Change in entropy is negative for

Options

A. `Br(l) to Br(g)`
B. `C(s)+H_(2)O(g) to CO(g)+H_(2)(g)`
C. `N_(2)(g, 10 atm) to N_(2), (g, 1 atm)`
D. `Fe(" at 400 K")to Fe (" at 300 K")`

Answer

To determine when the change in entropy (ΔS) is negative, we need to analyze the options provided in the question. Entropy is a measure of the randomness or disorder of a system. A negative change in entropy indicates that the system is becoming more ordered or less random.

### Step-by-Step Solution:

1. **Understanding Entropy**:
- Entropy (S) is a measure of the disorder or randomness of particles in a system. A higher entropy value indicates a more disordered state.

2. **Analyzing Each Option**:
- **Option 1**: A reaction that proceeds from a liquid state to a gaseous state.
- In this case, the particles in the gaseous state are more random than in the liquid state. Therefore, ΔS is positive.

- **Option 2**: A reaction with solid and gaseous reactants producing gaseous products.
- Here, since there are more gaseous particles in the products than in the reactants, the randomness increases, leading to a positive ΔS.

- **Option 3**: A reaction with gaseous reactants and products, but with a decrease in pressure.
- Decreasing pressure allows for an increase in volume, which means the particles have more space to move. This results in increased randomness, thus ΔS is positive.

- **Option 4**: A reaction where the temperature decreases from 400 K to 300 K.
- As temperature decreases, the kinetic energy of the particles also decreases. Lower kinetic energy means less movement and, consequently, less randomness. Thus, the entropy of the products is lower than that of the reactants, resulting in a negative ΔS.

3. **Conclusion**:
- The only option where the change in entropy is negative is **Option 4**.

### Final Answer:
The change in entropy is negative for **Option 4** (temperature decreases from 400 K to 300 K).