Originally Posted By: kschachn
Any time you take one compound, dissociate it, and turn it back into the same compound you're going to lose energy since nothing is 100% efficient.
Ding ding ding ding ding!
First law of thermodynamics - conservation of energy. If you start with water and add enough energy to get hydrogen and oxygen, when you burn the hydrogen with oxygen, you will get no more energy out than you put in to it.
And, since you're burning the hydrogen in a heat engine, you get the intrinsic energy losses (dictated by the second law of thermodynamics) so that the amount of work (useful engine output) will be significantly less than the electrical energy put in to the system to generate the hydrogen.
Now, if you created the hydrogen and used it in a fuel cell (a hydrogen powered battery), you'd get closer to the same amount of energy out that you put in to it.
Fuel cell technology isn't ready for this quite yet - putting the electrical energy into a battery is more efficient, and then you use it to power an electric car.
tl;dr: The first and second laws of thermodynamics argue that this cannot work as advertized.