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.