# 11.4: The Geometrical Arrangement of Electrons and Molecular Shape

**At Grade**Created by: CK-12

## Lesson Objectives

The student will:

- explain the meaning of the acronym VSEPR and state the concept on which it is based.
- state the main postulate in VSEPR theory.
- use VSEPR theory to predict the three-dimensional shapes of simple covalently bonded molecules.
- explain why we treat multiple bonds as if they were single bonds when are determining molecular geometry.
- identify both the electronic and the molecular geometry for simple binary compounds.

## Vocabulary

- electronic geometry
- molecular geometry
- unshared electron pair
- VSEPR theory

## Introduction

Many accurate methods now exist for determining molecular structure, the three-dimensional arrangement of the atoms in a molecule. These methods must be used if precise information about structure is needed. However, it is often useful to be able to predict the approximate structure of a molecule. A simple model that allows us to do this is called the **valence shell electron pair repulsion (VSEPR) theory.** This model is useful in predicting the geometries of molecules formed by covalent bonding. The main postulate of this theory is that in order to minimize electron-pair repulsion, the electron pairs around the central atom in a molecule will move as far away from each other as possible.

## Central Atom with Two Pairs of Electrons

Consider first the covalent compounds formed by Group 2A. An example of such a compound is \begin{align*}\text{BeCl}_2\end{align*}. The central beryllium atom has two pairs of electrons in its valence shell. VSEPR theory tells us that these two pairs of electrons will move as far away from each other as possible. The greatest distance that these two pairs of electrons can get between each other is when the two pairs are \begin{align*}180^\circ\end{align*} apart. Since these two pairs of electrons are involved in bonds with the chlorine atoms, the two chlorines will also be on opposite sides of the nucleus. The electronic geometry in this case is *linear*. Since the electron pairs are involved in bonds, the molecule itself will also be linear. As demonstrated in the figure below, a linear molecule means that a straight line would pass through all the nuclei in the molecule.

## Central Atom with Three Pairs of Electrons

We will look at boron trichloride, \begin{align*}\text{BCl}_3\end{align*}, as an example molecule for the covalent molecules in Group 3A. Boron has three valence electrons, with each chlorine that overlaps with a boron orbital contributing one more electron to boron’s valence shell. Therefore, boron will have six electrons (three pairs of electrons) in its valence shell. The farthest the three pairs of electrons can move away from each other is to occupy the points of a planar triangle, as illustrated below. Each bond angle will be \begin{align*}120^\circ\end{align*}. This shape is known as *trigonal planar*.

In the trigonal planar shape, all four atoms are in a single plane. None of the atoms project above or below the plane of the paper. You should note that if one pair of electrons is not shared, there will only be two attached chlorine atoms. The shape of such a molecule is called *angular* or *bent*.

## Central Atom with Four Pairs of Electrons

Consider methane, \begin{align*}\text{CH}_4\end{align*}, as an example of covalent bonding in Group 4A. Carbon has four valence electrons, with each hydrogen adding one more electron so that the central atom in methane has four pairs of electrons in its valence shell. To maximize the distance between them, the four pairs of electrons form a shape called *tetrahedral*. In the tetrahedral shape, the bond angle between any two hydrogen atoms is \begin{align*}109.5^\circ\end{align*}. If all four pairs of electrons are shared, the molecule shape is also tetrahedral.

## Central Atom with Five Pairs of Electrons

The molecules \begin{align*}\text{PCl}_3\end{align*} and \begin{align*}\text{PCl}_5\end{align*} will be considered as reference molecules for Group 5A. In the \begin{align*}\text{PCl}_3\end{align*} molecule illustrated below, the central phosphorus atom has five valence electrons. Each chlorine atom contributes one more electron, so the central atom has four pairs of electrons in its valence shell. These four pairs of electrons will form the tetrahedral shape in the effort to maximize the distance between them. Therefore, the electronic geometry for this molecule is tetrahedral. When the molecule is formed, however, one of the pairs of electrons is not shared. The resulting molecular geometry is called *pyramidal.*

It is important to note the difference between the pyramidal molecule and the trigonal planar molecule discussed earlier. In the trigonal planar molecule, none of the attached atoms is below or above the plane of the central atom. In this pyramidal molecule, however, all three of the attached atoms are below the plane of the central atom.

In the \begin{align*}\text{PCl}_5\end{align*} molecule, the phosphorus has five valence electrons, with each chlorine adding one more. As a result, the central atom will be surrounded by five pairs of electrons in its valence shell. When these five pairs of electrons maximize the distance between them, the shape is called *trigonal bipyramidal.* This shape has three attached atoms in a plane with the central atom and two atoms attached to the two ends of the molecule.

The bond angles between the three atoms in the plane with the central atom are all \begin{align*}120^\circ\end{align*}, while the bond angles between the two end atoms and the other three are \begin{align*}90^\circ\end{align*}.

## Central Atom with Six Pairs of Electrons

The two types of electronic geometry in Group 6A can be seen in the molecules \begin{align*}\text{SF}_2\end{align*} and \begin{align*}\text{SF}_6\end{align*}. In \begin{align*}\text{SF}_2\end{align*}, the central sulfur atom has six valence electrons. Each fluorine adds one more, so the central atom is surrounded by four pairs of electrons. The resultant electronic geometry is the tetrahedral shape we have seen before. However, when the compound \begin{align*}\text{SF}_2\end{align*} is formed, two of the pairs of electrons are unshared. This molecular shape, shown below, is called angular or bent.

In the molecule \begin{align*}\text{SF}_6\end{align*}, sulfur has six valence electrons, with each fluorine contributing another electron so that the central atom is surrounded by six pairs of electrons. The maximum distance six pairs of electrons can separate produces an electronic geometry called *octahedral.*

The bond angle between any two adjacent attached atoms is \begin{align*}90^\circ\end{align*}. The shape name is based on the number of triangular plates that can be placed on the surface of the molecule, as illustrated above. If you count carefully, you will see that the surface of the molecule contains eight triangular plates, hence the name octahedral.

**Table** below summarizes the electronic geometries that have been presented so far in this chapter.

Electron Pairs | Hybridization | Electronic Geometry |
---|---|---|

1 | None | Linear |

2 | \begin{align*}sp\end{align*} | Linear |

3 | \begin{align*}sp^2\end{align*} | Trigonal Planar |

4 | \begin{align*}sp^3\end{align*} | Tetrahedral |

5 | \begin{align*}sp^3d\end{align*} | Trigonal Bipyramidal |

6 | \begin{align*}sp^3d^2\end{align*} | Octahedral |

## Examples of Molecular Shapes

The electronic geometry for a given number of electron pairs surrounding a central atom is always the same. Electron pairs will distribute themselves in the same way to maximize their separation. The same thing cannot be said for molecular geometry. The molecular shape depends on not only the electronic geometry, but also the number of the shared electron pairs. In this section, we will consider a number of examples where some of the electron pairs are not shared.

There are only a few possible molecular geometries available to the members of Group 3A. Consider the shapes of the \begin{align*}\text{BH}_3\end{align*} molecule and the \begin{align*}\text{BH}_2^-\end{align*} ion. In \begin{align*}\text{BH}_3\end{align*} molecules, the central atom is surrounded by three pairs of electrons, so the electronic geometry is trigonal planar. When all three electron pairs are shared, the molecular geometry is also trigonal planar, as shown on the left in the diagram below. For the \begin{align*}\text{BH}_2^-\end{align*} ion, there are still three pairs of electrons around the central atom (3 electrons come from boron, 1 from each of the two hydrogens, and 1 from outside the ion), so the electronic geometry is still trigonal planar. The shape of the ion, however, will be a shape known as bent or angular, as shown on the right in the diagram below.

When the central atom is surrounded by four pairs of electrons, the electronic geometry will always be tetrahedral. When all four electron pairs are shared, like in the molecule \begin{align*}\text{CH}_4\end{align*}, the molecular shape will also be tetrahedral. In the case of ammonia, \begin{align*}\text{NH}_3\end{align*}, only three of the four pairs of electrons are shared. This results in a molecular shape called pyramidal. If a second pair of electrons is unshared, which is the case for \begin{align*}\text{H}_2\text{O}\end{align*}, the shape is angular again. The possible molecular geometries for molecules where the central atom is surrounded by four pairs of electrons are illustrated below.

When the central atom is surrounded by five pairs of electrons, the electronic geometry is trigonal bipyramidal. If all the electron pairs are shared, the molecular geometry will also be trigonal bipyramidal. An example of such a molecule is \begin{align*}\text{PF}_5\end{align*}. If one pair of electrons is not shared, the molecular shape is a *distorted tetrahedron*, which is sometimes called *seesaw.* An example of a molecule with trigonal bipyramidal electronic geometry and a distorted tetrahedron molecular shape is \begin{align*}\text{SF}_4\end{align*}. When the electronic geometry is trigonal bipyramidal and two pairs of electrons are unshared, the shape is *T-shaped.* An example of a T-shaped molecule is \begin{align*}\text{ClF}_3\end{align*}. \begin{align*}\text{ClF}_3\end{align*} has five pairs of electrons around the central atom, but only three of them are shared. When only two electron pairs in the trigonal bipyramidal electronic geometry are shared, the molecular geometry produced is linear, which is the case for \begin{align*}\text{I}_3^-\end{align*}. The trigonal bipyramidal, distorted tetrahedron, T-shaped, and linear molecular structures are shown in the diagram below.

Beginning with octahedral electronic geometry (six pairs of electrons), a number of molecular shapes can be produced depending on the number of electron pairs that are shared and unshared (see the illustration below).

For a trigonal bipyramidal electronic geometry, unshared electron pairs prefer to be in the equatorial positions (the points of the triangle in the “trigonal” plane). For an octahedral electronic geometry, unshared electron pairs prefer to be on opposite sides of the molecule. These rules help rule out other molecular shapes that could potentially occur when dealing with central atoms surrounded by five or six electron pairs.

**Table** below summarizes the different molecular geometries.

Valence Shell Electron Pairs Total | Valence Shell Electron Pairs Shared | Valence Shell Electron Pairs Unshared | Molecular Geometry |
---|---|---|---|

\begin{align*}1\end{align*} | \begin{align*}1\end{align*} | \begin{align*}0\end{align*} | Linear |

\begin{align*}2\end{align*} | \begin{align*}2\end{align*} | \begin{align*}0\end{align*} | Linear |

\begin{align*}2\end{align*} | \begin{align*}1\end{align*} | \begin{align*}1\end{align*} | Linear |

\begin{align*}3\end{align*} | \begin{align*}3\end{align*} | \begin{align*}0\end{align*} | Trigonal Planar |

\begin{align*}3\end{align*} | \begin{align*}2\end{align*} | \begin{align*}1\end{align*} | Angular |

\begin{align*}3\end{align*} | \begin{align*}1\end{align*} | \begin{align*}2\end{align*} | Linear |

\begin{align*}4\end{align*} | \begin{align*}4\end{align*} | \begin{align*}0\end{align*} | Tetrahedral |

\begin{align*}4\end{align*} | \begin{align*}3\end{align*} | \begin{align*}1\end{align*} | Trigonal Pyramidal |

\begin{align*}4\end{align*} | \begin{align*}2\end{align*} | \begin{align*}2\end{align*} | Angular |

\begin{align*}4\end{align*} | \begin{align*}1\end{align*} | \begin{align*}3\end{align*} | Linear |

\begin{align*}5\end{align*} | \begin{align*}5\end{align*} | \begin{align*}0\end{align*} | Trigonal Bipyramidal |

\begin{align*}5\end{align*} | \begin{align*}4\end{align*} | \begin{align*}1\end{align*} | Distorted Tetrahedron |

\begin{align*}5\end{align*} | \begin{align*}3\end{align*} | \begin{align*}2\end{align*} | T-shaped |

\begin{align*}5\end{align*} | \begin{align*}2\end{align*} | \begin{align*}3\end{align*} | Linear |

\begin{align*}5\end{align*} | \begin{align*}1\end{align*} | \begin{align*}4\end{align*} | Linear |

\begin{align*}6\end{align*} | \begin{align*}6\end{align*} | \begin{align*}0\end{align*} | Octahedral |

\begin{align*}6\end{align*} | \begin{align*}5\end{align*} | \begin{align*}1\end{align*} | Square Pyramidal |

\begin{align*}6\end{align*} | \begin{align*}4\end{align*} | \begin{align*}2\end{align*} | Square Planar |

\begin{align*}6\end{align*} | \begin{align*}3\end{align*} | \begin{align*}3\end{align*} | T-shaped |

\begin{align*}6\end{align*} | \begin{align*}2\end{align*} | \begin{align*}4\end{align*} | Linear |

\begin{align*}6\end{align*} | \begin{align*}1\end{align*} | \begin{align*}5\end{align*} | Linear |

*An animation showing the molecular shapes that are generated by sharing various numbers of electron pairs around the central atom (includes shapes when some pairs of electrons are non-shared pairs).*

## The Effect of Pi Bonds

For the process of predicting electronic or molecular geometry, double bonds and triple bonds should be counted as one effective pair when determining the number of electron pairs around the central atom. In order to repel other electron pairs, the electron pairs must be placed between the nuclei of two atoms. In pi bonds, the electron density is above and below the plane of the bond and therefore does not contribute to electron pair repulsion. *For the VSEPR model, multiple bonds count as only one effective pair of electrons.* We can use the nitrate ion, \begin{align*}\text{NO}_3^-\end{align*}, seen below as an example. In order to determine the shape of the nitrate ion, we count the number of electron pairs that are surrounding the central nitrogen atom. Since double bonds count as a single electron pair for the VSEPR model, we would count three pairs of electrons in the central atom's valence shell, and the shape of the ion would be trigonal planar.

## Examples of Determining Molecular Geometry

**Example:**

Determine the shape of the ammonium ion, \begin{align*}\text{NH}_4^+\end{align*}.

**Solution:**

First determine the number of electron pairs around the central nitrogen atom.

Electrons \begin{align*}= 5\end{align*} (from nitrogen) \begin{align*}+ \ 4\end{align*} (one from each hydrogen) \begin{align*}- \ 1\end{align*} (the positive charge on the ion indicates this ion has lost one electron to the outside) \begin{align*}= 8\end{align*} electrons \begin{align*}= 4\end{align*} electron pairs

The next step is to choose the electronic geometry based on the number of electron pairs.

The electronic geometry of a central atom with four pairs of electrons \begin{align*}=\end{align*} tetrahedral.

Finally, choose the molecular geometry based on the number of valence shell electron pairs that are shared and not shared.

Since all four pairs of electrons are shared in this ion, the ionic shape will be tetrahedral, as seen below.

**Example:**

Determine the molecular shape of the \begin{align*}\text{PF}_5\end{align*} molecule.

**Solution:**

Electrons in the valence shell of phosphorus \begin{align*}= 5\end{align*} (phosphorus) \begin{align*}+ \ 5\end{align*} (one from each fluorine) \begin{align*}= 10\end{align*} electrons \begin{align*}= 5\end{align*} pairs of electrons.

The electronic geometry is trigonal bipyramidal. Because all five pairs of electrons are shared, the molecular geometry will also be trigonal bipyramidal, illustrated below.

**Example:**

Determine the shape of the \begin{align*}\text{ICl}_3\end{align*} molecule.

**Solution:**

The number of electrons surrounding the central iodine atom 10: \begin{align*}7\end{align*} electrons come from the iodine atom, and \begin{align*}1\end{align*} electron comes from each chlorine atom. As a result, there are 10 electrons, or 5 electron pairs, surrounding the central iodine atom. Therefore, the electronic geometry is trigonal bipyramidal. Since only three of the electron pairs are shared, the molecular geometry is T-shaped.

**Example:**

Determine the shape of the \begin{align*}\text{CO}_2\end{align*} molecule.

**Solution:**

Since there are multiple bonds involved in this molecule, we need to write the Lewis structure for the molecule to make sure we do not count any double or triple bonds for VSEPR model determinations. The Lewis structure for \begin{align*}\text{CO}_2\end{align*} is shown below.

Only the sigma bonds count in determining the electron pairs surrounding the central carbon atom. This molecule, therefore, has two electron pairs in the valence shell of the central atom, which produces linear electronic geometry. Since both pairs are shared, the molecular geometry will also be linear.

**Example:**

Determine the shape of the \begin{align*}\text{SO}_2\end{align*} molecule.

**Solution:**

We will write the Lewis structure (shown below) to check for multiple bonds.

In writing the Lewis structure for \begin{align*}\text{SO}_2\end{align*}, we determined that a double bond is necessary to provide an octet of electrons for the central sulfur atom. Therefore, this molecule has three pairs of electrons around the central atom, so its electronic geometry will be trigonal planar. Since only two of the electron pairs are shared, the molecular geometry is angular.

**Example 6:**

Determine the molecular shape of the \begin{align*}\text{XeF}_4\end{align*} molecule.

**Solution:**

The number of electrons surrounding the central atom in \begin{align*}\text{XeF}_4\end{align*} is twelve: eight electrons from the Xe, and one each from the four fluorine atoms. As a result, there are twelve electrons, or six electron pairs, around the central atom Xe. Six pairs of electrons around the central atom produces an octahedral electronic geometry. Since two pairs are unshared, the molecular geometry will be square planar.

## Lesson Summary

- VSEPR theory suggests that the valence shell electron pairs will spread themselves around the central atom in an attempt to maximize the distance between them due to electrostatic repulsion.
- The electronic geometry of a molecule is dependent only on the number of electron pairs in the valence shell of the central atom.
- Molecular geometry is dependent on the electronic geometry and on the number of electron pairs that are unshared.
- Electrons in pi bonds do not contribute to electronic and molecular geometry.

## Further Reading / Supplemental Links

The *learner.org* website allows users to view the Annenberg series of chemistry videos. You are required to register before you can watch the videos, but there is no charge to register. The video called “Molecular Architecture” is related to this lesson.

This website reviews how to predict molecular structure by using the VSEPR theory.

This video is a ChemStudy film called “Shapes and Polarities of Molecules.”

## Review Questions

- What is the designation for the hybrid orbitals formed from each of the following combinations of atomic orbitals in
**Table**below, and what is the bond angle associated with the hybrid orbitals?

Orbitals Combined | Type of Hybridization | Bond Angles |
---|---|---|

one \begin{align*}s\end{align*} and one \begin{align*}p\end{align*} | ||

one \begin{align*}s\end{align*} and two \begin{align*}p\end{align*} | ||

one \begin{align*}s\end{align*} and three \begin{align*}p\end{align*} |

- Draw a Lewis structure for \begin{align*}\text{OF}_2\end{align*} that obeys the octet rule.
- Draw a Lewis structure for \begin{align*}\text{H}_2\text{CO}\end{align*} that obeys the octet rule. (C is the central atom.) What is the geometrical shape of this molecule?
- What is the bond angle in \begin{align*}\text{SCl}_2\end{align*}?
- What is the molecular shape of \begin{align*}\text{ICl}_3\end{align*}?
- What is the molecular shape of \begin{align*}\text{XeCl}_4\end{align*}?
- The ion \begin{align*}\text{I}_3^-\end{align*} molecule has been produced in the lab, but the ion \begin{align*}\text{F}_3^-\end{align*} has not. Offer an explanation as to why \begin{align*}\text{F}_3^-\end{align*} cannot be produced in the lab.
- The molecule shown here is formaldehyde. What is the hybridization of the carbon atom in this molecule?
- \begin{align*}sp^2\end{align*}
- \begin{align*}sp^2d\end{align*}
- \begin{align*}sp^3\end{align*}
- \begin{align*}5\end{align*} pi bonds

- The molecule shown here is acetylsalicylic acid, better known as aspirin.
- What is the hybridization of carbon \begin{align*}1\end{align*}?
- What is the hybridization of carbon \begin{align*}2\end{align*}?
- What is the hybridization of carbon \begin{align*}3\end{align*}?
- What is the total number of pi bonds in the molecule?

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