of H atoms attached to each other. They do not explode on contact with oxygen because they don't have energy to give off.
A good analogy is to imagine 2 rocks of exactly equal properties; one at the top of a hill and one at the bottom. You nudge the one at the top of the hill and notice it rolls away down the hill. You walk down and nudge the other rock and notice it doesn't roll away. Why not? It's already at the bottom!
Answered by: Rob Landolfi, Science Teacher, Washington, DC
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'I believe there is no philosophical high-road in science, with epistemological signposts. No, we are in a jungle and find our way by trial and error, building our road behind us as we proceed.'