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 the Number of Electrons

To begin, count the total number of electrons in each species. - **CN⁻**: Carbon has 6 electrons, Nitrogen has 7 electrons, and there is an extra electron due to the negative charge, totaling 6 + 7 + 1 = 14 electrons. - **CO**: Carbon has 6 electrons and Oxygen has 8 electrons, totaling 6 + 8 = 14 electrons. - **NO⁺**: Nitrogen has 7 electrons and Oxygen has 8 electrons, but one electron is removed due to the positive charge, totaling 7 + 8 - 1 = 14 electrons.

Check for Isoelectronic Nature

Species are isoelectronic if they have the same number of electrons. From Step 1, each of the species CN⁻, CO, and NO⁺ has 14 electrons. Therefore, these species are isoelectronic.

Assess Bond Order

Use molecular orbital (MO) theory to determine the bond order, which is given by the formula:\[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]Since all species are isoelectronic, they will have a similar MO diagram leading to the same bond order. For these 14-electron species, the bond order is 3.

Evaluate Ligand Field Strength

Check whether the species are likely weak or strong field ligands. All three species can act as ligands and typically have strong \(\pi\)-bonding capabilities, making them strong field ligands rather than weak field ligands.

Analyze the Options

Now, compare the findings from the previous steps with the given options:- (a) Bond order three and isoelectronic: matches because all have bond order 3 and are isoelectronic.- (b) Bond order three and weak field ligands: half correct, bond order is 3 but they are not weak field ligands.- (c) Bond order two and \(\pi\)-acceptors: incorrect, bond order is 3 and they are \(\pi\)-donors, not acceptors.- (d) Isoelectronic and weak field ligands: half correct, they are isoelectronic but not weak field ligands.

Key concepts

Bond Order

Understanding bond order is crucial in studying chemical bonding and stability. Bond order tells us how many chemical bonds exist between a pair of atoms. In simple terms, it indicates the strength and length of a bond. A higher bond order equates to a stronger, shorter bond, while a lower bond order indicates a weaker, longer bond.

Mathematically, bond order can be calculated using molecular orbital (MO) theory with the formula: \[ \text{Bond Order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \]Just remember to subtract the antibonding electrons from the bonding electrons and then divide by two. This gives an insight into the molecular stability. When we talk about species like \(\text{CN}^{-},\text{ CO},\) and \(\text{NO}^{+}\), the bond order comes out to be 3.

This means these bonds have a triple bond, making them very stable. Therefore, recognizing bond order helps in predicting the behavior and reactivity of molecules, especially in organic and inorganic chemistry.

Molecular Orbital Theory

Molecular Orbital (MO) Theory offers a more comprehensive way to think about how atomic orbitals combine in molecules, compared to the simpler Valence Bond Theory. This theory is essential for understanding the electronic structure and thus the chemical properties of molecules.

In MO theory, atomic orbitals of atoms in a molecule combine to form molecular orbitals, which are spread over the entire molecule. These molecular orbitals are categorized into bonding orbitals, which hold atoms together, and antibonding orbitals, which can weaken the bond if occupied.

• Bonding molecular orbitals are lower in energy and stabilize the molecule.
• Antibonding molecular orbitals are higher in energy and destabilize the molecule.
• Nonbonding orbitals do not significantly impact bond strength.

Atoms in species like \(\text{CN}^{-},\text{ CO},\) and \(\text{NO}^{+}\) form similar MOs due to their isoelectronic nature. All hold a bond order of 3, agreeing with MO theory predictions. Understanding MO theory is crucial when you study these molecular electronic structures that influence chemical reactivity and properties.

Ligand Field Strength

Ligand field strength is crucial in coordination chemistry, influencing the electronic splitting in metal complexes. This involves predicting how ligands impact the energy levels of d-orbitals in transition metal complexes, fundamentally affecting their color, magnetism, and reactivity.

In the context of ligands like \(\text{CN}^{-},\text{ CO},\) and \(\text{NO}^{+}\), the strength is primarily linked to their bonding characteristics. These molecules are known for being strong \(\pi\)-donors due to their ability to donate electron density through \(pi\)-bonds.

• Strong field ligands typically cause a larger splitting of d-orbitals. This can result in low-spin complexes in transition metal ions.
• Weak field ligands often lead to smaller orbital splitting, resulting in high-spin complexes.

The distinction between being a strong or weak field ligand affects the overall stabilization and properties of the metal-ligand complex. Knowing about ligand field strength helps students appreciate the complexities of electron interactions in metal coordination chemistry, enhancing their understanding of bond strength and molecular stability.