For a reversible process, the following equation describes the entropy changes of the universe, system, and surroundings.
ΔSuniv = ΔSsys + ΔSsurr = 0
For an irreversible process, the following equation applies.
ΔSuniv = ΔSsys + ΔSsurr > 0
For each of the following processes, predict whether ΔSsurr is positive, negative, or zero.
(a) Isothermally expanding a gas, ΔSsys > 0:

positive
negative
zero

(b) Reacting hydrogen and oxygen gas, ΔSsys < 0:

positive
negative
zero

For these questions, we need to predict the sign of \( \Delta S_{\text{surr}} \) (the entropy change of the surroundings) based on the entropy change of the system, \( \Delta S_{\text{sys}} \), and whether the process is reversible or irreversible. 

1. **Isothermal expansion of a gas (\( \Delta S_{\text{sys}} > 0 \))**  
   - When a gas expands isothermally, the entropy of the system increases because the molecules have more space to occupy, leading to increased disorder.
   - Since \( \Delta S_{\text{sys}} > 0 \), if this process is carried out in a reversible manner, \( \Delta S_{\text{surr}} \) would be negative (to ensure \( \Delta S_{\text{univ}} = 0 \)).
   - For an irreversible process, \( \Delta S_{\text{univ}} > 0 \), so while \( \Delta S_{\text{surr} } \) might still be negative, it would be smaller in magnitude than \( \Delta S_{\text{sys}} \) to result in a positive \( \Delta S_{\text{univ}} \).

   **Answer: \( \Delta S_{\text{surr}} \) is likely negative.**

2. **Reaction between hydrogen and oxygen gas (\( \Delta S_{\text{sys}} < 0 \))**  
   - In this reaction, hydrogen and oxygen combine to form water, which is a more ordered (lower entropy) state than the gaseous reactants, so \( \Delta S_{\text{sys}} < 0 \).
   - For this exothermic reaction, heat is released to the surroundings, increasing the entropy of the surroundings.
   - Thus, \( \Delta S_{\text{surr}} \) is positive because the surroundings gain entropy as they absorb the released heat.

   **Answer: \( \Delta S_{\text{surr}} \) is positive.**

Let me know if you'd like further details or have questions. 

**Related Questions:**
1. How does temperature affect \( \Delta S_{\text{surr}} \) during an exothermic reaction?
2. What would happen to \( \Delta S_{\text{univ}} \) if both \( \Delta S_{\text{sys}} \) and \( \Delta S_{\text{surr}} \) were negative?
3. In a reversible process, can \( \Delta S_{\text{sys}} \) be non-zero while \( \Delta S_{\text{univ}} \) remains zero?
4. How does the entropy change of a system compare between reversible and irreversible expansions?
5. Can an endothermic reaction ever have a positive \( \Delta S_{\text{surr}} \)?

**Tip:** For isothermal processes, remember that any heat transferred impacts both system and surroundings, influencing their entropy changes in opposite directions.

Explore entropy change (ΔS) in reversible and irreversible processes, focusing on surroundings' entropy (ΔSsurr) in isothermal gas expansion and hydrogen-oxygen reaction. This topic covers thermodynamic principles, the second law of thermodynamics, and ΔSuniv for system-surrounding interactions. Ideal for undergraduate chemistry and physics students.

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