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.

Short answer

(a) Bond order three and isoelectronic.

Step-by-step solution

Determine Electron Count for Each Species

To find out if the species are isoelectronic, we need to determine their total electron count. - For \(\mathrm{CN}^{-}\): Carbon has 6 electrons, Nitrogen has 7 electrons, and with an additional electron from the negative charge, the total is 14 electrons.- For \(\mathrm{CO}\): Carbon has 6 electrons, and Oxygen has 8 electrons, totaling 14 electrons.- For \(\mathrm{NO}^{+}\): Nitrogen has 7 electrons, Oxygen has 8 electrons, and removing one electron due to the positive charge gives a total of 14 electrons.

Verify Isoelectronic Species

Since each species has a total of 14 electrons, \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\) are isoelectronic.

Determine Bond Order

Calculate the bond order using the formula: \[ \text{Bond order} = \frac{1}{2} \times (\text{number of bonding electrons} - \text{number of antibonding electrons}) \]- For \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\), due to being isoelectronic, they will have similar molecular orbital diagrams. This gives a bond order of 3 for each species.

Identify Ligand Type

Examine the ligand strength and character for each species. \(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\) are known to be strong field ligands, not weak.

Conclusion: Determine the Correct Features

\(\mathrm{CN}^{-}\), \(\mathrm{CO}\), and \(\mathrm{NO}^{+}\) all have a bond order of 3 and are isoelectronic, matching option (a). They are not weak field ligands, so options (b) and (d) are incorrect, and they do not have a bond order of 2, eliminating option (c).

Key concepts

Bond Order

Bond order is a crucial concept in chemistry that helps determine the strength and stability of a bond between two atoms in a molecule. It indicates the number of chemical bonds between a pair of atoms.

Bond order can often be correlated with the bond length and bond strength: the higher the bond order, the stronger and shorter the bond. It is calculated using a simple formula: \[ \text{Bond order} = \frac{1}{2} \times (\text{Number of bonding electrons} - \text{Number of antibonding electrons}) \] To effectively calculate the bond order, you need to know the number of bonding electrons and antibonding electrons which can be determined using molecular orbital theory. In the case of isoelectronic species such as \(\text{CN}^-\), \(\text{CO}\), and \(\text{NO}^+\), they share the same bond order, as they have similar electronic configurations. For each of these species, the bond order is 3, indicating triple bonds, which reflect the high stability and strength of these species.

Molecular Orbital Theory

Molecular Orbital Theory (MOT) is a method used to describe the electronic structure of molecules. Unlike the Valence Bond Theory that focuses on bonding in terms of atomic orbitals, MOT considers that electrons in molecules occupy molecular orbitals spread over the entire molecule.

In molecular orbitals, electrons from the atoms combine to form new orbitals that can be classified as either bonding or antibonding. Bonding orbitals are lower in energy and contribute to the stability of a molecule, while antibonding orbitals are higher in energy.

• Bond order is derived from the difference between the number of electrons in bonding and antibonding orbitals.
• For isoelectronic species \(\text{CN}^-\), \(\text{CO}\), and \(\text{NO}^+\), the occupancy of these molecular orbitals determines their identical bond order.

MOT provides insight into the electronic transitions, magnetic properties, and chemical reactivity of molecules, making it fundamental to understanding molecular behavior.

Ligand Field Theory

Ligand Field Theory (LFT) is an extension of the Crystal Field Theory (CFT) that incorporates the covalent aspects of ligand interactions with transition metals. It is particularly useful in understanding the nature and behavior of coordination complexes.

In LFT, ligands, which are ions or molecules that donate an electron pair to the metal, can influence the distribution and energy of d-orbitals of the central metal atom. This affects the metal's electronic structure, shapes the geometry, color, magnetism, and reactivity of the complex.

• Strong field ligands can cause a significant splitting of d-orbitals leading to low-spin configurations.
• Weak field ligands result in smaller splitting and high-spin configurations.

In the original exercise, species like \(\text{CN}^-\), \(\text{CO}\), and \(\text{NO}^+\) are strong field ligands, contrary to being described as weak field ligands in one of the incorrect options. Their strong field nature is crucial in determining their ability to form stable compounds.