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 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 will be most rapid, we need to analyze the options provided based on the principles of solubility and reaction rates.

### Step-by-Step Solution:

1. **Understanding the Dissolution Process**:
- When sugar dissolves in water, it absorbs heat from the surroundings, making the solution feel cool to the touch. This indicates that the dissolution process is endothermic.

2. **Analyzing the Options**:
- We have four scenarios to consider:
1. Sugar crystals in cold water
2. Sugar crystals in hot water
3. Powdered sugar in cold water
4. Powdered sugar in hot water

3. **Surface Area Consideration**:
- Sugar crystals have a smaller surface area compared to powdered sugar. A larger surface area allows for more contact with water, leading to faster dissolution.
- Therefore, powdered sugar will dissolve faster than sugar crystals due to its greater surface area.

4. **Temperature Consideration**:
- Since the dissolution of sugar is an endothermic process, higher temperatures will favor the dissolution.
- Hot water has a higher temperature than cold water, which means that the dissolution will occur more rapidly in hot water.

5. **Combining Both Factors**:
- Among the options, the combination of powdered sugar (which has a larger surface area) and hot water (which provides a higher temperature) will result in the most rapid dissolution.

6. **Conclusion**:
- The most rapid dissolution of sugar occurs when using powdered sugar in hot water.

### Final Answer:
The dissolution of sugar will be most rapid in the case of **powdered sugar in hot water**.

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