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To clear up any confusion: water is not a mixture of hydrogen and oxygen; it is a compound. The hydrogen and oxygen are chemically bonded to each other to form a completely different substance.

There are two reasons for the difference in density. First, molecules of elemental hydrogen are only weakly attracted to one another, so hydrogen exists as a gas with a lot of space between molecules. Water molecules are very strongly attracted to one another and so water exists as a liquid with much less space between molecules. Second, a water molecule contains two hydrogen atoms and one oxygen atom. One oxygen atom has about 16 times the mass of a hydrogen atom, so most of the mass of water is actually oxygen. One water molecule is about 9 times the mass of a hydrogen molecule.

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