Explain the mechanism of the cleansing action of soaps

Explanation

Soaps are sodium salts of higher fatty acids such as stearic acid.
`underset("Sodium Stearate (Soap)")(C_(17)H_(35) COO^(-) Na^+) overset(H_2 O)hArr underset("Stearate ions")(C_(17) H_(35) COO^(-)) + Na^+`
The anionic part or sterate ion `(-COO^-)` is hydrophillic nature and thus has a great affinity for water. On the other hand, the hydrocarbon part `(C_2 H_(35)^-)` is hydrophobic in nature and thus has a great affinity for oil etc.

When soap is dissolved in water, and the resulting solution acts on oil present on dirty cloth, the anions `(C_(17) H_(35) COO^-)` form micelles encapasulating oil inside. These micelle are removed by rinsing with water forming oil in water type emulsion. The freed dirt either settle down or is washed away by water.