Problem 59 - Chemistry An Atoms First Approach

Question

How can the paramagnetism of \(\mathrm{O}_{2}\) be explained using the molecular orbital model?

Step-by-Step Solution

Answer

The paramagnetism of O2 can be explained using the molecular orbital model by analyzing its electronic configuration and filling the molecular orbitals. With a total of 12 valence electrons, the electron configuration in molecular orbitals is as follows: σ₁s(2), σ₁s*(2), σ₂s(2), σ₂s*(2), π2px(1), π2py(1), and the rest are empty. There are two unpaired electrons in the π2px and π2py orbitals, which indicate paramagnetism in O2 according to the molecular orbital model.

Step 1: Identify the atomic orbitals and number of valence electrons for oxygen

Oxygen has an electron configuration of 1s² 2s² 2p⁴. Since we are combining two oxygen atoms to form O2, we have a total of (2s² 2p⁴) × 2 = 2s⁴ 2p⁸ valence electrons to fill the molecular orbitals.

Step 2: Determine the molecular orbital diagram for O2

Now, we need to create a molecular orbital (MO) diagram for O2. The diagram should show the atomic orbitals of individual oxygen atoms on the sides and the molecular orbitals in the middle. Make sure you follow the Aufbau principle, Hund's rule, and the Pauli exclusion principle to correctly fill the orbitals. The molecular orbitals include: 1. Two sigma(σ) orbitals: σ₁s and σ₂s 2. Two sigma(*) anti-bonding orbitals: σ₁s* and σ₂s* 3. Two pi(π) bonding orbitals: π2px and π2py 4. Two pi(*) anti-bonding orbitals: π2px* and π2py* 5. One sigma(σ) bonding orbital: σ₂pz 6. One sigma(*) anti-bonding orbital: σ₂pz*

Step 3: Fill the molecular orbitals with electrons

Fill the molecular orbitals with the 12 valence electrons of O2, starting from the lowest energy level according to the Aufbau principle. The number of electrons are: 1. σ₁s: 2 electrons 2. σ₁s*: 2 electrons 3. σ₂s: 2 electrons 4. σ₂s*: 2 electrons 5. π2px and π2py: 4 electrons (2 in each orbital, as per Hund's rule) 6. σ₂pz: 0 electrons 7. π2px* and π2py*: 0 electrons 8. σ₂pz*: 0 electrons

Step 4: Analyze the electron configuration for paramagnetism

Observe the electron configuration in molecular orbitals and focus on the π2px and π2py molecular orbitals. As per Hund's rule, there are 2 unpaired electrons in these orbitals (one in each orbital). Since there are unpaired electrons in O2's molecular orbitals, it exhibits paramagnetism. Thus, the molecular orbital model can explain the paramagnetism of O2 due to the presence of unpaired electrons in its π orbitals.