Question

According to molecular orbital theory, the number of unpaired electron(s) in $\text{O}_2^{2-}$ is ________.

Hint:

$\text{O}_2$ (16e) is paramagnetic with 2 unpaired electrons in $\pi^*$. Adding electrons to form $\text{O}_2^-$ (17e) leaves 1 unpaired electron, and $\text{O}_2^{2-}$ (18e) pairs all electrons, becoming diamagnetic.

Answer 1

Correct Answer: 0

Step 1: Understanding the Concept:
Molecular Orbital (MO) theory describes the electronic structure of molecules by distributing electrons into orbitals that cover the entire molecule. The presence or absence of unpaired electrons in the highest occupied molecular orbitals (HOMO) determines the magnetic properties of the species.
Step 2: Detailed Explanation:
1. Each Oxygen atom has 8 electrons. For the peroxide ion ($\text{O}_2^{2-}$), total electrons $= 8 + 8 + 2 = 18$ electrons.
2. The MO configuration for $\text{O}_2^{2-}$ (similar to $\text{F}_2$) is:
\[ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2, \sigma 2p_z^2, (\pi 2p_x^2 = \pi 2p_y^2), (\pi^* 2p_x^2 = \pi^* 2p_y^2) \]
3. Distribution of valence electrons (14 electrons beyond $\sigma^* 1s$):
- $\sigma 2s$ takes 2, $\sigma^* 2s$ takes 2. (Remaining: 10)
- $\sigma 2p_z$ takes 2. (Remaining: 8)
- $\pi 2p_x$ and $\pi 2p_y$ take 2 each ($2+2 = 4$). (Remaining: 4)
- $\pi^* 2p_x$ and $\pi^* 2p_y$ take 2 each ($2+2 = 4$). (Remaining: 0)
4. Observation: All occupied orbitals, including the antibonding pi orbitals ($\pi^*$), are fully filled with pairs of electrons.
5. Number of unpaired electrons = 0.
Step 3: Final Answer:
The number of unpaired electrons is 0.