In which case change in entropy is negative?

Options

A. Sublimation of solid to gas
B. `2H(g) to H_2(g)`
C. Evaporation of water
D. Expansion of a gas at constant temperature.

Explanation

To determine in which case the change in entropy is negative, we need to analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Entropy**:
- Entropy (S) is a measure of the randomness or disorder of a system. A negative change in entropy (ΔS < 0) indicates a decrease in disorder.

2. **Analyzing Each Option**:
- **Option A: Sublimation of solid to gas**:
- In sublimation, a solid transforms directly into a gas. This process increases the randomness as gas molecules have higher kinetic energy and more freedom of movement compared to solids. Therefore, ΔS > 0. This option is not correct.

- **Option B: 2 H atoms in gaseous state to form H2 gaseous**:
- Here, we have two gaseous hydrogen atoms combining to form a single molecule of hydrogen gas (H2). The number of gaseous moles decreases from 2 (reactants) to 1 (product).
- The change in the number of gaseous moles (ΔnG) = 1 (product) - 2 (reactants) = -1.
- A decrease in the number of gaseous moles indicates a decrease in randomness, thus ΔS < 0. This option is correct.

- **Option C: Evaporation of water**:
- During evaporation, liquid water molecules transition to the gas phase. This process increases disorder because gas molecules have more freedom and energy than liquid molecules. Therefore, ΔS > 0. This option is not correct.

- **Option D: Expansion of gas at constant temperature**:
- When a gas expands at constant temperature, its volume increases, leading to greater randomness and disorder among the gas molecules. Thus, ΔS > 0. This option is not correct.

3. **Conclusion**:
- After analyzing all options, we find that the only case where the change in entropy is negative is **Option B**, where 2 H atoms in gaseous state combine to form H2 gaseous.

### Final Answer:
The change in entropy is negative in **Option B: 2 H atoms in gaseous state to form H2 gaseous**.

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