In which of the following processes, entropy increases?

Options

A. `I_(2)(s) to I_(2)(g)`
B. Crystallisation of sugar from sugar solution
C. `2NaHCO_(3)(s) to Na_(2)CO_(3)(s) + CO_(2)(g) + H_(2)O(g)`
D. `H_(2)O(l) iff H_(2)O(s)`

Answer

To determine in which of the given processes the entropy increases, we need to analyze each process based on the states of matter involved and how they change. Entropy is a measure of disorder or randomness in a system, and it generally increases when a system transitions from a more ordered state to a less ordered state.

### Step-by-Step Solution:

1. **Understanding Entropy**:
- Entropy (S) is a measure of disorder or randomness in a system. The more disordered a system is, the higher its entropy.

2. **Identifying States of Matter**:
- The three primary states of matter are solid, liquid, and gas.
- Entropy increases in the following order: solid < liquid < gas.

3. **Analyzing Each Process**:
- **Process A: Sublimation of Iodine (Solid to Gas)**:
- In this process, iodine transitions from a solid state directly to a gaseous state.
- This transition increases the randomness and disorder of the molecules.
- **Conclusion**: Entropy increases.

- **Process B: Crystallization of Sugar from Solution (Liquid to Solid)**:
- Here, sugar in a liquid solution crystallizes into a solid form.
- This process decreases the randomness as the molecules become more ordered in a solid state.
- **Conclusion**: Entropy decreases.

- **Process C: Dissociation of NaHCO3 (Solid to Solid + Gas)**:
- In this case, solid sodium bicarbonate (NaHCO3) dissociates into solid and gaseous products.
- The formation of gas from a solid increases the disorder of the system.
- **Conclusion**: Entropy increases.

- **Process D: Freezing of Water (Liquid to Solid)**:
- Water transitioning from a liquid to a solid (ice) results in a more ordered arrangement of molecules.
- **Conclusion**: Entropy decreases.

4. **Final Conclusion**:
- The processes in which entropy increases are:
- **Process A**: Sublimation of Iodine (Solid to Gas)
- **Process C**: Dissociation of NaHCO3 (Solid to Solid + Gas)

### Answer:
The processes in which entropy increases are **Process A and Process C**.

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