Question

Methyl nitrate, \(\mathrm{CH}_{3} \mathrm{NO}_{3}\), is used as a rocket propellant. The skeletal structure of the molecule is \(\mathrm{CH}_{3} \mathrm{ONO}_{2}\). The N and three O atoms all lie in the same plane, but the \(\mathrm{CH}_{3}\) group is not in the same plane as the \(\mathrm{NO}_{3}\) group. The bond angle \(\mathrm{C}-\mathrm{O}-\mathrm{N}\) is \(105^{\circ},\) and the bond angle \(\mathrm{O}-\mathrm{N}-\mathrm{O}\) is \(125^{\circ} .\) One nitrogen-to-oxygen bond length is \(136 \mathrm{pm},\) and the other two are \(126 \mathrm{pm}\) (a) Draw a sketch of the molecule showing its geometric shape. (b) Label all the bonds in the molecule as \(\sigma\) or \(\pi\), and indicate the probable orbital overlaps involved. (c) Explain why all three nitrogen-to-oxygen bond lengths are not the same.

Short answer

The Geometry of the \(CH_3NO_3\) molecule depicts that nitrogen and three oxygen atoms lie in the same plane and the \(CH_3\) group does not lie in the same plane as the \(NO_3\) group. The entire molecule has a combination of \(\sigma\) and \(\pi\) bonds, formed from different types of orbital overlaps. The reason that not all nitrogen-to-oxygen bonds are the same length is due to the resonance in the \(NO_3\) group.

Step-by-step solution

Drawing the Sketch of the Molecule

It is given that nitrogen and three oxygen atoms are in the same plane and the \(CH_3\) group is not in the same plane as the \(NO_3\) group. This means, firstly, complete the molecule by drawing a nitrogen atom bonded with three oxygen atoms in a trigonal planar arrangement, then attach the \(CH_3\) above the plane. Since, the bond angle \(C-O-N\) is \(105^{\circ}\), and the bond angle \(O-N-O\) is \(125^{\circ}\), it should be reflected in your sketch.

Labeling the Bonds

Observe your sketch. A single bond between two atoms usually represents a \(\sigma\) bond. So, the \(C-H\) bonds in the \(CH_3\) group and the \(C-O\), \(N-O\) (single) bonds are all \(\sigma\) bonds, formed by end-to-end overlap of orbitals. Double bond between \(N\) and \(\(O_2\)\) is composed of one \(\sigma\) bond and one \(\pi\) bond (formed by sideways overlap of p orbitals). Label all these on your sketch accordingly.

Explaining the Bond Lengths

Lastly, it is required to explain why all three nitrogen-to-oxygen bonds are not the same length. This is because of the presence of a resonance structure in \(NO_3\) group which causes the double bond to spread over the three \(N-O\) bonds, making the bond length shorter than a normal \(N-O\) single bond, but longer than a normal \(N-O\) double bond. Therefore, one nitrogen-to-oxygen bond length is \(136pm\) (longer) and the other two have \(126pm\) (shorter).

Key concepts

Covalent Bonds

Covalent bonds are a type of chemical bond where atoms share pairs of electrons. This helps them attain stable electron configurations, similar to noble gases. In methyl nitrate (\(\mathrm{CH}_{3} \mathrm{NO}_{3}\)), covalent bonds form between the carbon, nitrogen, and oxygen atoms. For example:

• The \(\mathrm{C}\) atom shares electrons with hydrogen atoms, forming \(\mathrm{C-H}\) bonds, which are single covalent bonds or \(\sigma\) bonds. These are formed by the overlap of atomic orbitals along the bond axis, allowing electrons to be shared.
• The \(\mathrm{C-O}\) and \(\mathrm{N-O}\) single bonds are also \(\sigma\) bonds.

This sharing of electrons is pivotal for the stability and formation of molecules, as it lowers the overall energy of the system, creating a molecule that is more energetically favorable.

Resonance Structures

Resonance structures occur when there are two or more valid Lewis Structures for the same molecule. This happens because of the delocalization of electrons, primarily in molecules with conjugated \(\pi\) bonds. In methyl nitrate, the \(\mathrm{NO}_{3}\) group exhibits resonance. This means that:

• The \(\mathrm{N-O}\) bonds are a hybrid of single and double bonds. This causes each bond to possess partial double-bond character as electrons are spread across all bonds, rather than residing in one specific location.
• Because of resonance, the observed bond lengths are intermediate between typical single and double bond lengths.

Resonance enhances the stability of the molecule by allowing charge and electron distribution over a larger volume, balancing electron density and minimizing potential energy.

Orbital Hybridization

Orbital hybridization is the concept of mixing atomic orbitals into new hybrid orbitals suitable for the pairing of electrons. This concept helps explain molecular geometry and the bonding properties. In methyl nitrate:

• The nitrogen atom is likely to be \(sp^2\)-hybridized, forming a planar triangular shape with its \(\mathrm{N-O}\) bonds.
• Each oxygen involved in single bonds with nitrogen would use orbitals that allow the \(\sigma\) bonds to form.
• The carbon atom in the \(\mathrm{CH}_{3}\) group will be \(sp^3\)-hybridized, providing a tetrahedral geometry, which explains why it's not coplanar with the \(\mathrm{NO}_{3}\) group.

This hybridization helps to clarify the structure and bond angles observed in the molecule, such as the \(105^{\circ}\) and \(125^{\circ}\) angles noted in the original exercise.