Question

The correct order of bond angle of \(\mathrm{NO}_{2}^{+}, \mathrm{NO}_{2}\) and \(\mathrm{NO}_{2}^{-}\) is: (a) \(\mathrm{NO}_{2}^{+}<\mathrm{NO}_{2}<\mathrm{NO}_{2}^{-}\) (b) \(\mathrm{NO}_{2}^{+}=\mathrm{NO}_{2}^{-}<\mathrm{NO}_{2}\) (c) \(\mathrm{NO}_{2}^{+}>\mathrm{NO}_{2}^{-}>\mathrm{NO}_{2}\) (d) \(\mathrm{NO}_{2}^{+}>\mathrm{NO}_{2}<\mathrm{NO}_{2}\)

Short answer

(c) \(\mathrm{NO}_{2}^{+} > \mathrm{NO}_{2}^{-} > \mathrm{NO}_{2}\).

Step-by-step solution

Determine the Molecular Shapes

Examine the electron group geometry of each species. For \(\mathrm{NO}_{2}^{+}\), \(\mathrm{NO}_{2}\), and \(\mathrm{NO}_{2}^{-}\), determine the hybridization and molecular shapes which affect bond angles.

NO2+ (Nitronium Ion) Analysis

\(\mathrm{NO}_{2}^{+}\) has 2 nitrogen-oxygen double bonds and no lone pairs on nitrogen. It is linear with a bond angle of 180° due to \(\mathrm{sp}\) hybridization.

NO2 Radical Analysis

\(\mathrm{NO}_{2}\) is a free radical with one lone electron on nitrogen. It shows a bent shape due to \(sp^2\) hybridization. Its bond angle is slightly larger than \(\mathrm{NO}_{2}^{-}\) due to less electron-electron repulsion.

NO2− (Nitrite Ion) Analysis

\(\mathrm{NO}_{2}^{-}\) has one lone pair on nitrogen and two nitrogen-oxygen bonds. It assumes a bent shape with bond angle less than \(\mathrm{NO}_{2}\) due to increased lone pair-bond pair repulsion.

Establish Order Based on Bond Angles

Evaluate bond angles: \(\mathrm{NO}_{2}^{+}\) (180°) > \(\mathrm{NO}_{2}\) (115-134°) > \(\mathrm{NO}_{2}^{-}\) (120° minus more deviation due to lone pairs). The bond angles follow \(\mathrm{NO}_{2}^{+} > \mathrm{NO}_{2}^{-} > \mathrm{NO}_{2}\).

Key concepts

Molecular Shapes

Molecular shapes are determined by the 3D arrangement of atoms within a molecule. This arrangement is crucial as it affects properties such as reactivity and polarity. Shapes are influenced by the number of bonded pairs and lone pairs of electrons surrounding the central atom. Here are some common molecular shapes:

• Linear: This shape occurs when there are two atoms bonded to a central atom, with the angle between them being 180°, like in the nitronium ion (\(\mathrm{NO}_{2}^{+}\)).
• Bent: Occurs when there are lone pairs on the central atom, altering the bond angle to less than 180°, as seen in \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{2}^{-}\).
• Trigonal planar: Found in molecules with three bonds and no lone pairs, typically having 120° between bonds.

Understanding molecular shapes helps in predicting the bond angles, which pertain to how the atom "stretches" in molecular space.

Hybridization

Hybridization is the concept explaining how atomic orbitals mix together to form new, hybrid orbitals which accommodate the pairs of electrons in a molecule. This determines the geometry and bond angles of molecules. For the ions in question:

• The nitronium ion (\(\mathrm{NO}_{2}^{+}\)) shows \(sp\) hybridization because it forms a linear shape with an angle of 180° between the bonds.
• The \(\mathrm{NO}_{2}\) radical and the nitrite ion (\(\mathrm{NO}_{2}^{-}\)) both exhibit \(sp^2\) hybridization, allowing for a bent shape.

These hybridizations illustrate how the electrons configure spatially and energetically to optimize the molecule's structure. Appreciating these concepts clarifies how different species manifest their unique shapes and angles.

Electron Repulsion

Electron repulsion pertains to how electrons in a molecule influence its shape by repelling each other. The VSEPR (Valence Shell Electron Pair Repulsion) theory explains this phenomenon by stating that electron pairs will arrange themselves around the central atom to minimize repulsion. For example:

• \(\mathrm{NO}_{2}^{+}\), with no lone pairs on the nitrogen, forms a linear structure with maximum separation.
• \(\mathrm{NO}_{2}\) and \(\mathrm{NO}_{2}^{-}\), having lone electron pairs, adopt bent geometries. Lone pairs exert more repulsion than bonded pairs, compressing bond angles further.

This aspect is essential for predicting molecular structure, as seen in the differing angles of the nitronium ion, the \(\mathrm{NO}_{2}\) radical, and the nitrite ion.

Nitronium Ion

The nitronium ion (\(\mathrm{NO}_{2}^{+}\)) is an example of a species with a linear molecular shape due to its electronic configuration. The ion is characterized by two equivalent nitrogen-oxygen double bonds without any lone pairs on the nitrogen atom.

• Bond Angle: As a result of \(sp\) hybridization, the bonds are straightened to 180° due to minimal electron-electron repulsion.
• Applications: It functions as an electrophile in nitration reactions, commonly used in the synthesis of nitro compounds in organic chemistry.

Understanding the simple linear structure and characteristics of the nitronium ion enriches insights into chemical reactivity.

Nitrite Ion

The nitrite ion (\(\mathrm{NO}_{2}^{-}\)) highlights the effect of electron repulsion on molecular shapes, owing to its structure comprising of one lone pair on the nitrogen and two bonded oxygen atoms.

• Molecular Shape: It is bent due to the presence of one lone pair, which forces the bonds away from the usual 120° angle seen in an \(sp^2\) coordinated system.
• Bond Angles: Electron repulsion from the lone pair compresses the angle slightly to less than 120°, making it smaller than some similar systems without lone pairs.
• Functionality: Nitrite ions are significant in various biological and industrial processes, such as in nitrogen cycles and as preservatives.

Comprehending how its structure arises from electron pair geometry provides valuable knowledge on predictions in complex molecular behavior.