For the process, `H_(2)O(l) to H_(2)O(g)`

Options

A. `DeltaS_("system") gt 0` and `DeltaS_("surrouding") gt 0`
B. `DeltaS_("system") gt 0` and `DeltaS_("surrounding") lt 0`
C. `DeltaS_("system") lt 0` and `DeltaS_("surrounding") gt 0`
D. `DeltaS_("system") lt 0` and `DeltaS_("surrounding") gt 0`

Explanation

To solve the problem regarding the process of converting liquid water (H₂O(l)) to water vapor (H₂O(g)), we need to analyze the changes in entropy for both the system and the surroundings.

### Step-by-Step Solution:

1. **Identify the Process**: The process in question is the phase change from liquid water to water vapor. This is a transition from a more ordered state (liquid) to a less ordered state (gas).

2. **Understand Entropy**: Entropy (S) is a measure of disorder or randomness in a system. When a substance changes from a liquid to a gas, the molecules have more freedom to move, resulting in an increase in disorder.

3. **Change in Entropy of the System**:
- For the system (H₂O), when it transitions from liquid to gas, the number of gas molecules increases.
- Therefore, the entropy change (ΔS_system) for the system is positive (ΔS_system > 0).

4. **Change in Entropy of the Surroundings**:
- When the system absorbs heat during the phase change (endothermic process), the surroundings lose heat.
- This results in a decrease in the entropy of the surroundings (ΔS_surroundings < 0).

5. **Conclusion**:
- The entropy of the system increases (ΔS_system > 0).
- The entropy of the surroundings decreases (ΔS_surroundings < 0).

6. **Final Answer**: Based on the analysis, the correct option would be one that states that the entropy change for the system is greater than zero and for the surroundings is less than zero.