Question

Hydrogen azide, \(\mathrm{HN}_{3}\), is a liquid that explodes violently when subjected to physical shock. In the \(\mathrm{HN}_{3}\) molecule, one nitrogen- to-nitrogen bond length is \(113 \mathrm{pm},\) and the other is \(124 \mathrm{pm} .\) The \(\mathrm{H}-\mathrm{N}-\mathrm{N}\) bond angle is \(112^{\circ} .\) Draw Lewis structures and a sketch of the molecule consistent with these facts.

Short answer

Hydrogen azide (HN3) has 16 total valence electrons. After attaching the Hydrogen to one Nitrogen atom and connecting the three Nitrogen atoms consecutively, three lone pairs of electrons are distributed across the Nitrogen atoms. A lone pair from an outer Nitrogen forms a double bond with the central Nitrogen to maintain the octet rule for all atoms. The sketch of the molecule then shows the Hydrogen atom forming a bond with a Nitrogen atom with an H-N-N angle of 112 degrees and the Nitrogen atoms connected with bond lengths of 113 pm and 124 pm.

Step-by-step solution

Determine the Total Number of Valence Electrons

For the \(HN_3\) molecule, the total number of valence electrons can be determined from the periodic table. The elements Hydrogen and Nitrogen have 1 and 5 valence electrons respectively. So, the total number of valence electrons = 1(H) + 3(N) = 1 + 3*5 = 16

Draw Skeleton and Connect Atoms with Single Bonds

In \(HN_3\) molecule, Hydrogen cannot be the central atom because it can only form one bond. Then the molecule can be represented as H-N-N-N. Next, connect these atoms with single bonds, each single bond costs 2 electrons leaving us with 16 - 2*3 = 10 electrons.

Distribute Remaining Valence Electrons

Place the remaining electrons as lone pairs on the atoms to fulfill the octet rule for Nitrogen atoms (8 electrons for each nitrogen atom). After attaching the three lone pairs to the center Nitrogen and two lone pairs to the other two Nitrogen atoms, no electron remains.

Check and Adjust for the Octet Rule

The central Nitrogen only has 6 electrons, violates the octet rule. The Nitrogen atom next to it has a lone pair of electrons, these electrons can move to form a double bond with the central Nitrogen. Now each atom has a full octet.

Draw the Molecule

The right most Nitrogen atom has a single bond with the neighboring Nitrogen and is 124 pm long. The left Nitrogen atom has a double bond with the central Nitrogen which is 113 pm long. The H-N-N bond angle is 112 degrees.

Key concepts

Valence Electrons

Valence electrons are the outermost electrons in an atom and are crucial for bond formation, as they can be shared or transferred during chemical interactions. To understand how molecules like hydrogen azide (\( \text{HN}_3 \)) form, it’s important to count these electrons. Hydrogen has 1 valence electron while nitrogen has 5. For the entire \( \text{HN}_3 \) molecule, we sum up these electrons: 1 from hydrogen and 15 from nitrogen (\(3 \times 5\)), giving us a total of 16 valence electrons.

These 16 valence electrons must be distributed in the molecule, ensuring all stability criteria such as the octet rule, which we discuss next, are met.

Octet Rule

The octet rule is a chemical dictum stating that atoms tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. Nitrogen atoms aim to achieve this stable state. However, following the initial drawing of \( \text{HN}_3 \) with single bonds, the octet rule isn't met for all nitrogen atoms. Adjustments like forming a double bond between central and adjacent nitrogen atoms are therefore made to ensure each nitrogen atom complies with the octet rule, ultimately leading to a more stable molecular structure.

Molecular Shape

Molecular shape is directly influenced by the number of valence electrons and their arrangement according to the octet rule. The \(\text{HN}_3\) molecule arranges itself in a linear fashion with nitrogen atoms connected in a straight line and hydrogen attached to one end. When drawing a sketch of the molecule, it is essential to place the atoms in such a line to correctly represent the molecular structure. The difference in nitrogen-nitrogen bond lengths also hints at the linear but unsymmetrical molecular shape of \(\text{HN}_3\).

Bond Angles

Bond angles are the angles between adjacent lines representing bonds that emanate from a common atom. In \(\text{HN}_3\), the H-N-N bond angle is given as \(112^\circ\). This bond angle corresponds to the shape adapted by the molecule and reflects the repulsion between the electrons pairs in the valence shell of the central nitrogen. The bond angle can be slightly less than the typical \(120^\circ\) found in a perfectly trigonal planar arrangement due to the lone pairs of electrons contributing to electron-electron repulsion.

Nitrogen-Nitrogen Bond Length

Nitrogen-nitrogen bond length refers to the distance between the nuclei of two bonded nitrogen atoms. In \(\text{HN}_3\), there are two distinct N-N bond lengths: 113 pm and 124 pm. The shorter bond length of 113 pm corresponds to the double bond, which is stronger and therefore shorter than the single bonded N-N length of 124 pm. These lengths are predictable based on the type of bond (single or double) and the hybridization state of the nitrogen atoms.