Problem 202 - Introductory Chemistry Atoms First

Question

Consider two molecules, \(\mathrm{BH}_{3}\) and \(\mathrm{NH}_{3} .\) Draw dot diagrams for both and indicate which one possesses and electron deficient atom.

Step-by-Step Solution

Answer

Lewis structures for both molecules are shown below: \(\mathrm{BH}_{3}\): \[ \begin{array}{c} \text{H} \\ | \\ \text{B}--\text{H} \\ | \text{H} \end{array} \] \(\mathrm{NH}_{3}\): \[ \begin{array}{c} \text{H} \\ | \text{N}--\text{H} \\ | \\ \text{H} \end{array} \] \(\mathrm{BH}_{3}\) possesses the electron deficient atom as Boron (B) only has 6 electrons in its valence shell, while Nitrogen (N) in \(\mathrm{NH}_{3}\) has a complete octet.

Step 1: Determine the Number of Valence Electrons for each Atom

Firstly, one needs to decide how many valence electrons each atom in the molecules BH3 and NH3 has. Boron (B) is in group 13 (3A) and has 3 valence electrons. Hydrogen (H) is in group 1 (1A) and has 1 valence electron. Nitrogen (N) is in group 15 (5A) and has 5 valence electrons.

Step 2: Draw Dot Diagrams for \(\mathrm{BH}_{3}\) and \(\mathrm{NH}_{3}\)

Dot diagrams, or Lewis Structures, are drawn by locating the atoms, pairing up the valence electrons, and then distributing the remaining electrons. In \(\mathrm{BH}_{3}\), Boron (B) is the central atom with hydrogen atoms surrounding it. This is due to boron having less valence electrons. Here's how to draw it: - Place Boron (B) at the center and position the three Hydrogen (H) atoms around it. - Since Boron has 3 valence electrons and each Hydrogen has 1, pair them up. \[ \begin{array}{c} \text{H} \\ | \\ \text{B}--\text{H} \\ | \text{H} \end{array} \] For \(\mathrm{NH}_{3}\), Nitrogen (N) is the central atom surrounded by three Hydrogen atoms (H): - Place Nitrogen (N) at the center and three Hydrogen atoms around it. - Nitrogen has 5 valence electrons, each Hydrogen has 1. Start pairing up the electrons. Two electrons will remain unpaired on Nitrogen. \[ \begin{array}{c} \text{H} \\ | \text{N}--\text{H} \\ | \\ \text{H} \end{array} \] The two unpaired electrons are typically represented as a lone pair.

Step 3: Determine which Molecule contains an Electron-Deficient Atom

An electron-deficient atom is an atom that doesn't have a complete octet (8 electrons) in its valence shell. In \(\mathrm{BH}_{3}\), the central atom Boron (B) only has 6 electrons, so it's electron-deficient. In \(\mathrm{NH}_{3}\), the central atom Nitrogen (N) has a complete octet, so it's not electron-deficient. So, \(\mathrm{BH}_{3}\) possesses the electron deficient atom.

Key Concepts

Electron Deficient Atoms

In the world of chemistry, the concept of electron-deficient atoms is an important one to grasp, especially when studying Lewis Structures. When an atom has fewer than eight electrons in its valence shell, it is considered electron-deficient. This lack of electrons makes it unable to reach a full octet, which is the ideal state as per the octet rule.
For example, in the molecule \(\text{BH}_3\), Boron acts as the central atom. Boron belongs to group 13 of the periodic table and comes with only three valence electrons. During the formation of \(\text{BH}_3\), each valence electron of Boron pairs with an electron from a hydrogen atom, totaling six electrons in Boron's valence shell.
This situation results in Boron being electron-deficient because it does not meet the octet rule's requirement of eight valence electrons. Such electron-deficient atoms are often reactive and seek to achieve a stable configuration by forming additional bonds or participating in reactions to gain more electrons.

Valence Electrons

Valence electrons are the outermost electrons of an atom and play a crucial role in the chemistry of elements. They are the electrons involved in bonding and chemical reactions. To determine the number of valence electrons in an atom, one can look at the group number of the element in the periodic table.
For the molecules \(\text{BH}_3\) and \(\text{NH}_3\), let's explore their valence electrons. In \(\text{BH}_3\):

• Boron (B) has three valence electrons, as it is in group 13.
• Each Hydrogen (H) atom possesses one valence electron, being in group 1.

In \(\text{NH}_3\):

• Nitrogen (N), which is in group 15, brings in five valence electrons.
• Each Hydrogen atom, again, has one valence electron.

Understanding valence electrons helps design Lewis Structures and predict molecules' behavior during chemical reactions. By knowing how many valence electrons an element contains, we can pair them with those of other atoms to model molecules accurately.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. This concept is essential for predicting the physical and chemical properties of a molecule. By knowing how atoms are positioned relative to one another, we can infer the molecule's shape and bonding angles.
The molecule \(\text{BH}_3\) has a trigonal planar geometry. In this shape, Boron is at the center with three Hydrogen atoms symmetrically arranged around it, forming 120-degree angles between each bond. This arrangement arises because Boron is electron-deficient and does not have a lone pair to distort this symmetry.
On the other hand, \(\text{NH}_3\) adopts a trigonal pyramidal geometry. Nitrogen, as the central atom, is surrounded by three Hydrogen atoms. However, Nitrogen also retains a lone pair of electrons, which causes a push, or repulsion, distorting the angles slightly less than the typical 109.5 degrees found in a tetrahedral arrangement. This lone pair effect makes \(\text{NH}_3\) an example of how lone pairs can affect molecular shape, a key aspect of VSEPR (Valence Shell Electron Pair Repulsion) theory.