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Soap is a sodium salt or potassium salt of long-chain fatty acids having cleansing properties when dissolved in water. It consists of two parts – one hydrophilic polar part which interacts with water and anotherhydrophobic non-polar part that consists of a long fatty acids chain, which interacts with dirt particles by dispersion forces.

They form a micelle while trapping the dirt in the middle. This forms a colloidal solution and dirt can be rinsed off.

The non-polar tail of sodium acetate comes from acetic acid$\left({\mathrm{CH}}_3\mathrm{COOH}\right)$while that of sodium stearate comes from stearic acid$\left({\mathrm{C}}_{18}{\mathrm{H}}_{36}{\mathrm{O}}_2\right)$.Stearic acid has a longer hydrocarbon tail than acetic acid. So, dispersion forces will be greater in stearic acid and cleansing action will be better.

Hence, sodium stearate is a better soap than sodium acetate because of more dispersion forces of the long hydrocarbon chain.