Which of the following relationships is true?

Options

A. Bond dissociation energy of `O_(2) and O_(2)^(-)` are same.
B. Bond dissociation energy of `O_(2)^(+)` is higher than `O_(2)`,
C. Bond dissociation energy of `O_(2)^(-) and O_(2)^(2-)` are same.
D. Bond dissociation energy of `O_(2)^(2-) ` is higher than `O_(2)^(-)`.

Explanation

To solve the question regarding the bond dissociation energies of the given molecules, we will follow these steps:

### Step 1: Identify the Molecules
The molecules we need to analyze are:
- O2 (dioxygen)
- O2- (superoxide)
- O2+ (dioxygen cation)
- O2-2 (peroxide)

### Step 2: Determine the Number of Electrons
We need to find the total number of electrons for each species:
- O2: 16 electrons (8 from each oxygen atom)
- O2-: 17 electrons (16 from O2 + 1 extra)
- O2+: 15 electrons (16 from O2 - 1)
- O2-2: 18 electrons (16 from O2 + 2 extra)

### Step 3: Write the Molecular Orbital Configurations
Now, we will write the molecular orbital configurations for each molecule:

1. **O2**:
- Configuration: \(1s^2 \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^1 \pi^* 2p_y^1\)

2. **O2-**:
- Configuration: \(1s^2 \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^2 \pi^* 2p_y^1\)

3. **O2+**:
- Configuration: \(1s^2 \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^1 \pi^* 2p_y^1\)

4. **O2-2**:
- Configuration: \(1s^2 \sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 \pi 2p_x^2 \pi 2p_y^2 \pi^* 2p_x^2 \pi^* 2p_y^2\)

### Step 4: Calculate the Bond Order
The bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{n_B - n_A}{2} \]
where \(n_B\) is the number of bonding electrons and \(n_A\) is the number of anti-bonding electrons.

1. **For O2**:
- Bonding electrons (n_B) = 10
- Anti-bonding electrons (n_A) = 6
- Bond Order = \(\frac{10 - 6}{2} = 2\)

2. **For O2-**:
- Bonding electrons = 10
- Anti-bonding electrons = 7
- Bond Order = \(\frac{10 - 7}{2} = 1.5\)

3. **For O2+**:
- Bonding electrons = 10
- Anti-bonding electrons = 5
- Bond Order = \(\frac{10 - 5}{2} = 2.5\)

4. **For O2-2**:
- Bonding electrons = 10
- Anti-bonding electrons = 8
- Bond Order = \(\frac{10 - 8}{2} = 1\)

### Step 5: Compare Bond Orders
From the calculated bond orders:
- O2: 2
- O2-: 1.5
- O2+: 2.5
- O2-2: 1

### Step 6: Relate Bond Order to Bond Dissociation Energy
Bond dissociation energy is directly proportional to bond order. Therefore, the order of bond dissociation energy is:
- O2+ > O2 > O2- > O2-2

### Step 7: Analyze the Options
Now we can analyze the options given in the question:
1. Bond dissociation energy of O2 and O2- are the same: **False**
2. Bond dissociation energy of O2+ is higher than that of O2: **True**
3. Bond dissociation energy of O2- and O2-2 are the same: **False**
4. Bond dissociation energy of O2-2 is higher than O2-: **False**

### Conclusion
The correct relationship is that the bond dissociation energy of O2+ is higher than that of O2.

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