
Hard water is not water containing dirt or grit. It is water with relatively high concentrations of dissolved calcium and magnesium ions. Ordinary soap molecules have a negatively charged carboxylate “head” and a long oil-attracting hydrocarbon “tail”. In soft water, many soap molecules can surround grease in tiny aggregates, dispersing it through the water; agitation also produces lather more readily.
In hard water, calcium and magnesium ions first combine with the carboxylate heads to form poorly soluble calcium or magnesium soaps. These precipitate as the grey-white soap scum often seen around a bath, and they remove soap molecules that could otherwise surround grease. More soap must therefore be added before enough remains in solution to produce an obvious lather.
The amount of foam is not a precise measure of cleaning power, but here poor lather does reveal a chemical competition: hard-water ions consume part of the soap. Synthetic detergents commonly use sulfate or sulfonate head groups, whose products with calcium and magnesium are more likely to remain in solution, so they continue working in hard water. “Hardness” describes the water’s ion composition; the water has not literally become harder.
https://www.usgs.gov/water-science-school/science/hardness-water
https://openstax.org/books/chemistry/pages/11-5-colloids
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