For the process `CO_(2(s)) rarr CO_(2(g))`

Options

A. Both `triangleH and triangleS` are positive
B. `triangleH` is negative and `triangleS` is positive
C. `triangleH` is +ve and `triangleS` is negative
D. Both `triangleH and triangleS` are negative

Answer

To solve the problem regarding the process of converting solid carbon dioxide (CO₂(s)) to gaseous carbon dioxide (CO₂(g)), we need to analyze the changes in enthalpy (ΔH) and entropy (ΔS) that occur during this phase transition.

### Step-by-Step Solution:

1. **Identify the Process**:
The process we are considering is the sublimation of solid carbon dioxide (dry ice) to gaseous carbon dioxide. This can be represented as:
\[ CO_{2(s)} \rightarrow CO_{2(g)} \]

2. **Determine the Nature of the Process**:
Sublimation is a phase transition where a solid turns directly into a gas without passing through the liquid phase. This process requires heat energy to break the intermolecular forces holding the solid structure together.

3. **Analyze Enthalpy Change (ΔH)**:
Since the process of sublimation requires the absorption of heat, it is classified as an endothermic process. In endothermic reactions, the change in enthalpy (ΔH) is positive. Therefore:
\[ \Delta H > 0 \]

4. **Analyze Entropy Change (ΔS)**:
Entropy is a measure of the disorder or randomness in a system. In the solid state, carbon dioxide molecules are closely packed and have low entropy. When these molecules transition to the gaseous state, they become more spread out and disordered, leading to an increase in entropy. Thus:
\[ \Delta S > 0 \]

5. **Conclusion**:
Based on the analysis:
- ΔH is positive (endothermic process).
- ΔS is positive (increase in disorder).

Therefore, the correct conclusion for the process is that both ΔH and ΔS are positive.

6. **Select the Correct Option**:
From the given options, the one that states both ΔH and ΔS are positive is the correct choice:
- **Option 1**: Both ΔH and ΔS are positive.

### Final Answer:
The correct option is: **Both ΔH and ΔS are positive**.

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