Ah, see, soap's fatty acid tail grabs onto dirt, its hydrophilic head loves water—so it forms micelles and washes grime away. But in hard water, those calcium ions form a scummy precipitate with soap, making it fail. Detergents have sulfonate groups that don't react with hard water ions, so they work fine. Reminds me of my borewell water—full of salts, just like hard water. When I used soap to wash my hands after tending the chillies, it left that same sticky film; detergents for my clothes never betrayed me like that.
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