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It is a chemical change because you are breaking the water into its elements, hydrogen and oxygen, and it is no longer water.

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Oxidation of ions or neutral molecules occurs at the anode, and the reduction of ions or neutral molecules occurs at the cathode. For example, it is possible to oxidize ferrous ions to ferric ions at the anode:Fe2+

aq → Fe3+

aq + e-

It is also possible to reduce ferricyanide ions to ferrocyanide ions at the cathode:Fe(CN)3-

6 + e- → Fe(CN)4-

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Willard Bayer

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Q: Is electrolysis of water chemical change or physical change?
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