Question
Why hard water does not form lather with soap? What advantage has soap over detergents?

Answer

It is because $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ ions present in hard water react with soap to form $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ salts of fatty acids which are insoluble in water.
$\text{Ca}^{2+}+\text{C}_{17}\text{H}_{35}\text{COONa}\xrightarrow{\ \ \ \ \ \ \ \ \ \ }(\text{C}_{17}\text{H}_{35}\text{COO)}_2\text{Ca}+0\text{Na}^+$
$\text{Mg}^{2+}+\text{C}_{17}\text{H}_{35}\text{COONa}\\\xrightarrow{\ \ \ \ \ \ \ \ \ }(\text{C}_{17}\text{H}_{35}\text{COO})_2\text{Mg}+2\text{Na}^+$
Advantage of soap over detergents: Soaps are biodegradable whereas detergents are non biodegradable.

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