The sequence that correctly describes the relative bond strengths pertaining to oxygen molecule and its cation or anion is

Options

A. `O_(2)^(2-) gt O_(2)^(-) gt O_(2) gt O_(2)^(+)`
B. `O_(2) gt O_(2)^(+) gt O_(2)^(-) gt O_(2)^(2-)`,
C. `O_(2)^(+) gt O_(2) gt O_(2)^(2-) gt O_(2)^(-)`
D. `O_(2)^(+) gt O_(2) gt O_(2)^(-) gt O_(2)^(2-)`

Explanation

To determine the relative bond strengths of the oxygen molecule (O₂) and its cations (O₂⁺) and anions (O₂⁻, O₂²⁻), we will follow these steps:

### Step 1: Understand Bond Order
Bond order is defined as the number of covalent bonds between two atoms. It is directly proportional to bond strength; higher bond order means stronger bonds.

### Step 2: Use Molecular Orbital Theory
According to molecular orbital theory, the bond order can be calculated using the formula:
\[ \text{Bond Order} = \frac{1}{2} (\text{Number of electrons in bonding orbitals} - \text{Number of electrons in anti-bonding orbitals}) \]

### Step 3: Calculate Bond Order for O₂
The electronic configuration of O₂ (16 electrons) is:
- σ1s² σ*1s² σ2s² σ*2s² σ2p_z² π2p_x² π2p_y²
- Bonding electrons: 10 (σ and π orbitals)
- Anti-bonding electrons: 6 (σ* and π* orbitals)

Using the formula:
\[ \text{Bond Order}_{O_2} = \frac{1}{2} (10 - 6) = 2 \]

### Step 4: Calculate Bond Order for O₂⁻
For O₂⁻ (17 electrons), one additional electron goes into the anti-bonding π* orbital:
- Bonding electrons: 10
- Anti-bonding electrons: 7

Using the formula:
\[ \text{Bond Order}_{O_2^-} = \frac{1}{2} (10 - 7) = 1.5 \]

### Step 5: Calculate Bond Order for O₂²⁻
For O₂²⁻ (18 electrons), two additional electrons go into the anti-bonding orbitals:
- Bonding electrons: 10
- Anti-bonding electrons: 8

Using the formula:
\[ \text{Bond Order}_{O_2^{2-}} = \frac{1}{2} (10 - 8) = 1 \]

### Step 6: Calculate Bond Order for O₂⁺
For O₂⁺ (15 electrons), one electron is removed from the anti-bonding orbital:
- Bonding electrons: 10
- Anti-bonding electrons: 5

Using the formula:
\[ \text{Bond Order}_{O_2^+} = \frac{1}{2} (10 - 5) = 2.5 \]

### Step 7: Compare Bond Orders
Now we can summarize the bond orders:
- O₂⁺: 2.5
- O₂: 2
- O₂⁻: 1.5
- O₂²⁻: 1

### Step 8: Determine Relative Bond Strengths
Since bond strength is directly related to bond order, we can conclude the following order of bond strengths:
1. O₂⁺ (strongest)
2. O₂
3. O₂⁻
4. O₂²⁻ (weakest)

### Final Answer
The sequence that correctly describes the relative bond strengths pertaining to the oxygen molecule and its cation or anion is:
**O₂⁺ > O₂ > O₂⁻ > O₂²⁻**