Assertion (A) : Synthetic detergents can lather well in hard water. Reason (R) : Synthetic detergents form soluble calcium and magnesium salts with hard water.

Assertion is correct: synthetic detergents do lather well in hard water because their ionic head groups do not give insoluble curdy precipitates with Ca2+ and Mg2+ as soaps do. Textbook explanation states detergents (sodium salts of sulphonic acids or similar) have charged ends that do not form insoluble precipitates with calcium and magnesium ions, so they remain effective in hard water [1]. Additional sources explain that the anionic sulfonate/sulfate groups of many detergents form water‑soluble salts with hardness ions (unlike fatty‑acid carboxylates of soap), allowing detergents to maintain lathering and cleaning action in hard water [2]. Thus R is a true and correct explanation of A.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 4: Carbon and its Compounds > Activity 4.12 > p. 76
2. [2] https://www.sciencedirect.com/topics/earth-and-planetary-sciences/synthetic-detergent