Question

Which of the following statements does not correct from the point of view of molecular orbital? (1) \(\mathrm{Be}_{2}\) is not a stable molecule (2) \(\mathrm{He}_{2}\) is 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 \(E(\sigma 2 s)

Short answer

Statement (4) is incorrect.

Step-by-step solution

Analyzing Statement (1)

Each molecular orbital (MO) must be considered according to its stability. The molecule \( \text{Be}_2 \) consists of two beryllium atoms. The electronic configuration of Be is 1s2 2s2. Since both bonding and antibonding MOs are filled equally, they cancel each other out, making \( \text{Be}_2 \) not a stable molecule. Thus, statement (1) is correct.

Analyzing Statement (2)

The \( \text{He}_2 \) molecule is generally not stable because adding electrons to both bonding and antibonding MOs leads to zero bond order. The ion \( \text{He}_2^+ \), however, has one less electron, so it has a non-zero bond order and is expected to exist. Hence, statement (2) is also correct.

Analyzing Statement (3)

The bond strength in homonuclear diatomic molecules can be correlated with bond order. The molecule \( \text{N}_2 \) has a triple bond, which is the strongest bond among homonuclear diatomic molecules, making statement (3) correct.

Analyzing Statement (4)

The order of energies of molecular orbitals in \( \text{O}_2 \) provided in statement (4) is incorrect. For \( \text{O}_2 \), the correct order is: \[ E(\text{σ} 2s) < E(\text{σ}^* 2s) < E(\text{σ} 2p_z) < E(\text{π} 2p_x) = E(\text{π} 2p_y) < E(\text{π}^* 2p_x) = E(\text{π}^* 2p_y) < E(\text{σ}^* 2p_z) \]. Thus, statement (4) is not correct.

Key concepts

Molecular orbital stability

Molecular orbital (MO) stability is a key concept when determining the existence and behavior of molecules. Each molecular orbital is formed by the combination of atomic orbitals from bonding atoms. These MOs can be either bonding or antibonding. Bonding MOs contribute to the stability of a molecule, while antibonding MOs work against it.

For a molecule to be stable, the number of electrons in bonding orbitals must exceed those in antibonding orbitals. This balance is crucial for molecules like \( \text{Be}_2 \) and \( \text{He}_2 \). For example, \( \text{Be}_2 \) consists of two beryllium atoms, each with an electronic configuration of \(1s^2 2s^2 \). The molecular orbitals formed from these atomic orbitals include equal numbers of bonding and antibonding electrons. Hence, their effects cancel out, leading to an unstable molecule.

Similarly, \( \text{He}_2 \) is generally unstable because electrons fill both bonding and antibonding orbitals equally, resulting in zero net stability. However, the ion \( \text{He}_2^+ \) with one less electron, tips the balance in favor of bonding orbitals, making it relatively stable.

Bond order

Bond order is a vital factor in analyzing the stability and strength of a molecule. It is calculated by the formula: \[ \text{Bond Order} = \frac{(\text{Number of bonding electrons}) - (\text{Number of antibonding electrons})}{2} \]

A higher bond order indicates a stronger bond and greater stability of the molecule. For instance, nitrogen \( \text{N}_2 \) has a high bond order due to its triple bond, making it one of the strongest homonuclear diatomic molecules. In contrast, \( \text{He}_2 \) has a bond order of zero, confirming its instability. However, \( \text{He}_2^+ \) has a bond order of 0.5 because the ion has unpaired electrons in the antibonding orbital, lending some stability.

Bond order can directly correlate with bond strength and length. As seen with \( \text{N}_2 \), a high bond order results in an exceptionally strong and short bond, reflecting its stability.

Electronic configuration

Understanding the electronic configuration of molecules is essential to grasp molecular orbital theory. Electronic configuration tells you how electrons are distributed among the molecular orbitals in a molecule.

For homonuclear diatomic molecules, the order of molecular orbitals can vary. For example, in oxygen \( \text{O}_2 \), the actual order is different from what might be expected. The correct order for \( \text{O}_2 \) is: \[ E(\text{σ} 2s) < E(\text{σ}^* 2s) < E(\text{σ} 2p_z) < E(\text{π} 2p_x) = E(\text{π} 2p_y) < E(\text{π}^* 2p_x) = E(\text{π}^* 2p_y) < E(\text{σ}^* 2p_z) \]

This deviates from simpler atomic orbital filling rules and must be remembered for accurate molecular predictions. Incorrect assumptions here can lead to misunderstandings of molecular behavior, such as incorrect bond strength or stability predictions.

Thus, each molecule may require a specific consideration of its electronic configuration, which accurately reflects the distribution of electrons among its molecular orbitals.