When a fat or oil is heated with sodium hydroxide solution, it is saponified, giving the sodium salts of fatty acids and glycerol. These sodium salts are soap.
(\mathrm{RCOO})_3\mathrm{C_3H_5} + 3\mathrm{NaOH} \longrightarrow 3\mathrm{RCOONa} + \mathrm{C_3H_5(OH)_3}
When saturated salt solution is added, the soap separates and floats, so it can be collected. This is called salting out.
A soap molecule, such as sodium stearate, \mathrm{C_{17}H_{35}COONa}, has a long hydrocarbon chain with a carboxylate group, -\mathrm{COO^-}, at one end.
The hydrocarbon chain mixes easily with oil but not with water, and it is called the hydrophobic part. The -\mathrm{COO^-} part mixes easily with water and is called the hydrophilic part.
Substances whose molecules have both parts gather at the surface of water and lower its surface tension. They are called surfactants.
In water, soap molecules gather in small clusters, with their hydrophobic parts pointing inwards and their hydrophilic parts outwards. These clusters are called micelles.
When soap comes into contact with oily dirt, the hydrophobic parts enter the oil and surround it. The dirt is lifted off the cloth and broken up into small droplets that spread through the water. This action is called emulsification.
Water that contains many calcium and magnesium ions is called hard water. In hard water, soap forms an insoluble scum with these ions and lathers poorly.
2\mathrm{RCOO^-} + \mathrm{Ca^{2+}} \longrightarrow (\mathrm{RCOO})_2\mathrm{Ca}
Fatty acids are weak acids, so soap solution is weakly basic. For this reason, soap is not suitable for washing wool and silk, which are damaged by bases.
Synthetic detergents, such as sodium alkylbenzenesulfonates, have a sulfonate group, -\mathrm{SO_3^-}, as their hydrophilic part instead of a carboxylate group.
They are salts of strong acids, so their solutions are almost neutral, and their calcium and magnesium salts dissolve in water. As a result, they work well in hard water and can be used to wash wool and silk.
Early synthetic detergents had branched chains that bacteria could not easily break down, and they left foam on rivers. Detergents with straight chains, which bacteria break down more easily, are now used.