Question

Use VSEPR to predict the geometry (including bond angles) about each interior atom of methyl azide \(\left(\mathrm{CH}_{3} \mathrm{N}_{3}\right)\) and draw the molecule. Would you expect the bond angle between the two interior nitrogen atoms to be the same or different? Would you expect the two nitrogen-nitrogen bond lengths to be the same or different?

Short answer

Carbon has tetrahedral geometry with approximately 109.5-degree angles. The first nitrogen (N1) adopts a bent geometry with angles less than 109.5 degrees due to the lone pairs. The bond angle between N1 and N2 may be slightly less than 180 degrees, and the N1-N2 bond is expected to be longer than the N2-N3 bond.

Step-by-step solution

Identify the Interior Atoms

First, identify all the interior atoms in methyl azide \(CH_3N_3\). Interior atoms are those that connect two or more other atoms. Here, we have two interior atoms: the carbon atom (C) and the first nitrogen (N1) attached to carbon.

Predict the Geometry of the Carbon Atom

Using VSEPR theory, predict the geometry around the carbon atom. Carbon in \(CH_3\) has four single bonds, which means it is surrounded by four regions of electron density. Thus, according to VSEPR theory, it will adopt a tetrahedral arrangement, with an ideal bond angle of 109.5 degrees.

Predict the Geometry of the First Nitrogen Atom

The first nitrogen atom (N1) in \(N_3\) is bonded to two other atoms: carbon and the second nitrogen (N2). There are also two lone pairs on N1. According to VSEPR theory, it has four regions of electron density (two bonding pairs and two lone pairs). The molecular geometry will thus be bent or angular, and the ideal bond angle is less than 109.5 degrees, typically around 109.5 degrees due to the repulsion by the lone pairs.

Assess the N-N-N Angle and Bond Lengths

The bond angle between the two interior nitrogen atoms (N1 and N2) is affected by the presence of the lone pair on N1, which is likely to decrease the angle slightly from the ideal 180 degrees found in a linear arrangement. Alternately, due to resonance and electronic effects, these angles can fluctuate. The bond lengths between the nitrogen atoms in the \(N_3\) group are likely to be different because of the differences in the type of bonding; N1 is single-bonded to N2, while N2 is double-bonded to N3.

Predict the Geometry of the Second Nitrogen Atom

The second nitrogen atom (N2) in \(N_3\) is bonded to the first and third nitrogen atoms (N1 and N3). There is one lone pair on N2. The geometry is also bent or angular, but the angle between N2-N3 and N1-N2 will be closer to 180 degrees because of the linear arrangement influenced by the multiple bonding.

Determine the N-N Bond Length Variations

Usually, double bonds are shorter than single bonds because of the increased electron sharing and stronger attraction between atoms. Therefore, we would expect the N2-N3 bond to be shorter than the N1-N2 bond.

Draw the Molecule

Now, draw the structure of methyl azide based on the geometries predicted. Carbon has a tetrahedral shape with N1 and the three hydrogens attached. N1 has a bent geometry with a lone pair, linked to N2. And N2 has a linear arrangement with N3. Indicate the bond angle reductions near lone pairs and the difference in bond lengths on the drawing.

Key concepts

Molecular Geometry

Understanding molecular geometry is essential for interpreting the shapes of molecules and how they behave in different physical and chemical contexts. Using Valence Shell Electron Pair Repulsion (VSEPR) theory provides insight into molecular structure by predicting the arrangement of electron pairs around a central atom to minimize repulsion. For instance, a carbon atom with four single bonds, like in methyl azide's CH₃ group, forms a tetrahedral geometry with roughly equal bond angles of 109.5 degrees between each pair of bonds.

This principle reveals why the nitrogen in the N₃ group has a different shape. With two bonding pairs and two lone pairs, the electron geometry would be tetrahedral, but the molecular geometry becomes bent or angular, altering the ideal bond angles due to the repulsive force of the lone pairs.

Bond Angle Prediction

When predicting bond angles in a molecule, VSEPR theory comes into play by considering the electron density around the central atom. Lone pairs exert more repulsion than bonding pairs, leading to smaller bond angles. For example, in methyl azide, the nitrogen's lone pairs will push the bonding pairs closer together, reducing the bond angle from the tetrahedral ideal to less than 109.5 degrees. The precise prediction of such angles, especially when a molecule exhibits resonance or has double and single bonds, as with the nitrogens in N₃, becomes more complex. Understanding these nuances helps us grasp the 3-dimensional shape of molecules and predict their reactivity and interaction with other molecules.

Lone Pair Repulsion

Lone pairs of electrons are significant in molecular geometry because they occupy more space around the central atom compared to bonding electrons, leading to greater repulsion forces. This is primarily due to the fact that lone pairs are held by only one nucleus, while bonding pairs are held by two, giving lone pairs more freedom to repel each other. In the VSEPR model, this repulsion results in adjusted shapes and bond angles in a molecule. In methyl azide, the repulsion from the lone pairs on the first nitrogen atom forces the bond angle to compress, illustrating the impact of these invisible forces on observable properties like molecular shape.

Nitrogen-Nitrogen Bond Lengths

Bond lengths vary based on the type and strength of bonds between atoms. Typically, double bonds are shorter and stronger than single bonds due to the greater number of electrons shared between the atoms. In a molecule such as methyl azide, the difference in bond lengths between nitrogen atoms arises from these principles. The bond between the second and third nitrogen atoms involves a double bond, thus, it is expected to be shorter than the single-bonded nitrogen-nitrogen bond. Comprehending these differences is pivotal in visualizing and understanding the 3-dimensional structure of molecules, and it also factors into predicting the molecule's reactivity and interactions with other substances.