Oxygen & ozone are gases at standard temperature. Their molar entropies are in the sequence `O_(2) lt O_(3).` Using molecular properties , explain why ozone is more disordered than oxygen.

Answer

To explain why ozone (O₃) is more disordered than oxygen (O₂) in terms of molecular properties and their respective molar entropies, we can follow these steps:

### Step-by-Step Solution:

1. **Definition of Entropy**:
- Entropy is a measure of the degree of disorder or randomness in a system. The higher the entropy, the more disordered the system is.

2. **States of Matter**:
- Entropy values vary with the state of matter: solids have lower entropy than liquids, and liquids have lower entropy than gases. In gases, molecules move freely and randomly, leading to higher entropy.

3. **Molecular Composition**:
- Oxygen (O₂) is a diatomic molecule, meaning it consists of two oxygen atoms.
- Ozone (O₃) is a triatomic molecule, consisting of three oxygen atoms.

4. **Comparison of Molecular Complexity**:
- The presence of more atoms in a molecule generally increases the number of possible arrangements (microstates) of that molecule.
- Since ozone has three atoms, it can have more vibrational modes and configurations compared to the two atoms in oxygen.

5. **Implication of More Atoms**:
- The increased number of atoms in ozone allows for greater freedom of movement and more ways to arrange itself, leading to a higher degree of disorder.
- Therefore, ozone (O₃) has a higher molar entropy than oxygen (O₂).

6. **Conclusion**:
- As a result of having more atoms and thus more possible arrangements, ozone is more disordered than oxygen, which is reflected in their molar entropies.

### Final Statement:
Thus, the sequence of molar entropies, where O₂ < O₃, can be explained by the molecular properties that contribute to the disorder of the substances, with ozone being more disordered due to its greater number of atoms.