Which of the following option the first compound has less entropy than second:

Options

A. `(i)` aqueous solution of `1 "M of" MgCI_(2) (ii)` aqueous solution of `1 "M of" NaCI`
B. `(1) Br_(2)` liquid at `25^(@) (ii) Br_(2)` liquid at `20^(@)C`
C. `(i) HgO` solid `(ii) HgS` solid
D. `(i) Br_(2)` liquid `(ii) I_(2)` solid

Answer

To determine which of the given compounds has less entropy than the other, we will analyze the options one by one based on the principles of thermodynamics and entropy.

### Step-by-Step Solution:

1. **Understanding Entropy**:
- Entropy is a measure of the disorder or randomness in a system. Generally, gases have higher entropy than liquids, and liquids have higher entropy than solids. Additionally, compounds with more moles of particles in solution tend to have higher entropy.

2. **Analyzing Option 1**:
- **Compounds**: 1 M MgCl2 (aqueous) and 1 M NaCl (aqueous).
- **Dissociation**:
- MgCl2 → Mg²⁺ + 2 Cl⁻ (produces 3 moles)
- NaCl → Na⁺ + Cl⁻ (produces 2 moles)
- **Conclusion**: Since MgCl2 produces more moles (3) compared to NaCl (2), MgCl2 has higher entropy. Therefore, this option is not correct.

3. **Analyzing Option 2**:
- **Compounds**: Br2 (liquid) at 25°C and Br2 (liquid) at 20°C.
- **Temperature Effect**: Higher temperature generally increases the entropy of a substance.
- **Conclusion**: The Br2 at 25°C has higher entropy than at 20°C. Thus, this option is also not correct.

4. **Analyzing Option 3**:
- **Compounds**: HgO (solid) and HgS (solid).
- **Molar Mass Consideration**: Entropy can also depend on molar mass. HgS has a higher molar mass than HgO.
- **Conclusion**: Since HgO has a lower molar mass compared to HgS, it is expected that HgO has lower entropy than HgS. This option is correct.

5. **Analyzing Option 4**:
- **Compounds**: Br2 (liquid) and I2 (solid).
- **State of Matter**: Liquids generally have higher entropy than solids.
- **Conclusion**: Br2 (liquid) has higher entropy than I2 (solid), making this option incorrect.

### Final Conclusion:
The only option where the first compound has less entropy than the second is **Option 3: HgO (solid) has less entropy than HgS (solid)**.