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Either distillation or deionization (reverse osmosis) will produce fairly
pure water.
as the names imply deionized water is water that has been passed through a column or membrane to remove ions present. If
it is of the type used in homes, it is not truly a de-ionizer, removing all
ions, but rather an ion exchange column that exchanges polyvalent ions such as Mg++ and Ca++ for Na+ ions. A de-ionizing column will not remove nonionic organic substances from the water.
In contrast, distilled water is actually boiled in a still and the
condensate collected and distributed. Distillation removes both ionic and
nonionic organic contaminants.
The uses of deionized water are many and varied, often having application in scientific experimentation such as when very pure chemical reaget solutions