For which of the process, `Delta S` is negative?

Options

A. `H_(2(g)) rarr 2H_((g))`
B. `N_(2(g)) (1 "atm") rarr N_(2(g)) (8 "atm")`
C. `2SO_(3(g)) rarr 2SO_(2(g)) + O_(2(g))`
D. `C_(("diamond")) rarr C_(("graphite"))`

Answer

To determine for which process the change in entropy (ΔS) is negative, we need to analyze the randomness or disorder of the system in each case. A negative ΔS indicates a decrease in randomness.

### Step-by-Step Solution:

1. **Understanding Entropy (ΔS)**:
- Entropy is a measure of the disorder or randomness in a system. A positive ΔS indicates an increase in disorder, while a negative ΔS indicates a decrease in disorder.

2. **Analyzing the First Process**:
- **Process**: One molecule of hydrogen (H₂) splits into two atoms of hydrogen (2H).
- **Analysis**: The number of particles increases from 1 to 2, which leads to an increase in randomness.
- **Conclusion**: ΔS is positive.

3. **Analyzing the Second Process**:
- **Process**: Nitrogen gas (N₂) at 1 atmosphere pressure is compressed to 8 atmospheres.
- **Analysis**: Increasing pressure causes gas molecules to come closer together, reducing their kinetic energy and randomness.
- **Conclusion**: ΔS is negative.

4. **Analyzing the Third Process**:
- **Process**: Sulfur trioxide (SO₃) decomposes into sulfur dioxide (SO₂) and oxygen (O₂).
- **Analysis**: The number of molecules increases from 1 (SO₃) to 3 (SO₂ + O₂), leading to an increase in randomness.
- **Conclusion**: ΔS is positive.

5. **Analyzing the Fourth Process**:
- **Process**: Carbon in the diamond allotrope converts to graphite.
- **Analysis**: In diamond, carbon atoms are arranged in a tetrahedral structure, which is more ordered than the sheet-like structure of graphite. Thus, the randomness increases when converting from diamond to graphite.
- **Conclusion**: ΔS is positive.

6. **Final Conclusion**:
- Among the processes analyzed, only the second process (compression of nitrogen gas) results in a negative ΔS. Therefore, the answer is that ΔS is negative for the process where nitrogen gas is compressed from 1 atmosphere to 8 atmospheres.