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Acids and bases are key components of the chemistry of life. For our purposes, we can consider an acid to be any chemical that, when dissolved in water, increases the concentration of hydrogen ions (H+) of the solution. (Actually, a free hydrogen ion immediately reacts with a water molecule, H2O, to form a hydronium ion, H3O+, but the effect is the same.) A base is any chemical that, when dissolved in water, increases the concentration of the hydroxide ion, OH-.
In pure water, only a tiny percentage of water molecules dissociate to form hydrogen ions and hydroxide ions. In any aqueous solution, including pure water, the product of the concentrations of the hydrogen and hydroxide ions is 10-14.