Question

Consider the following list of small molecules and ions: \(\mathrm{C}_{2}, \mathrm{O}_{2}^{-}, \mathrm{CN}^{-}, \mathrm{O}_{2}, \mathrm{CO}, \mathrm{NO}, \mathrm{NO}^{+}, \mathrm{C}_{2}^{2-}, \mathrm{OF}^{-} .\) Identify (a) all species that have a bond order of 3 (b) all species that are paramagnetic (c) species that have a fractional bond order

Short answer

(a) \(\mathrm{CN}^{-}, \mathrm{CO}, \mathrm{NO}^{+}\). (b) \(\mathrm{O}_{2}, \mathrm{O}_{2}^{-}, \mathrm{NO}\). (c) \(\mathrm{O}_{2}^{-}, \mathrm{NO}, \mathrm{OF}^{-}\).

Step-by-step solution

Calculate Bond Orders

To find bond orders, use the formula \[ \text{Bond order} = \frac{(\text{Number of bonding electrons} - \text{Number of antibonding electrons})}{2} \].- \(\mathrm{C}_{2}\): 12 bonding electrons = bond order 1.- \(\mathrm{O}_{2}^{-}\): Uses MO diagram, bond order 1.5.- \(\mathrm{CN}^{-}\): Equivalent to \(\mathrm{N}_{2}\), bond order 3.- \(\mathrm{O}_{2}\): 10 bonding and 6 antibonding electrons, bond order 2.- \(\mathrm{CO}\): Similar to \(\mathrm{N}_{2}\), bond order ~3.- \(\mathrm{NO}\): Bond order 2.5.- \(\mathrm{NO}^{+}\): Bond order 3 (isoelectronic with \(\mathrm{CO}\)).- \(\mathrm{C}_{2}^{2-}\): Bond order 2.- \(\mathrm{OF}^{-}\): Bond order 1.5.

Identify Paramagnetic Species

A molecule is paramagnetic if it has unpaired electrons. Use molecular orbital theory to identify species with unpaired electrons.- \(\mathrm{O}_{2}\): Paramagnetic with 2 unpaired electrons.- \(\mathrm{O}_{2}^{-}\): One more electron than \(\mathrm{O}_{2}\) causing one unpaired electron.- \(\mathrm{NO}\): Has one unpaired electron making it paramagnetic.

Identify Fractional Bond Orders

Fractional bond orders occur when electrons partially occupy an orbital.- \(\mathrm{O}_{2}^{-}\): Bond order 1.5 due to partial occupation.- \(\mathrm{NO}\): Bond order 2.5, indicating a fractional bond order.- \(\mathrm{OF}^{-}\): Bond order 1.5 due to partially filled antibonding orbitals.

Key concepts

Bond Order

To understand the stability and strength of a molecule's bonds, we use the concept of bond order. This helps us in predicting the strength, length, and dissociation ability of a bond. Bond order is determined 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, more stable bond. For instance, a bond order of 3, as seen in \(\mathrm{CN}^{-}\), suggests a triple bond, while a bond order of 1, as in \(\mathrm{C}_{2}\), represents a single bond.

By calculating bond orders, we understand which bonds in molecules are the strongest and most stable, aiding predictions in reactivity and properties of molecules.
In the original exercise, bond orders of 3 were found in \(\mathrm{CN}^{-}\) and \(\mathrm{NO}^{+}\), indicating these molecules have triple bonds. This understanding is essential in predicting the behavior and interaction of molecules.

Paramagnetism

Paramagnetism is a property that indicates the presence of unpaired electrons within a molecule. This property can be checked using molecular orbital (MO) theory. If a molecule exhibits unpaired electrons in its molecular orbitals, it is considered paramagnetic, which means it will be attracted to an external magnetic field.

From our original step-by-step solution, we identified that molecules such as \(\mathrm{O}_{2}\), \(\mathrm{O}_{2}^{-}\), and \(\mathrm{NO}\) are paramagnetic. This is because:

• \(\mathrm{O}_{2}\): Has 2 unpaired electrons in its pi* orbitals.
• \(\mathrm{O}_{2}^{-}\): Contains one additional electron compared to \(\mathrm{O}_{2}\), resulting in one unpaired electron.
• \(\mathrm{NO}\): Has one unpaired electron in its molecular orbitals.

Understanding paramagnetism helps in determining electron configurations and magnetic properties of molecules, which is key in fields like chemistry and materials science.

Fractional Bond Order

Fractional bond orders arise when electrons do not completely fill the available molecular orbitals, leading to partial occupation. This is often the case in molecules that have electrons shared between multiple atoms but not forming a complete bond.

In the given exercise, molecules like \(\mathrm{O}_{2}^{-}\), \(\mathrm{NO}\), and \(\mathrm{OF}^{-}\) were identified as having fractional bond orders:

• \(\mathrm{O}_{2}^{-}\): The addition of an electron causes a bond order of 1.5 due to incomplete occupation of molecular orbitals.
• \(\mathrm{NO}\): Shows a bond order of 2.5, reflecting partial bonding between nucleus atoms.
• \(\mathrm{OF}^{-}\): Exhibits a bond order of 1.5, linked to its antibonding orbitals being partially filled.

Fractional bond orders indicate bonds that are between single and double, or double and triple, reflecting intermediate bond strengths and properties. This concept is crucial for understanding complex bonding in molecules, especially those involved in resonance or delocalization.