The structural component that makes detergent dissolve more quickly in water than soap is
Soaps are made up of a fatty acid with a long alkyl chain and a '-COONa' group, while detergents are made up of a long alkyl chain and a '-SO3 Na\(^+\) group. The polar sulfonate in detergents makes them more soluble in hard water than soaps because it's less likely to bind to calcium and other ions in hard water.
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