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I know that soap molecules have a hydrophilic end and a hydrophobic end which attract to water and oil respectively. However, does a chemical reaction take place?

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Chemical 'reactions' are normally defined by changes in 'bonding'. Related to soap micelles, for the micelle to exist and have integrity enough to be characterized from a situation where they did not previously exist, some 'bonding' must come into being. That bonding is normally described as 'London Forces' or 'Vander Waals Bonds' or 'Hydrogen bonding' or 'electrostatic' interactions. Since equivalent concentrations produce equivalent results, the micelle formation is also reproducible. In the purest sense this does imply that soap micelle formation is a chemical reaction.

The question is more philosophical than anything.

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