Problem 68 - Chemistry and Chemical Reactivity

Question

Which has the greater O-N-O bond angle, \(\mathrm{NO}_{2}^{-}\) or \(\mathrm{NO}_{2}^{+} ?\) Explain briefly.

Step-by-Step Solution

Answer

The O-N-O bond angle in \(\mathrm{NO}_{2}^{+}\) is greater than in \(\mathrm{NO}_{2}^{-}\).

Step 1: Identify Molecular Shapes using VSEPR

The shape of a molecule can be predicted using VSEPR (Valence Shell Electron Pair Repulsion) theory. For \(\mathrm{NO}_2^-\), we have a total of 18 valence electrons, and for \(\mathrm{NO}_2^+\), we have a total of 16 valence electrons. For both, nitrogen is the central atom bonded to two oxygen atoms.

Step 2: Determine Electron Pair Arrangement

In \(\mathrm{NO}_2^-\), there are 3 regions of electron density: 2 bonding pairs and 1 lone pair (bent shape). For \(\mathrm{NO}_2^+\), there are 2 regions of electron density: 2 bonding pairs and no lone pairs (linear shape).

Step 3: Evaluate Impact on Bond Angles

Lone pairs repel more strongly than bonding pairs, reducing the bond angle. In \(\mathrm{NO}_2^-\), the presence of a lone pair causes the bond angle to be less than the 120° typical for a trigonal planar arrangement. In \(\mathrm{NO}_2^+\), the molecule remains linear with an ideal bond angle of 180°.

Step 4: Compare Bond Angles

The \(\mathrm{NO}_2^+\) ion has a larger bond angle (180°) compared to \(\mathrm{NO}_2^-\), which has a reduced bond angle due to the lone pair repulsion, making it less than 120°.

Key Concepts

Molecular Shapes

Understanding the shape of a molecule is essential when discussing its properties and behaviors. The VSEPR theory, which stands for Valence Shell Electron Pair Repulsion, helps us predict the 3D structure or shape of molecules based on the number of valence electrons around the central atom.

For example, let's take two molecular ions: - ** two molecular ions: - ** NO_{2}^{-}") and - ** NO_{2}^{+}"). - ** - ** For NO_{2}^{-}") and consider the 18 valence electrons available. The VSEPR model suggests that this ion adopts a bent shape due to the presence of two bonding pairs and one lone pair of electrons around the central nitrogen atom.
In contrast, NO_{2}^{+}"), with its 16 valence electrons, forms a linear shape without any lone pairs. The different arrangements of electrons lead to different molecular shapes, impacting their geometry and interactions.

Bond Angles

Bond angles are the angles formed between adjacent bonds of a molecule and are influenced by electron repulsion around the central atom. The arrangement of electron pairs using VSEPR theory allows chemists to predict these angles, as it demonstrates how electron pairs spread out to minimize repulsion.

For instance, in NO_{2}^{+}"), the absence of lone pairs results in a linear molecular shape, giving it a bond angle of 180°. This is because the two bonding pairs position themselves directly opposite each other, maximizing their distance to minimize repulsive forces.
In NO_{2}^{-}") however, the presence of a lone pair distorts the geometry. The VSEPR theory indicates that lone pairs occupy more space, causing the adjacent bond pairs to angle towards each other, thus reducing the bond angle to be less than the classic 120° of a trigonal planar shape.

Lone Pair Repulsion

In VSEPR theory, an important concept is the effect of lone pair repulsion on molecular geometry. Lone pairs are non-bonding pairs of electrons, and they exert a stronger repulsive force compared to bonding pairs. This stronger repulsion is due to their higher electron density, as they are not shared between atoms.

In molecules such as NO_{2}^{-}"), the lone pair on the nitrogen atom creates a region of high electron density. This causes the bonding pairs to be pushed closer together, leading to a smaller bond angle compared to the hypothetical angle without the lone pair.
Understanding the impact of lone pair repulsion helps in evaluating why some molecular shapes deviate from the ideal geometries you might expect if each electron pair behaved identically.