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

Options

A. Sugar crystals in cold water
B. Sugar crystals in hot water
C. Powdered sugar in cold water
D. Powdered sugar in hot water

Explanation

To determine under which conditions the dissolution of sugar in water will be most rapid, we need to analyze the options provided. The key factors that affect the rate of dissolution include temperature of the solvent (water) and the surface area of the solute (sugar).

### Step-by-Step Solution:

1. **Understanding the Dissolution Process**:
- When sugar is added to water, the sugar molecules interact with water molecules. The rate at which sugar dissolves depends on how quickly these interactions can occur.

2. **Effect of Temperature**:
- Higher temperatures increase the kinetic energy of the water molecules. This means that the molecules move faster and collide with the sugar particles more frequently, leading to a quicker dissolution.
- Conversely, lower temperatures result in slower-moving water molecules, which decreases the rate of dissolution.

3. **Effect of Surface Area**:
- The form of sugar also plays a role. Powdered sugar has a larger surface area compared to sugar crystals. A larger surface area allows more water molecules to interact with the sugar at the same time, which increases the dissolution rate.

4. **Analyzing the Options**:
- **Option A**: Sugar crystal in cold water - slow dissolution due to low temperature and larger sugar crystals.
- **Option B**: Sugar crystal in hot water - faster than cold water but still limited by the size of sugar crystals.
- **Option C**: Powdered sugar in cold water - faster than sugar crystals in cold water due to increased surface area, but still limited by low temperature.
- **Option D**: Powdered sugar in hot water - this option combines both high temperature and increased surface area, leading to the fastest dissolution rate.

5. **Conclusion**:
- The most rapid dissolution of sugar will occur when using powdered sugar in hot water. Therefore, the correct answer is **Option D: powdered sugar in hot water**.