In `O_(2)` and `H_(2)O_(2)` the O-O bond lengths are 1.21 and 1.48Å respectively. In ozone, the average O-O bond length is

Options

A. 1.28 Å
B. 1.18Å
C. 1.44Å
D. 1.52 Å

Explanation

To find the average O-O bond length in ozone (O₃), we will analyze the bond lengths in O₂ and H₂O₂, and use the concept of bond order.

### Step-by-Step Solution:

1. **Identify the Bond Lengths**:
- The O-O bond length in O₂ (dioxygen) is given as 1.21 Å.
- The O-O bond length in H₂O₂ (hydrogen peroxide) is given as 1.48 Å.

2. **Understand the Structure of Ozone (O₃)**:
- Ozone consists of three oxygen atoms. Its structure can be represented as:
```
O=O-O
```
- Ozone exhibits resonance, meaning it can be represented by multiple structures. The resonance structures include one with a double bond between the first two oxygen atoms and a single bond between the second and third oxygen atom.

3. **Determine the Bond Order**:
- The bond order is defined as the number of bonds between two atoms divided by the number of resonance structures.
- For O₂, the bond order is 2 (one double bond).
- For H₂O₂, the bond order between the two oxygen atoms is 1 (one single bond).
- For O₃, the bond order can be calculated as follows:
- There are two bonds (one double bond and one single bond) and two resonance structures, giving a bond order of \( \frac{2}{2} = 1.5 \).

4. **Relate Bond Length to Bond Order**:
- Bond length is inversely proportional to bond order. This means that as the bond order increases, the bond length decreases.
- Since O₂ has the highest bond order (2), it has the shortest bond length (1.21 Å).
- H₂O₂ has the lowest bond order (1), resulting in the longest bond length (1.48 Å).
- O₃, with a bond order of 1.5, will have a bond length that is between those of O₂ and H₂O₂.

5. **Estimate the Ozone Bond Length**:
- Since the bond length of O₂ is 1.21 Å and that of H₂O₂ is 1.48 Å, we can estimate the bond length of O₃ to be closer to that of O₂ but longer than 1.21 Å.
- A reasonable estimate for the average O-O bond length in O₃ would be approximately 1.28 Å.

### Final Answer:
The average O-O bond length in ozone (O₃) is approximately **1.28 Å**.