Why does hard water not form lather with soap? What advantages does soap have over detergents.

Hint: Soaps are triacylglycerols. They are esters of fatty acids with glycerol. Detergents contain a hydrophilic polar group and a long hydrophobic non polar chain.
We can use both soaps and detergents for cleansing purposes.

Complete answer:
Hard water contains magnesium and calcium cations. When We add soap to hard water, We observe the formation of curdy white precipitate. We can call the curdy white precipitate as scum. This precipitate is magnesium or calcium salt of the organic acid. The formation of this precipitate decreases the effectiveness of hard water so that We do not get lather when We add soap to hard water. Due to this, the cleansing action of the soap will not be proper.
To obtain lather, We should add soap to soft water. Or We should add detergent to either hard or soft water. Detergent works in soft water as well as in hard water. Soap works only in soft water.
Due to this, We should prefer detergent over soap. This is because detergents form lather even in hard water and the cleansing power of detergents is better as compared to that of soaps.
We need not use expensive vegetable oil to prepare detergents. For the preparation of detergents, We need petroleum hydrocarbons.

Note: We can also use detergents in acidic solutions. If We add soap to an acidic solution, We will observe that free fatty acids will get precipitated.
Impurities from soft water can be easily removed by a simple boiling method but it’s not possible in hard water.