To determine which species will most likely gain an electron to form a thermodynamically more stable species, we will analyze the given species using molecular orbital theory. We will calculate the number of electrons, fill the molecular orbitals, and then determine the bond order before and after gaining an electron.
### Step 1: Determine the number of electrons in each species.
- **CN**: Carbon (C) has 6 electrons and Nitrogen (N) has 7 electrons. Total = 6 + 7 = **13 electrons**.
- **NO**: Nitric oxide (NO) has 7 (N) + 8 (O) = **15 electrons**.
- **O2^2+**: Oxygen (O) has 8 electrons, and since it is in a +2 oxidation state, we subtract 2 electrons. Total = (2 * 8) - 2 = **14 electrons**.
- **N2**: Nitrogen (N) has 7 electrons, so total = 2 * 7 = **14 electrons**.
### Step 2: Fill the molecular orbitals for each species.
1. **O2^2+ and N2 (14 electrons)**:
- Fill the molecular orbitals in order: 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.
- Bonding electrons = 10, Anti-bonding electrons = 4.
- Bond order = (10 - 4) / 2 = 3.
2. **CN (13 electrons)**:
- 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)¹.
- Bonding electrons = 9, Anti-bonding electrons = 4.
- Bond order = (9 - 4) / 2 = 2.5.
3. **NO (15 electrons)**:
- 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)¹.
- Bonding electrons = 10, Anti-bonding electrons = 5.
- Bond order = (10 - 5) / 2 = 2.5.
### Step 3: Analyze the effect of gaining an electron.
- **O2^2+**: After gaining an electron, the bond order becomes (10 - 5) / 2 = 2.5 (decreases).
- **N2**: After gaining an electron, bond order remains the same (14 electrons, no change).
- **CN**: After gaining an electron, bonding electrons increase to 10, so bond order becomes (10 - 4) / 2 = 3 (increases).
- **NO**: After gaining an electron, anti-bonding electrons increase, bond order becomes (10 - 6) / 2 = 2 (decreases).
### Conclusion:
The species that will most likely gain an electron to form a thermodynamically more stable species is **CN**, as its bond order increases from 2.5 to 3 after gaining an electron.
