Answer :
Molecular Orbital Theory (MOT) provides an excellent framework for understanding the electronic structure and properties of molecules, including oxygen gas, [tex]\(O_2\)[/tex].
In the case of [tex]\(O_2\)[/tex], the molecular orbital configuration can be constructed by combining the atomic orbitals of the two oxygen atoms. Here is a step-by-step explanation:
1. Atomic Configuration of Oxygen: Each oxygen atom has an atomic number of 8, so its electronic configuration is [tex]\(1s^2 2s^2 2p^4\)[/tex].
2. Molecular Orbitals Formation: When two oxygen atoms combine, their atomic orbitals overlap to form molecular orbitals. The [tex]\(2p\)[/tex] orbitals combine to form two sets of molecular orbitals ([tex]\(\sigma\)[/tex] and [tex]\(\pi\)[/tex]) and their corresponding antibonding orbitals.
The ordering of these molecular orbitals for oxygen is:
[tex]\[ \sigma_{2s} < \sigma_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z} \][/tex]
3. Population of Molecular Orbitals:
- The total number of electrons in [tex]\(O_2\)[/tex] is [tex]\(16\)[/tex] since each oxygen atom contributes [tex]\(8\)[/tex] electrons.
- These electrons are placed in the molecular orbitals in the following order:
[tex]\[ 2\sigma_{1s}^2, 2\sigma_{1s}^2, 2\sigma_{2s}^2, 2\sigma_{2s}^2, 2\sigma_{2p_z}^2, 4\pi_{2p_x}^2 = 4\pi_{2p_y}^2, 2\pi_{2p_x}^1 = 2\pi_{2p_y}^1 \][/tex]
4. Unpaired Electrons in [tex]\(O_2\)[/tex]: The critical observation here is the filling of the [tex]\(\pi_{2p_x}\)[/tex] and [tex]\(\pi_{2p_y}\)[/tex] orbitals. Each of these [tex]\(\pi_{2p}\)[/tex] antibonding orbitals hosts one unpaired electron.
5. Paramagnetism of [tex]\(O_2\)[/tex]: According to Molecular Orbital Theory, the presence of unpaired electrons in an orbital leads to paramagnetism. Since [tex]\(O_2\)[/tex] has two unpaired electrons in the [tex]\(\pi_{2p_x}\)[/tex] and [tex]\(\pi_{2p_y}\)[/tex] orbitals, it exhibits paramagnetism.
To summarize, the correct reason why Molecular Orbital Theory correctly predicts the paramagnetism of oxygen gas, [tex]\(O_2\)[/tex], is:
[tex]\[ \text{there are two unpaired electrons in the MO electron configuration of } O_2. \][/tex]
Therefore, the correct answer is:
- there are two unpaired electrons in the MO electron configuration of [tex]\(O_2\)[/tex].
In the case of [tex]\(O_2\)[/tex], the molecular orbital configuration can be constructed by combining the atomic orbitals of the two oxygen atoms. Here is a step-by-step explanation:
1. Atomic Configuration of Oxygen: Each oxygen atom has an atomic number of 8, so its electronic configuration is [tex]\(1s^2 2s^2 2p^4\)[/tex].
2. Molecular Orbitals Formation: When two oxygen atoms combine, their atomic orbitals overlap to form molecular orbitals. The [tex]\(2p\)[/tex] orbitals combine to form two sets of molecular orbitals ([tex]\(\sigma\)[/tex] and [tex]\(\pi\)[/tex]) and their corresponding antibonding orbitals.
The ordering of these molecular orbitals for oxygen is:
[tex]\[ \sigma_{2s} < \sigma_{2s} < \sigma_{2p_z} < \pi_{2p_x} = \pi_{2p_y} < \pi_{2p_x} = \pi_{2p_y} < \sigma_{2p_z} \][/tex]
3. Population of Molecular Orbitals:
- The total number of electrons in [tex]\(O_2\)[/tex] is [tex]\(16\)[/tex] since each oxygen atom contributes [tex]\(8\)[/tex] electrons.
- These electrons are placed in the molecular orbitals in the following order:
[tex]\[ 2\sigma_{1s}^2, 2\sigma_{1s}^2, 2\sigma_{2s}^2, 2\sigma_{2s}^2, 2\sigma_{2p_z}^2, 4\pi_{2p_x}^2 = 4\pi_{2p_y}^2, 2\pi_{2p_x}^1 = 2\pi_{2p_y}^1 \][/tex]
4. Unpaired Electrons in [tex]\(O_2\)[/tex]: The critical observation here is the filling of the [tex]\(\pi_{2p_x}\)[/tex] and [tex]\(\pi_{2p_y}\)[/tex] orbitals. Each of these [tex]\(\pi_{2p}\)[/tex] antibonding orbitals hosts one unpaired electron.
5. Paramagnetism of [tex]\(O_2\)[/tex]: According to Molecular Orbital Theory, the presence of unpaired electrons in an orbital leads to paramagnetism. Since [tex]\(O_2\)[/tex] has two unpaired electrons in the [tex]\(\pi_{2p_x}\)[/tex] and [tex]\(\pi_{2p_y}\)[/tex] orbitals, it exhibits paramagnetism.
To summarize, the correct reason why Molecular Orbital Theory correctly predicts the paramagnetism of oxygen gas, [tex]\(O_2\)[/tex], is:
[tex]\[ \text{there are two unpaired electrons in the MO electron configuration of } O_2. \][/tex]
Therefore, the correct answer is:
- there are two unpaired electrons in the MO electron configuration of [tex]\(O_2\)[/tex].
