Step 1: Understanding the Concept:
Both are cleansing agents, but they interact differently with the minerals present in hard water.
Step 2: Detailed Explanation:
Synthetic detergents are generally more useful than ordinary soaps.
The primary reason is their behavior in hard water.
Hard water contains dissolved Calcium (\(\text{Ca}^{2+}\)) and Magnesium (\(\text{Mg}^{2+}\)) ions.
When soap is used in hard water, it reacts with these ions to form an insoluble, sticky white precipitate called 'scum'. This wastes soap and hinders cleaning.
Detergents, on the other hand, do not form insoluble precipitates with calcium and magnesium ions.
Therefore, detergents lather well and maintain their cleansing action even in hard water.
Step 3: Final Answer:
Detergent is more useful because it can be used for cleaning even in hard water, without forming scum.