Ian –
Your last question is the correct answer.
Two atoms of Hydrogen combine with one of Oxygen to create a molecule of H20 (please forgive the full-size rather than correct subscript 2!). I.e., a molecule of water.
The two gases, which are elements, are not "destroyed". Elements are formed of atoms that cannot be destroyed except by nuclear processes. Instead, chemical combinations simply stick the elements together to form compounds with, usually, physical and chemical characteristics vastly different from those of the individual elements. This is important, as I will show.
For example, in our case here:
– Hydrogen and Oxygen are colourless, odourless, taste-less gases, of quite different densities.
– Hydrogen is flammable but does not intrinsically support combustion (though it would certainly add to a fire).
– Oxygen is not flammable, but certainly supports combustion (high-rate oxidation that emits heat).
– Hydrogen burns in the presence of Oxygen, by the two gases combining to form water….
… which is a colourless, odourless, taste-less, fairly dense liquid that is neither flammable nor supports combustion!
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Since both gases can be derived by electrolysing water the nett trade is neutral, since the exhaust from them is water-vapour that merely joins that already in the atmosphere naturally. The total exhaust from an i.c. engine will also contain some Nitrous Oxides, but a science-teacher explained to me that these can be, and are, broken down by catalytic converters using urea – the "Ad-Blue" fluid you see sold in garages.
The problem from any "green" point of view is that water is a deceptively simple compound with some very odd properties and abilities including enormous molecular strength. So though breaking lots of it into worthwhile volumes of Hydrogen and Oxygen by electrolysis produces no awkward by-products, it demands a lot of electricity that has to be generated….. somehow.
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From a Phsyics point of view, it absorbs a certain amount of energy (as electricity) to divorce the hydrogen from the bigamist oxygen, but when that hydrogen is then burnt the chemical reaction repays the energy (as emitted heat). Though the balance is never achieved in practical processes because they can never be 100% efficient.
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There is actually nothing very new in all of this except that using hydrogen as a direct fuel in an i.c. engine has always proven difficult in the past, I believe due mainly to its combustion characteristics. I think the gas mixture compressed in the engine cylinder tends to detonate rather than "simply" burn, but I am not sure of that.
Nor is there anything new in storing hydrogen compressed into cylinders, and oxy-hydrogen rather than oxy-acetylene has long been the better combination for underwater flame-cutting. (The torch is lit before submerging it!)
Safety fears are somewhat specious because a cylinder of hydrogen is not only no more intrinsically dangerous than one of LPG, but leaking hydrogen can be vented to rise and disperse in the atmosphere. LPG and petrol vapour are fairly dense, collecting in low points such as car floor-pans and boat hulls. I think it is also non-toxic, though will suffocate if it displaces the oxygen available. The disadvantage is that hydrogen is odourless so a leak may not be evident, but that could be overcome with a suitable "scent" as is added to the mains supply of odourless methane that is natural-gas.