The correct order in which oxygen - oxygen bond dissociation energy increases is

Options

A. `H_(2)O_(2) ltO_(2) lt O_(3)`
B. `H_(2)O_(2) lt O_(3) lt O_(2)`
C. `O_(2) lt O_(3) lt H_(2)O_(2)`
D. `O_(2) lt H_(2)O_(2) lt O_(3)`

Answer

To determine the correct order in which oxygen-oxygen bond dissociation energy increases, we need to analyze the bond order of the relevant molecules: O2, H2O2, and O3. The bond dissociation energy is related to the bond order, with higher bond orders corresponding to higher bond dissociation energies.

### Step-by-Step Solution:

1. **Identify the Molecules**: We are looking at three molecules: O2 (dioxygen), H2O2 (hydrogen peroxide), and O3 (ozone).

2. **Determine the Bond Order**:
- **For O2**:
- The electronic configuration of O2 is:
\[ \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^1 \pi^* 2p_y^1 \]
- Count the electrons in bonding and antibonding orbitals:
- Bonding electrons = 10
- Antibonding electrons = 6
- Bond order = \( \frac{1}{2} \times (10 - 6) = \frac{1}{2} \times 4 = 2 \)

- **For H2O2**:
- H2O2 has a single O-O bond.
- The bond order can be calculated as follows:
- Bonding electrons = 10
- Antibonding electrons = 8
- Bond order = \( \frac{1}{2} \times (10 - 8) = \frac{1}{2} \times 2 = 1 \)

- **For O3**:
- O3 has resonance structures, and the bond order can be calculated as follows:
- The bond order is calculated as the average of the bonds in the resonance structures.
- There are 3 bonds shared among 3 oxygen atoms, so:
- Bond order = \( \frac{3}{2} = 1.5 \)

3. **Compare the Bond Orders**:
- O2: Bond order = 2
- H2O2: Bond order = 1
- O3: Bond order = 1.5

4. **Relate Bond Order to Bond Dissociation Energy**:
- Higher bond order means higher bond dissociation energy. Therefore, the order of increasing bond dissociation energy is:
- H2O2 < O3 < O2

5. **Final Answer**:
- The correct order in which oxygen-oxygen bond dissociation energy increases is:
- H2O2 < O3 < O2