Question

Use VSEPR theory to predict the geometry (including bond angles) about each interior atom of methyl azide \(\left(\mathrm{CH}_{3} \mathrm{~N}_{3}\right),\) and make a sketch of 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

The bond angle around carbon in the methyl group is 109.5 degrees, and for the nitrogen chain, the angles are 180 degrees for the first two nitrogens and less than 120 degrees for the third. Nitrogen-nitrogen bond lengths are expected to be different: the N1-N2 triple bond is shorter than the N2-N3 single bond.

Step-by-step solution

Determine the Lewis Structure

The first step in predicting geometry using VSEPR theory is to draw the Lewis structure of methyl azide ((CH3N3)). Carbon (C) will be the central atom of the methyl group, bonded to three hydrogen atoms. The nitrogen atoms will be connected in a chain NN-N because nitrogen tends to form multiple bonds. The Lewis structure shows that the first nitrogen is triple-bonded to the second nitrogen, which in turn is single-bonded to the third nitrogen. The third nitrogen has a lone pair.

Predict the Geometry of the Methyl Group

For the methyl group (CH3), the central carbon has four regions of electron density (three C-H bonds and one C-N bond). According to VSEPR theory, four regions of electron density around a central atom will result in a tetrahedral geometry. Thus, the H-C-H bond angles will be approximately 109.5 degrees.

Predict the Geometry of the Interior Nitrogen Atoms

For the first nitrogen (N1) in the N-N-N chain, it has two regions of electron density due to the triple bond with the second nitrogen (N2). This will result in a linear geometry with a bond angle of approximately 180 degrees. The second nitrogen (N2) will also have a linear geometry with a bond angle of approximately 180 degrees because it has two regions of electron density (triple bond with N1 and single bond with third nitrogen). The third nitrogen (N3) has three regions of electron density (one N-N bond and two lone pairs), which results in a bent geometry under the influence of the lone pair, with an expected bond angle of less than 120 degrees.

Create a Sketch of the Molecule

Draw the molecule with the central carbon atom bonded to three hydrogens and one nitrogen, ensuring the atoms are spaced approximately 109.5 degrees apart for the tetrahedral geometry. Draw a linear chain of nitrogen atoms starting from the carbon's bonded nitrogen with bond angles of 180 degrees for N1 and N2, and less than 120 degrees for the bond angle adjacent to N3.

Compare the Bond Angles and Bond Lengths

The bond angle between the two interior nitrogen atoms (N1 and N2) is predicted to be 180 degrees, which is the same due to the linear geometry. The bond lengths between the nitrogen atoms, however, are expected to be different. A triple bond between N1 and N2 will be shorter and stronger than the single bond between N2 and N3 due to the difference in bond order.

Key concepts

Lewis Structure

Understanding the Lewis structure is a foundational step in predicting molecular geometry using the Valence Shell Electron Pair Repulsion (VSEPR) theory. The Lewis structure provides a visual representation of the valence electrons in a molecule, which are the electrons that participate in bonding. Drawing the Lewis structure for methyl azide (CH₃N₃) requires identifying the total number of valence electrons and arranging them to satisfy the octet rule for each atom.

In methyl azide, carbon (C) is the central atom of the methyl group, bonded to three hydrogen (H) atoms and one nitrogen (N) atom. The nitrogen atoms form a chain with the first nitrogen triple-bonded to the second nitrogen, which is single-bonded to the third nitrogen. The Lewis structure also shows a lone pair of electrons on the third nitrogen, which plays a crucial role in determining molecular geometry. By accurately representing these details, students can better predict the molecule's shape and bond angles.

Molecular Geometry

After establishing the Lewis structure, VSEPR theory helps in determining the molecular geometry. It considers the number of regions of electron density—which include bonds and lone pairs—around the central atom to predict the arrangement that minimizes repulsion. For example, the carbon atom in methyl azide has four regions of electron density forming a tetrahedral geometry, typical for compounds with a tetravalent central atom like CH₄.

The nitrogen atoms in methyl azide also have distinct arrangements based on their electron density regions. The first two nitrogens (N1 and N2) with linear geometry form a straight line due to their double or triple bonds to one another, while the last nitrogen (N3) with a lone pair leads to a bent geometry. Understanding these substructures in molecules is crucial for predicting the overall shape.

Bond Angles

Bond angles give insight into the spatial arrangement of atoms in a molecule. VSEPR theory posits that electron pairs, both bonding and non-bonding, repel each other and tend to maximize the space between them, thus defining the bond angles. The tetrahedral geometry around the methyl group's carbon results in bond angles of approximately 109.5 degrees.

The linear geometry between the first two nitrogen atoms (N1 and N2) in methyl azide dictates that the bond angles will be around 180 degrees, a feature of linear molecules like CO₂. However, the presence of a lone pair on the third nitrogen (N3) means that its bond angle will be smaller due to the increased repulsion from the lone pair. Students should note how lone pairs can influence bond angles and differ from bond to bond within the same molecule.

Nitrogen-Nitrogen Bond Lengths

Bond lengths between atoms within molecules can vary significantly and are influenced by the bond order—the number of shared electron pairs between two atoms. In methyl azide, the nitrogen-nitrogen bond lengths are not uniform. The triple bond between the first and second nitrogen atoms (N1 and N2) will be significantly shorter than the single bond between the second and third nitrogen atoms (N2 and N3) because more shared electron pairs pull the atoms closer together.

This results in a stronger, shorter bond for the triple bond and a longer, weaker bond for the single bond. It's important for students to recognize that multiple bonding can greatly affect the structural attributes of molecules, influencing both their reactivity and physical properties.