Several chemical principles must be understood to understand how hydrogen storage and fuel cells work.

Water can demonstrate
both forms of bonding. Generally water is covalently bonded where electrons
are shared. The atoms are held together because all the same electrons
are surrounding the different nucleus. In water, the oxygen attracts the
electrons more than the hydrogen. This causes the hydrogen end of the molecule
to be slightly positive and the oxygen end to be slightly negative. A molecule
with charged ends, or poles, is called polar.
Small amounts
of water become so charged that the electrons totally leave the hydrogen
and go to the oxygen leaving OH- and H+ ions. Ions are atoms
with a charge. These are still bonded but ionically because one of hydrogen's
electrons has been traded to the OH-. The OH- has an extra
electron making the charge negative, and H+ is missing an electron
making the charge positive. These opposite charges attract like the opposite
ends of a magnet; this is called ionic bonding.

However, the oxidation half of the reaction can be separated from the reduction half of the reaction. The electron trade still must occur, so the locations of each half-reaction is connected by a wire and some kind of porous material also connects the two half reactions to allow for the positive ions to flow to keep this circuit running. If the two reactions produce more stable products an electric flow will occur. At one end with an electrode called the anode, the reducing agent is oxidized and produces an electron that goes across the wire and produces a positive ion that passes through the porous material. At another electrode (the cathode), the electrons are added to the oxidizing agents which produce negative ions.
The water is divided by the following reactions:

Here the water at the anode is oxidized because it loses electrons. Water at the cathode takes these electrons and becomes reduced. The total reaction shows the products are hydrogen and oxygen gas and the H+ and OH- combine back to form more water.
This process is commonly 65-67% efficient, but 80-85% efficiency is possible. Unfortunately, cryogenically cooling the gas into a liquid is very energy intensive and makes the entire process of electrolysis, cooling, and combusting very inefficient (25% efficiency).
The electric energy is now stored in the chemical energy of the bonds in hydrogen and oxygen. This is how the energy can be stored from any electric generating source (solar cells, windmills, dams, fossil fuel, or anything else that makes electricity). The energy can be retrieved from the hydrogen and oxygen in two different ways. One is by fuel cells where basically the electrolysis process is reversed. The other way is combustion.
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Notice, the only product is water and energy. The only negative is that the great energy produced, heats the surrounding air to make nitrogen oxides. This process is simple, but fuel cells are more controlled and produce a higher efficiency.
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