Asked by: Rudiger Jonser, by email
Hard water contains calcium and magnesium ions. These react with the sodium stearate molecules in soap to give calcium or magnesium stearate, which forms an insoluble scum but at least rinses away. Artificially softened water swaps calcium and magnesium ions for sodium and potassium ions, which doesn't precipitate out so easily and instead clings to the slightly charged surface of your skin. Naturally soft water has no ions and rinses away soap the most effectively.
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