On dissolving sugar in water at room temperature it feels cool to the touch. Under which of the following cases, dissolution of sugar will be most rapid?

Powdered sugar in Hot Water

The correct answer is Option (4) → Powdered sugar in Hot Water.

The rate of dissolution of a solid in a liquid depends on several factors:

Surface area of the solute: The greater the surface area, the faster the solute will dissolve. Powdered sugar has more surface area than sugar crystals, making it dissolve more quickly.

Temperature of the solvent: An increase in temperature generally increases the kinetic energy of the molecules in the solvent. This higher energy causes the water molecules to move faster, interact more with the sugar molecules, and dissolve the sugar more quickly. Hot water dissolves sugar faster than cold water

Comparing the options:

Sugar Crystals in Cold Water: The dissolution will be slow because sugar crystals have a smaller surface area, and cold water provides less energy for dissolving.

Sugar Crystals in Hot Water: This will be faster than in cold water due to the higher temperature, but still slower compared to powdered sugar due to the larger crystal size.

Powdered Sugar in Cold Water: While powdered sugar has more surface area, the cold temperature will slow down the dissolution process compared to hot water.

Powdered Sugar in Hot Water: This option combines the greater surface area of powdered sugar and the higher temperature of hot water, making dissolution the most rapid.

Therefore, Powdered sugar in hot water will result in the most rapid dissolution of sugar.