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The above video demonstrates the Peebco Energy Group's capability to create hydrogen fuel on remote locations and on demand.

As one can witness from the video, the amount of hydrogen extracted from a gallon of water can be found very easily using the molecular weight of H20 (water), Hydrogen and Oxygen, along with mass conservation. The molecular weight of water is 2 H (molecular weight 1) + 1 Oxygen (Molecular weight 16) for a total of 18. And for every Molecule of water converted, we would get 2 Molecules of Hydrogen. 

So, now the question is, how many molecules of water are there in a gallon of water? The density of water is 1g/(cm3) so in 1 gallon of water (about 3.785 Liters or 3785 cm3) the mass of the water is, 3785g. 1 mole of 6.02x1023 molecules of water is equal has the mass in grams equal to the molecular weight or 18 grams per mole. As a result 3,785 grams corresponds to about 1.265 x 1026 molecules of water. 

Consequently, if every single water molecule was converted into Hydrogen we would get twice as much Hydrogen as we had of water, or 2.53 x 1026 molecules of hydrogen. However, since hydrogen is a diatomic molecule, meaning that the hydrogen that we talk about is H2, we would get 1.265 x 1026 molecules of hydrogen. at 1 atmospheric pressure and 273K, 1 mole of hydrogen fills approximately 22.4L of volume. Thus, 1.265 x 1026 molecules or about 210 moles would fill 4,707 Liters of volume.

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