Question

Predict the electron pair geometry, the molecular shape, and the bond angle for a nitrogen triiodide molecule, \(\mathbf{N I}_{3},\) using VSEPR theory.

Short answer

The electron pair geometry of \(\mathbf{NI}_{3}\) is tetrahedral, the molecular shape is trigonal pyramidal, and the bond angle is slightly less than \(109.5^\circ\).

Step-by-step solution

Determine the Central Atom

In the molecular formula \(\mathbf{NI}_{3}\), nitrogen (N) is the central atom because it is less electronegative compared to iodine (I) and can form multiple bonds with iodine atoms.

Count Total Valence Electrons

Nitrogen has 5 valence electrons, and each iodine atom has 7 valence electrons. Thus, the total number of valence electrons is \(5 + 3 \times 7 = 26\) electrons.

Draw the Lewis Structure

Arrange the 26 valence electrons to form bonds between nitrogen and the three iodine atoms, with each iodine atom holding three lone pairs, and nitrogen holding one lone pair. Each iodine forms a single bond with nitrogen.

Determine Electron Pair Geometry

Using VSEPR theory, the structure must minimize electron-pair repulsion. The central nitrogen atom has 3 bonding pairs (with iodine) and 1 lone pair of electrons, totaling 4 electron densities, which corresponds to a tetrahedral electron pair geometry.

Predict Molecular Shape

The shape of the molecule is based on the positions of the atoms only. With one lone pair, the molecular shape of \(\mathbf{NI}_{3}\) is trigonal pyramidal.

Determine Bond Angle

In a perfect tetrahedral geometry, bond angles are \(109.5^\circ\). However, the presence of a lone pair slightly reduces the bond angle. Thus, the bond angle in \(\mathbf{NI}_{3}\) is slightly less than \(109.5^\circ\), typically around \(107^\circ\).

Key concepts

Electron Pair Geometry

When predicting the electron pair geometry of a molecule, VSEPR (Valence Shell Electron Pair Repulsion) theory is crucial. It's based on the idea that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion. In the case of nitrogen triiodide, \(\text{NI}_3\), the nitrogen atom is surrounded by three iodine atoms and one lone pair of electrons. This alignment consists of four regions of electron density. According to VSEPR theory, these four regions form a tetrahedral electron pair geometry.
As such:

• Four regions of electron density around the central atom.
• An arrangement that allows for equal repulsion among electron pairs.
• Electron pair geometry that dictates overall spatial arrangement.

Understanding this helps in predicting the arrangement of molecules in three-dimensional space and their subsequent chemical behavior.

Molecular Shape

While the electron pair geometry gives us a general idea of the arrangement, molecular shape focuses on the position of atoms themselves. For \(\text{NI}_3\), the nitrogen atom is bonded to three iodine atoms. Since there is one lone pair on the nitrogen, the shape derived will not be purely tetrahedral. The influence of the lone pair adjusts the visible molecular shape to be trigonal pyramidal.
This means:

• Three iodine atoms form the base of the pyramid.
• The lone pair causes the nitrogen to appear at the apex.
• The molecular shape reflects the visible shape of the atomic arrangement.

The adjustment of shape due to lone pairs is crucial for understanding real molecule behaviors in reactions and interactions.

Lewis Structure

Lewis structures are diagrams that show the bonding and lone pairs of electrons in a molecule. For \(\text{NI}_3\), to construct the Lewis structure:

• First count total valence electrons: nitrogen provides 5 and each iodine contributes 7, totaling 26 electrons.
• Connect the nitrogen atom to the three iodine atoms with single bonds, using 6 electrons (2 per bond).
• Distribute the remaining 20 electrons to satisfy the octets, assigning three lone pairs to each iodine and one lone pair to the nitrogen.

The Lewis structure not only helps in visualizing electronic distribution but also sets the stage for predicting molecule geometry based on electron pairs.

Trigonal Pyramidal

The term 'trigonal pyramidal' describes a specific molecular shape. This occurs when there are three bonded atoms and one lone pair on the central atom. In the context of VSEPR theory, \(\text{NI}_3\) embodies this shape. The nitrogen atom forms the tip of the pyramid, while the three iodine atoms form the base. The presence of the lone pair pushes the iodine atoms slightly closer, deviating from a perfect tetrahedral shape.
Key points:

• The overall shape resembles a three-sided pyramid.
• Lone pairs exert greater repulsion than bonding pairs.
• This shape characterizes many molecules with a similar configuration of three bonds and one lone pair.

Recognizing a trigonal pyramidal shape is critical in understanding the nuances of bond angles and molecular structure.

Bond Angle

Bond angles, defined as angles between adjacent bonds, play a fundamental role in molecular geometry. In a perfect tetrahedral arrangement, we expect bond angles of \(109.5^\circ\). However, in molecules like \(\text{NI}_3\), which are trigonal pyramidal, lone pairs impact these angles. Lone pairs occupy more space and tend to decrease bond angles. In \(\text{NI}_3\):

• The repulsion from the lone pair reduces the bond angle between the iodine atoms.
• The standard tetrahedral angle decreases from \(109.5^\circ\) to approximately \(107^\circ\).
• This slight alteration impacts how molecules interact and their chemical reactivity.

Understanding bond angles helps in predicting molecular polarity and interactions with other molecules.