Problem 114 - A Complete Resource Book in Chemistry for JEE Main

Question

The common features among the species \(\mathrm{CN}^{-}, \mathrm{CO}\) and \(\mathrm{NO}^{+}\)are (a) bond order three and isoelectronic (b) bond order three and weak field ligands (c) bond order two and \(\pi\)-acceptors (d) isoelectronic and weak field ligands.

Step-by-Step Solution

Answer

Option (a) bond order three and isoelectronic.

Step 1: Understanding Isoelectronic Concepts

Species are considered isoelectronic if they have the same number of electrons. To determine if the molecules \(\mathrm{CN}^{-}, \mathrm{CO},\) and \(\mathrm{NO}^{+}\) are isoelectronic, we calculate their total number of electrons. For \(\mathrm{CN}^{-}\), the number of electrons is 14 (\(C:6 + N:7 + 1\) from the negative charge). For \(\mathrm{CO}\), the total is 14 (\(C:6 + O:8\)). For \(\mathrm{NO}^{+}\), the total is also 14 (\(N:7 + O:8 - 1\) due to the positive charge). Therefore, all three species are isoelectronic.

Step 2: Calculating Bond Order

Bond order is calculated using the formula: \(\text{Bond Order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons})\). For \(\mathrm{CN}^{-}, \mathrm{CO},\) and \(\mathrm{NO}^{+}\), molecular orbital theory shows that each has 10 bonding and 4 antibonding electrons, leading to a bond order of \(\frac{1}{2}(10 - 4) = 3\). Thus, they all have bond order three.

Step 3: Analyzing Ligand Field Strength

Weak field ligands are typically those that do not force pairing of electrons inside the d orbitals of central metal ions in coordination complexes. \(\mathrm{CN}^{-}\) and \(\mathrm{CO}\) are known as strong field ligands usually, while \(\mathrm{NO}^{+}\) can either act as a strong field or weak field ligand depending on specific conditions. The common characteristic of all being weak field ligands is not applicable.

Step 4: Conclusion

From the above analysis, we find that all three species are isoelectronic and have a bond order of three. They are not all weak field ligands, hence option (a) "bond order three and isoelectronic" is the correct description of common features for \(\mathrm{CN}^{-}, \mathrm{CO},\) and \(\mathrm{NO}^{+}\).

Key Concepts

Bond Order

Bond order is an important concept in chemistry that helps us understand the strength and stability of a bond between two atoms. It is defined as the difference between the number of bonding electrons and antibonding electrons, divided by two. This can be mathematically expressed as:\[\text{Bond Order} = \frac{1}{2}(\text{Number of Bonding Electrons} - \text{Number of Antibonding Electrons})\]To get a clearer picture, let's consider the species \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\). Using molecular orbital theory, we find that each of these molecules has 10 bonding electrons and 4 antibonding electrons. Applying our bond order formula:

• \[\text{Bond Order} = \frac{1}{2}(10 - 4) = 3\]

This means each of these molecules has a bond order of three, indicating strong triple bonds. A higher bond order signifies more electron sharing between the atoms, thereby resulting in stronger, more stable molecules.

Molecular Orbital Theory

Molecular Orbital (MO) Theory provides a modern understanding of how atomic orbitals combine to form molecular orbitals in a molecule. This theory explains the electronic structure of molecules with a more comprehensive framework compared to other theories, such as Valence Bond Theory.In MO Theory, atomic orbitals from each atom involved overlap to create molecular orbitals. This results in bonding and antibonding orbitals:

• Bonding Orbitals: These orbitals have lower energy and are filled first, helping atoms bind together.
• Antibonding Orbitals: These have higher energy and are detrimental to bond formation when filled with electrons.

The arrangement of electrons in these orbitals determines the molecule's properties, including bond order and magnetic properties. For molecules like \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\), MO Theory helps us visualize why they are isoelectronic and possess similar bond orders. This framework also provides insights into their electronic transitions and spectroscopic behaviors.

Ligand Field Strength

Ligand field strength is a concept related primarily to coordination chemistry. It describes the ability of a ligand to split the d orbital energies of a metal ion in a complex. This splitting, known as ligand field splitting, is a fundamental factor in understanding and predicting the color and magnetic properties of coordination complexes.Ligands can be categorized into two types based on their field strength:

• Strong Field Ligands: These ligands cause a large splitting of the d orbitals and can lead to low spin complexes, which result in paired electron configurations.
• Weak Field Ligands: These cause lesser splitting, often resulting in high spin complexes, with unpaired electrons.

In the context of \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\), \(\mathrm{CN}^{-}\) and \(\mathrm{CO}\) are typically strong field ligands, causing considerable d orbital splitting. \(\mathrm{NO}^{+}\), however, can exhibit variability, sometimes acting as a strong or weak field ligand, depending on the specific conditions and surrounding coordination environment. This variability is why it's essential to carefully consider the context when analyzing ligand behaviors.