Sum of antibonding `pi` electrons (`pi` electrons ) in species `O_2, O_2^(-) and O_2^(2-)` are.

Explanation

To solve the problem of finding the sum of antibonding π electrons in the species O₂, O₂⁻, and O₂²⁻, we will follow these steps:

### Step 1: Determine the Molecular Orbital Configuration for O₂
1. Oxygen (O) has an atomic number of 8, which means each O atom has 8 electrons. Therefore, O₂ has a total of 16 electrons.
2. The molecular orbital (MO) configuration for O₂ can be derived from the molecular orbital theory:
- The order of filling for O₂ is:
- 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 filled molecular orbitals for O₂ are:
- σ(1s)², σ*(1s)², σ(2s)², σ*(2s)², σ(2p_z)², π(2p_x)², π(2p_y)².
- The antibonding π electrons in O₂ are in the π*(2p_x) and π*(2p_y) orbitals.

### Step 2: Count the Antibonding π Electrons in O₂
- In O₂, there are no electrons in the antibonding π orbitals (π*(2p_x) and π*(2p_y)), so the count is:
- Antibonding π electrons in O₂ = 0.

### Step 3: Determine the Molecular Orbital Configuration for O₂⁻
1. O₂⁻ has one additional electron compared to O₂, making a total of 17 electrons.
2. The additional electron will occupy one of the antibonding π orbitals:
- The configuration becomes:
- 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.
- Thus, the count of antibonding π electrons in O₂⁻ is:
- Antibonding π electrons in O₂⁻ = 1.

### Step 4: Determine the Molecular Orbital Configuration for O₂²⁻
1. O₂²⁻ has two additional electrons compared to O₂, making a total of 18 electrons.
2. The second additional electron will also occupy the other antibonding π orbital:
- The configuration becomes:
- 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.
- Thus, the count of antibonding π electrons in O₂²⁻ is:
- Antibonding π electrons in O₂²⁻ = 2.

### Step 5: Sum the Antibonding π Electrons
- Now, we can sum the antibonding π electrons from all three species:
- O₂: 0
- O₂⁻: 1
- O₂²⁻: 2
- Total = 0 + 1 + 2 = 3.

### Final Answer
The sum of antibonding π electrons in the species O₂, O₂⁻, and O₂²⁻ is **3**.