Which of the following statement is/are correct

Options

A. The peroxide ion has a bond order of 1 while the oxygen molecule has a bond order of 2
B. The peroxide ion has a weaker bond than the dioxygen molecule has.
C. The peroxide ion as well as the dioxygen molecules are paramagnetic
D. The bond length of the peroxide ion is greater than that of the dioxygen molecule

Answer

To solve the question regarding the correctness of the statements about the peroxide ion (O2^2-) and the oxygen molecule (O2), we will analyze each statement step by step.

### Step 1: Determine the bond order of O2
1. **Count the total number of electrons in O2**: Oxygen has 8 electrons, so O2 has a total of 16 electrons.
2. **Fill the molecular orbitals according to the Aufbau principle**:
- σ(1s)²
- σ*(1s)²
- σ(2s)²
- σ*(2s)²
- σ(2p_z)²
- π(2p_x)², π(2p_y)²
- π*(2p_x)¹, π*(2p_y)¹ (the last two electrons go into the degenerate π* orbitals)
3. **Calculate the bond order**:
\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]
- Bonding electrons = 10 (σ(1s)² + σ(2s)² + σ(2p_z)² + π(2p_x)² + π(2p_y)²)
- Antibonding electrons = 6 (σ*(1s)² + σ*(2s)² + π*(2p_x)¹ + π*(2p_y)¹)
- Thus, Bond Order = \(\frac{10 - 6}{2} = 2\)

### Step 2: Determine the bond order of O2^2-
1. **Count the total number of electrons in O2^2-**: O2^2- has 18 electrons (16 from O2 + 2 additional electrons).
2. **Fill the molecular orbitals**:
- σ(1s)²
- σ*(1s)²
- σ(2s)²
- σ*(2s)²
- σ(2p_z)²
- π(2p_x)², π(2p_y)²
- π*(2p_x)², π*(2p_y)² (the two added electrons fill the π* orbitals)
3. **Calculate the bond order**:
- Bonding electrons = 10
- Antibonding electrons = 8 (σ*(1s)² + σ*(2s)² + π*(2p_x)² + π*(2p_y)²)
- Thus, Bond Order = \(\frac{10 - 8}{2} = 1\)

### Step 3: Analyze the statements
1. **Statement about bond order**: "The peroxide ion has a bond order of 1 while the oxygen molecule has a bond order of 2." - **Correct**
2. **Statement about bond strength**: "The bond strength is directly proportional to the bond order." - **Correct**
3. **Statement about paramagnetism**: "Both the peroxide ion and the oxygen molecule are paramagnetic." - **Incorrect** (O2 is paramagnetic, O2^2- is diamagnetic)
4. **Statement about bond length**: "The bond length of the peroxide ion is greater than that of the oxygen molecule." - **Correct** (Bond length is inversely proportional to bond order)

### Conclusion
The correct statements are:
- The peroxide ion has a bond order of 1 while the oxygen molecule has a bond order of 2.
- The bond strength is directly proportional to the bond order.
- The bond length of the peroxide ion is greater than that of the oxygen molecule.

### Final Answer
The correct statements are A, B, and D.