Question

Which of the following statements is not correct from the point of view of molecular orbital? (1) \(\mathrm{Be}_{2}\) is not a stable molecule (2) \(\mathrm{He}_{2}\) not stable but \(\mathrm{He}^{+}\)is expected to exist (3) Bond strength of \(\mathrm{N}_{2}\) is maximum amongst the homonuclear diatomic molecules (4) The order of energies of molecular orbitals in \(\mathrm{O}_{2}\) molecule is \(\mathrm{E}(\sigma 2 \mathrm{~s})<\mathrm{E}\left(\sigma^{*} 2 \mathrm{~s}\right)<\mathrm{E}\left(\pi 2 p_{\mathrm{x}}\right)=\mathrm{E}\left(\pi 2 \mathrm{p}_{\mathrm{y}}\right)<\) \(\mathrm{E}\left(\sigma 2 \mathrm{p}_{2}\right)<\mathrm{E}\left(\pi^{\star} 2 \mathrm{p}_{\mathrm{x}}\right)=\mathrm{E}\left(\pi^{*} 2 \mathrm{p}_{y}\right)<\mathrm{E}\left(\sigma^{\star} 2 \mathrm{p}_{\mathrm{z}}\right)\)

Short answer

Statement (4) is not correct.

Step-by-step solution

- Understanding Molecular Stability

Assess the stability of \(\mathrm{Be}_{2}\), \(\mathrm{He}_{2}\), and \(\mathrm{He}^{+}\). According to molecular orbital theory, \(\mathrm{Be}_{2}\) is not stable due to its zero bond order. \(\mathrm{He}_{2}\) is also unstable due to a bond order of zero, whereas \(\mathrm{He}^{+}\) has a bond order of 0.5 and is expected to exist.

- Bond Strength Analysis

Examine the bond strength of \(\mathrm{N}_{2}\). The bond order of \(\mathrm{N}_{2}\) is 3, due to its electronic configuration in the molecular orbitals. \(\mathrm{N}_{2}\) therefore has a very strong triple bond, making it one of the strongest homonuclear diatomic molecules.

- Orbital Energy Order in \(\mathrm{O}_{2}\)

Evaluate the given order of molecular orbital energies for \(\mathrm{O}_{2}\). The correct order should be: \[\mathrm{E}(\sigma 2 \mathrm{~s})<\mathrm{E}(\sigma^{*} 2\mathrm{~s})<\mathrm{E}(\sigma 2p_{z})<\mathrm{E}\big(\pi 2\mathrm{p}_{x}(=\pi 2 \mathrm{p}_{y})\big)<\mathrm{E}(\pi^{*}2\mathrm{p}_{x}(=\pi^{*}2 \mathrm{p}_y))<\mathrm{E}(\sigma^{*}2\mathrm{p}_{z})\].

- Identifying Incorrect Statement

Review the statements again and identify the incorrect statement based on molecular orbital theory and correct theoretical order of molecular orbital energies. The fourth statement is incorrect as it does not match the correct energy order for \(\mathrm{O}_{2}\).

Key concepts

Molecular Stability

In molecular orbital theory, the stability of a molecule is determined by its bond order. Bond order is calculated based on the difference between the number of bonding electrons and the number of antibonding electrons, divided by two. The bond order can give us insight into whether a molecule is likely to exist. For instance, in the case of \(\text{Be}_2\), the bond order is zero, meaning it has an equal number of bonding and antibonding electrons. This leads to no net bond between the atoms, resulting in an unstable molecule. Similarly, \(\text{He}_2\) has a bond order of zero, making it unstable as well. However, \(\text{He}^+\) has one less electron, resulting in a bond order of 0.5, which allows it to exist, albeit as a weakly bound molecule. Understanding bond order is crucial in predicting molecular stability and determining whether a molecule will form or not.

Bond Strength

Bond strength is closely related to bond order. A higher bond order generally means stronger bonds, as there are more electrons in bonding orbitals compared to antibonding orbitals. Taking nitrogen gas (\(\text{N}_2\)) as an example, it has a bond order of 3. This is because there are three pairs of electrons in bonding orbitals (including the \(\text{π}\) and \(\text{σ}\) bonds) and no electrons in antibonding orbitals for these bonds. The result is a very strong triple bond, making \(\text{N}_2\) one of the most stable diatomic molecules, with a higher bond dissociation energy compared to other homonuclear diatomic molecules. This exceptionally high bond strength is why \(\text{N}_2\) is so prevalent in Earth's atmosphere, as it is difficult to break down.

Orbital Energy Order

The arrangement of molecular orbitals (MOs) by energy levels is essential in molecular orbital theory, as it helps predict the electron configuration in a molecule. For diatomic oxygen (\(\text{O}_2\)), the correct order of molecular orbital energies is: E(\(\text{σ}\) 2\text{s}) < E(\(\text{σ}^*\) 2\text{s}) < E(\(\text{σ}\) 2\text{p}_{z}) < E(\(\text{π}\) 2\text{p}_{x}) = E(\(\text{π}\) 2\text{p}_{y}) < E(\(\text{π}^*\) 2\text{p}_{x}) = E(\(\text{π}^*\) 2\text{p}_{y}) < E(\(\text{σ}^*\) 2\text{p}_{z}). In this order:

• \text{σ} bonds are formed by head-on overlap and are typically lower in energy than \(\text{π}\) bonds, which are formed by side-on overlap.
• The \(\text{π}^*\) and \(\text{σ}^*\) orbitals are antibonding and higher in energy than their bonding counterparts.
• Degenerate orbitals (same energy level) include \(\text{π}\) 2\text{p}_{x} and \(\text{π}\) 2\text{p}_{y}, as well as \(\text{π}^*\) 2\text{p}_{x} and \(\text{π}^*\) 2\text{p}_{y}.

Understanding this order helps in assigning electrons to the correct MOs and predicting magnetic properties and bond orders in molecules.