Question

\(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) are converted into monoanions \(\mathrm{N}_{2}^{-}\)and \(\mathrm{O}_{2}^{-}\)respectively. Which of the following statements is wrong? (1) In \(\mathrm{N}_{2}^{-}\), N-N bond weakens (2) In \(\mathrm{O}_{2}^{-}\), O-O bond order increases (3) In \(\mathrm{O}_{2}^{-}, \mathrm{O}-\mathrm{O}\) bond order decreases (4) \(\mathrm{N}_{2}^{-}\)becomes paramagnetic

Short answer

Statement (2) is wrong because the bond order in \(\text{O}_2^{-}\) decreases.

Step-by-step solution

Analyze the N-N Bond in \(\text{N}_2^{-}\)

Adding one electron to \(\text{N}_2 \) results in \(\text{N}_2^{-}\). This additional electron enters the \(\text{anti-bonding}\) molecular orbital, which weakens the N-N bond by decreasing the bond order.

Analyze the O-O Bond Order in \(\text{O}_2^{-}\)

Adding one electron to \(\text{O}_2 \) results in \(\text{O}_2^{-}\). This electron also enters an \(anti-bonding\) molecular orbital, thereby decreasing the O-O bond order, not increasing it.

Confirm the statement about O-O Bond Order Decrease

Since in \(\text{O}_2^{-}\), the added electron enters an \(anti-bonding\) orbital, the bond order decreases.

Determine Magnetism in \(\text{N}_2^{-}\)

By adding an electron to \(\text{N}_2\), \(\text{N}_2^{-}\) gains an unpaired electron, making it paramagnetic.

Conclusion: Identify the Incorrect Statement

Statement (2) is incorrect because in \(\text{O}_2^{-}\), the bond order decreases rather than increases.

Key concepts

Bond Order

Bond order is a concept that helps understand the strength and stability of a bond between two atoms. 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 means a stronger, more stable bond. For example, in a diatomic nitrogen molecule \(\text{N}_2\), the bond order is 3, indicating a triple bond. When an electron is added to form \(\text{N}_2^{-}\), this electron enters an antibonding orbital, reducing the overall bond order and weakening the bond. Similarly, in the oxygen molecule \(\text{O}_2\), the bond order decreases when an extra electron is added to form \(\text{O}_2^{-}\) due to the same reasoning.

Paramagnetism

Paramagnetism is a form of magnetism whereby certain materials are weakly attracted by an externally applied magnetic field. This property is due to the presence of unpaired electrons in the material. In the context of molecular orbital theory, consider the nitrogen molecule \(\text{N}_2\). When it gains an electron to form \(\text{N}_2^{-}\), this added electron occupies an antibonding orbital and remains unpaired. The presence of this unpaired electron makes \(\text{N}_2^{-}\) paramagnetic. In contrast, a molecule like \(\text{O}_2\), which already contains unpaired electrons in its neutral state, becomes even more affected when it gains or loses electrons, altering its magnetic properties.

Antibonding Orbitals

Antibonding orbitals are molecular orbitals that weaken the bond between two atoms when occupied by electrons. These orbitals have higher energy than bonding orbitals. They are denoted with an asterisk, as in \(\text{σ}^*\) or \(\text{π}^*\). For instance, when an electron is added to the nitrogen molecule \(\text{N}_2\) forming \(\text{N}_2^{-}\), the electron enters an antibonding orbital. This reduces the electron density between the two nuclei, thus weakening the bond. Similarly, adding an electron to \(\text{O}_2\) to form \(\text{O}_2^{-}\) fills an antibonding orbital, decreasing the bond order and making the bond weaker. Understanding antibonding orbitals is crucial for explaining changes in bond properties when electrons are added or removed from a molecule.