Consider the following molecules `underset("I")(O_(2)),underset("II")(O_(2)(AsF_(6)),underset("III")(KO_(2))`
Choose the correct answer regarding `O-O` bond from the following .

Options

A. The correct decreasing bond order is `I gt III gt II`
B. The correct decreasing order of bond length is `III gt I gt II`
C. The bond strength of I is less than that of III
D. Bond dissociation energy is highest in case of III

Answer

To analyze the O-O bond in the given molecules \( O_2 \), \( O_2(AsF_6) \), and \( KO_2 \), we will calculate the bond order for each molecule step by step.

### Step 1: Determine the bond order for \( O_2 \)

1. **Molecular Orbital Configuration**:
- Oxygen has an atomic number of 8, so \( O_2 \) has a total of 16 electrons.
- The molecular orbital configuration for \( O_2 \) is:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \]

2. **Count the Electrons**:
- Bonding electrons: \( 2 + 2 + 2 + 2 + 2 + 2 = 10 \)
- Antibonding electrons: \( 2 + 2 = 4 \)

3. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2} = \frac{10 - 6}{2} = 2 \]

### Step 2: Determine the bond order for \( O_2(AsF_6) \)

1. **Molecular Configuration**:
- \( O_2(AsF_6) \) has one additional electron compared to \( O_2 \) due to the negative charge.
- Total electrons = 17.

2. **Adjust the Molecular Orbital Configuration**:
- The additional electron goes into the antibonding orbital:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^2 \]

3. **Count the Electrons**:
- Bonding electrons: 10
- Antibonding electrons: 7 (6 + 1)

4. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{10 - 7}{2} = 1.5 \]

### Step 3: Determine the bond order for \( KO_2 \)

1. **Molecular Configuration**:
- \( KO_2 \) has a positive charge on \( O_2 \), meaning one electron is removed.
- Total electrons = 15.

2. **Adjust the Molecular Orbital Configuration**:
- The electron is removed from the antibonding orbital:
\[ \sigma_{1s}^2 \sigma^*_{1s}^2 \sigma_{2s}^2 \sigma^*_{2s}^2 \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi^*_{2p_x}^1 \pi^*_{2p_y}^1 \]

3. **Count the Electrons**:
- Bonding electrons: 10
- Antibonding electrons: 5 (4 + 1)

4. **Calculate Bond Order**:
\[ \text{Bond Order} = \frac{10 - 5}{2} = 2.5 \]

### Summary of Bond Orders
- \( O_2 \): Bond Order = 2
- \( O_2(AsF_6) \): Bond Order = 1.5
- \( KO_2 \): Bond Order = 2.5

### Final Order of Bond Strength
- The bond strength is inversely related to bond order. Therefore, the order of bond strength from highest to lowest is:
1. \( KO_2 \) (Bond Order = 2.5)
2. \( O_2 \) (Bond Order = 2)
3. \( O_2(AsF_6) \) (Bond Order = 1.5)