Question

Compare the electron-dot formulas of \(\mathrm{PH}_{3}\) and \(\mathrm{NH}_{3}\). Why do these molecules have the same shape?

Short answer

The same shape is due to having 1 lone pair and 3 bonding pairs around the central atom, resulting in a trigonal pyramidal geometry for both molecules.

Step-by-step solution

Draw Lewis Structures

Draw the electron-dot (Lewis) structures of \(\text{PH}_3\) and \(\text{NH}_3\).\(\text{PH}_3\) has 5 valence electrons from phosphorus and 3 from each hydrogen. \(\text{NH}_3\) has 5 valence electrons from nitrogen and 3 from each hydrogen. The Lewis structure for both molecules will show the central atom with three single bonds to hydrogen atoms and one lone pair.

Identify Lone Pairs and Bonding Pairs

In \(\text{PH}_3\) and \(\text{NH}_3\), the central atom (P or N) has 1 lone pair of electrons and 3 bonding pairs.

Determine Molecular Geometry

Using the VSEPR (Valence Shell Electron Pair Repulsion) theory, the molecular geometry is determined. With 1 lone pair and 3 bonding pairs, both molecules have a trigonal pyramidal shape.

Key concepts

electron-dot formulas

Electron-dot (or Lewis) formulas are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. They are essential tools for understanding molecular structure and bonding. To draw these formulas, follow these steps:

• Count all the valence electrons in the molecule.
• Determine the central atom (usually the least electronegative).
• Arrange the electrons to form bonds between atoms.
• Distribute the remaining electrons to satisfy the octet rule (or duet rule for hydrogen).

For \(\text{PH}_3\) and \(\text{NH}_3\), both phosphorus and nitrogen have five valence electrons. Each hydrogen contributes one electron. By following these steps, we draw each central atom with three single bonds to hydrogen atoms and one lone pair of electrons.

VSEPR theory

The VSEPR (Valence Shell Electron Pair Repulsion) theory helps predict the geometry of molecules based on the electrons around the central atom repelling each other.
This theory is grounded on the idea that:

• Electron pairs around a central atom will arrange themselves to be as far apart as possible.
• Both bonding pairs (shared between atoms) and lone pairs (non-bonding pairs) must be considered.

For molecules like \(\text{PH}_3\) and \(\text{NH}_3\), which both have one lone pair and three bonding pairs, the VSEPR theory predicts that these pairs will adopt a trigonal pyramidal arrangement to minimize repulsions between them.

molecular geometry

Molecular geometry describes the three-dimensional arrangement of atoms within a molecule.
Based on the VSEPR theory, this geometry can be predicted by considering the repulsions between electron pairs around the central atom.
For example:

• In \(\text{PH}_3\) and \(\text{NH}_3\), the geometrical shape is influenced by the one lone pair and three bonding pairs of electrons.
• This results in a trigonal pyramidal molecular geometry.

Understanding this arrangement helps explain many physical and chemical properties of the molecule, including its bond angles and polarity.

trigonal pyramidal shape

A trigonal pyramidal shape is a type of molecular geometry where a central atom is at the apex, and three other atoms form the base of a pyramid.
This shape is typically seen when there are four electron pairs around the central atom, including both bonding and lone pairs.
For \(\text{PH}_3\) and \(\text{NH}_3\):

• The central atom (P or N) has one lone pair and three bonding pairs.
• The three hydrogen atoms form a triangular base, while the lone pair pushes these bonds down, resulting in a pyramid-like shape.

This trigonal pyramidal shape is why both \(\text{PH}_3\) and \(\text{NH}_3\) have the same molecular geometry.