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# 9.2: Molecular Geometry

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

• Explain the basis of VSEPR theory.
• Predict the shapes of molecules and polyatomic ions using VSEPR theory.
• Account for variations in bond angles based on the relative repulsive forces exerted by lone pairs and bonding pairs of electrons.
• Describe the relationship between molecular geometry and electron domain geometry.

## Lesson Vocabulary

• electron domain geometry
• molecular geometry
• valence shell
• valence shell electron pair repulsion (VSEPR)

### Recalling Prior Knowledge

• How are Lewis electron dot structures determined?
• What are bonding pairs of electrons and what are lone pairs?

Molecular geometry is the three-dimensional arrangement of atoms in a molecule. The molecular geometry, or shape, of a molecule is an important factor that affects the physical and chemical properties of a compound. Those properties include melting and boiling points, solubility, density, and the types of chemical reactions that a compound undergoes. In this lesson, you will learn a technique to predict molecular geometry based on a molecule’s Lewis electron dot structure.

## VSEPR Theory

The valence shell is the outermost occupied shell of electrons in an atom. This shell holds the valence electrons, which are the electrons that are involved in bonding and shown in a Lewis structure. The valence-shell electron pair repulsion model, or VSEPR model, states that a molecule will adjust its shape so that the valence electron pairs stay as far apart from each other as possible. This makes sense, based on the fact that negatively charged electrons repel one another. We will systematically classify molecules according to the number of bonding pairs of electrons and the number of nonbonding or lone pairs around the central atom. For the purposes of the VSEPR model, a double or triple bond is no different in terms of repulsion than a single bond. We will begin by examining molecules in which the central atom does not have any lone pairs.

## Central Atom with No Lone Pairs

In order to easily understand the types of molecules possible, we will use a simple system to identify the parts of any molecule.

A = central atom in a molecule
B = atoms surrounding the central atom

Subscripts after the B will denote the number of B atoms that are bonded to the central A atom. For example, AB4 is a molecule with a central atom surrounded by four covalently bonded atoms. Again, it does not matter if those bonds are single, double, or triple bonds.

### AB2: Beryllium Hydride (BeH2)

Beryllium hydride consists of a central beryllium atom with two single bonds to hydrogen atoms. Recall that it violates the octet rule.

According to the requirement that electron pairs maximize their distance from one another, the two bonding pairs in the BeH2 molecules will arrange themselves on directly opposite sides of the central Be atom. The resulting geometry is a linear molecule, shown in a “ball and stick” model in Figure below.

The H-Be-H bond angle is 180° because of its linear geometry.

Carbon dioxide is another example of a molecule which falls under the AB2 category. Its Lewis structure consists of double bonds between the central carbon atom and each oxygen atom.

The repulsion between the two groups of four electrons (two pairs) is no different than the repulsion between the two groups of two electrons (one pair) in the BeH2 molecule. Carbon dioxide is also linear.

### AB3: Boron Trifluoride (BF3)

Boron trifluoride consists of a central boron atom with three single bonds to fluorine atoms. The boron atom also has an incomplete octet.

The geometry of the BF3 molecule is called trigonal planar. The fluorine atoms are positioned at the vertices of an equilateral triangle. The F-B-F angle is 120°, and all four atoms lie in the same plane.

### AB4: Methane (CH4)

Methane is an organic compound that is the primary component of natural gas. Its structure consists of a central carbon atom with four single bonds to hydrogen atoms.

In order to maximize their distance from one another, the four groups of bonding electrons do not lie in the same plane. Instead, each of the hydrogen atoms lies at the corners of a geometrical shape called a tetrahedron. The carbon atom is at the center of the tetrahedron. Each face of a tetrahedron is an equilateral triangle.

(left) Tetrahedron. (right) Ball and stick model of methane.

The molecular geometry of the methane molecule is referred to as tetrahedral. The H-C-H bond angles are 109.5°, which is larger than the 90° that they would be if the molecule was planar. When drawing a structural formula for a molecule such as methane, it is advantageous to be able to indicate the three-dimensional character of its shape. The structural formula below is called a perspective drawing. The dotted line bond should be visualized as receding into the page, while the solid triangle bond should be visualized as coming out of the page.

### AB5: Phosphorus Pentachloride (PCl5)

The central phosphorus atom in a molecule of phosphorus pentachloride has ten electrons surrounding it, exceeding the octet rule.

Unlike the other basic shapes, the five chlorine atoms in this arrangement are not equivalent with respect to their geometric relationship to the phosphorus atom. Three of the chlorine atoms lie in a plane, with Cl-P-Cl bond angles of 120°. This portion of the molecule is essentially the same as a trigonal planar arrangement. These chlorine atoms are referred to as the equatorial atoms because they are arranged around the center of the molecule. The other two chlorine atoms are oriented exactly perpendicular to the plane formed by the phosphorus atom and the equatorial chlorine atoms. These are called the axial chlorine atoms.

(left) Trigonal bipyramidal. (right) Ball and stick model of phosphorus pentachloride.

In the figure above, the axial chlorine atoms form a vertical axis with the central phosphorus atom. There is a 90° angle between P-Claxial bonds and P-Clequitorial bonds. The molecular geometry of PCl5 is called trigonal bipyramidal. A surface covering the molecule would take the shape of two three-sided pyramids pointing in opposite directions.

### AB6: Sulfur Hexafluoride (SF6)

The sulfur atom in sulfur hexafluoride also exceeds the octet rule.

Unlike the trigonal bipyramidal structure, all of the fluorine atoms in SF6 are equivalent. The molecular geometry is called octahedral, because a surface covering the molecule would have eight sides. All of the F-S-F angles are 90° in an octahedral molecule, with the exception of the fluorine atoms that are directly opposite one another.

## Central Atom with One or More Lone Pairs

The molecular geometries of molecules change when the central atom has one or more lone pairs of electrons. The total number of electron pairs, both bonding pairs and lone pairs, leads to what is called the electron domain geometry. Electron domain geometries are one of the five learned so far: linear, trigonal planar, tetrahedral, trigonal bipyramidal, or octahedral. However, when one or more of the bonding pairs of electrons is replaced with a lone pair, the molecular geometry, or actual shape of the molecule, is altered. In keeping with the A and B symbols established in the previous section, we will use E to represent a lone pair on the central atom (A). A subscript will be used when there is more than one lone pair. Lone pairs on the surrounding atoms (B) do not affect the geometry.

### AB2E: Ozone (O3)

The Lewis structure for ozone consists of a central oxygen atom that has a double bond to one of the outer oxygen atoms and a single bond to the other.

This leaves one lone pair on the central atom, and the molecule displays resonance. Since VSEPR does not distinguish between double and single bonds, the resonance does not affect the geometry. Molecules with three electron pairs have a domain geometry that is trigonal planar. Here, the lone pair on the central atom repels the electrons in the two bonds, causing the atom to adopt a bent molecular geometry.

Ozone, O3.

One might expect the O-O-O bond angle to be 120°, as in a trigonal planar molecule. However, within the context of the VSEPR model, lone pairs of electrons can be considered to be slightly more repulsive than bonding pairs of electrons, due to their closer proximity to the central atom. In other words, lone pairs take up more space. Therefore the O-O-O angle is slightly less than 120°.

### AB3E: Ammonia (NH3)

The ammonia molecule contains three single bonds and one lone pair on the central nitrogen atom.

The domain geometry for a molecule with four electron pairs is tetrahedral, as was seen with CH4. In the ammonia molecule, one of the electron pairs is a lone pair rather than a bonding pair. The molecular geometry of NH3 is called trigonal pyramidal.

Ammonia, NH3.

Recall that the bond angles in the tetrahedral CH4 molecule are all equal to 109.5°. Again, the replacement of one of the bonded electron pairs with a lone pair compresses these angles slightly. The H-N-H angle is approximately 107°.

### AB2E2: Water (H2O)

A water molecule consists of two bonding pairs and two lone pairs.

As for methane and ammonia, the domain geometry for a molecule with four electron pairs is tetrahedral. In the water molecule, two of the electron pairs are lone pairs rather than bonding pairs. The molecular geometry of the water molecule is referred to as bent. The H-O-H bond angle is 104.5°, which is smaller than the bond angle in NH3.

Water, H2O.

### AB4E: Sulfur Tetrafluoride (SF4)

The Lewis structure for SF4 contains four single bonds and a lone pair on the sulfur atom.

The sulfur atom has five electron groups around it, which corresponds to the trigonal bipyramidal domain geometry, as in PCl5. Recall that the trigonal bipyramidal geometry has three equatorial atoms and two axial atoms attached to the central atom. Because of the greater repulsion of a lone pair, it is one of the equatorial atoms that is replaced by a lone pair. The geometry of the molecule is called a distorted tetrahedron or seesaw.

Sulfur tetrafluoride, SF4.

### AB3E2: Chlorine Trifluoride (ClF3)

The Lewis structure of ClF3 consists of three Cl-F single bonds and two lone pairs on the central chlorine atom.

As in the case of SF4, the central atom has five electron groups and a trigonal bipyramidal domain geometry. In ClF3, both of the bonded pairs that have been replaced with lone pairs are equatorial. The resulting molecular geometry is called T-shaped.

### AB2E3: Triiodide Ion (I3−)

The triiodide ion consists of three iodine atoms linked together by covalent bonds. Its overall charge of 1- gives this structure 22 total valence electrons, resulting in a Lewis structure with three lone pairs on the central iodine atom.

The five electron groups around the central atom give it a trigonal bipyramidal domain geometry, and all three equatorial atoms have been replaced by lone pairs. The result is a linear ion – the central atom and the two axial atoms.

Triiodide ion, I3-.

### AB5E: Bromine Pentafluoride (BrF5)

The bromine pentafluoride molecule has a central bromine atom, five single bonds to fluorine atoms, and one lone pair.

The six groups of electrons around the central atom give it an octahedral domain geometry. Since all of the peripheral atoms in an octahedral molecule are equivalent, any one of them could equally be replaced by the lone pair. The resulting geometry is called square pyramidal. A surface covering a square pyramidal molecule is a four sided pyramid on a flat base.

Bromine pentafluoride, BrF5.

### AB4E2: Xenon Tetrafluoride (XeF4)

Xenon tetrafluoride has a Lewis structure consisting of four single bonds and two lone pairs on the central xenon atom.

The six groups of electrons give it an octahedral domain geometry, but two of the atoms are replaced by two lone pairs. In order to maximize the space available to each of the lone pairs, they occupy positions that are directly opposite each other. As a result, the four remaining fluorine atoms are in the same plane as the xenon atom, and all F-Xe-F angles are equal to 90°. This molecular geometry is called square planar.

Xenon tetrafluoride, XeF4.

## Summary of VSEPR

The VSEPR model can be applied to predict the molecular geometry of a given molecular compound. The steps to follow can be summarized as follows:

• Draw the Lewis electron dot structure for the molecule.
• Count the total number of electron pairs around the central atom. This is referred to as the electron domain geometry.
• If there are no lone pairs around the central atom, refer to Table below, to determine the molecular geometry, which is the same as the electron domain geometry.
• If there are one or more lone pairs on the central atom, the molecular geometry (the actual shape of the molecule) will not be the same as the electron domain geometry. Refer to Table below.
• In predicting bond angles, remember that a lone pair takes up more space than a bonding pair or pairs of electrons.
Geometries of Molecules and Ions in Which the Central Atom Has No Lone Pairs
Number of Electron Pairs Around Central Atom Electron Domain Geometry Molecular Geometry Examples
2 linear linear BeCl2, CO2
3 trigonal planar trigonal planar BF3, CO32−
4 tetrahedral tetrahedral CH4, NH4+
5 trigonal bipyramidal trigonal bipyramidal PCl5
6 octahedral octahedral SF6
Geometries of Molecules and Ions in Which the Central Atom Has One or More Lone Pairs
Total Number of Electron Pairs Number of Bonding Pairs Number of Lone Pairs Electron Domain Geometry Molecular Geometry Examples
3 2 1 trigonal planar bent O3
4 3 1 tetrahedral trigonal pyramidal NH3
4 2 2 tetrahedral bent H2O
5 4 1 trigonal bipyramidal distorted tetrahedron (seesaw) SF4
5 3 2 trigonal bipyramidal T-shaped ClF3
5 2 3 trigonal bipyramidal linear I3
6 5 1 octahedral square pyramidal BrF5
6 4 2 octahedral square planar XeF4

Practice with basic molecule shapes at http://phet.colorado.edu/en/simulation/molecule-shapes-basics.

## Lesson Summary

• Valence shell electron pair repulsion (VSEPR) theory is a technique for predicting the molecular geometry of a molecule. A molecule's shape provides important information that can be used to understand its chemical and physical properties.
• According to VSEPR, electron pairs distribute themselves around a central atom in such a way as to maximize their distance from each other.
• Electron domain geometries are based on the total number of electron pairs, while molecular geometries describe the arrangement of atoms and bonding pairs in a molecule.

## Lesson Review Questions

### Reviewing Concepts

1. Why is it important to know the geometry or shape of a molecule?
2. What is the difference between electron domain geometry and molecular geometry? Use an example.
3. In terms of its effect on molecular geometry, how does the repulsion from a lone pair of electrons compare to the repulsion from a bonding pair of electrons?
4. How many atoms are directly bonded to the central atom in molecules that have the following molecular geometries?
1. trigonal bipyramidal
2. tetrahedral
3. octahedral
4. bent
5. trigonal pyramidal
6. square planar
5. Explain why the bond angle in an H2O molecule is smaller than the bond angle in an NH3 molecule.
6. SF4 and CH4 have similar molecular formulas. Why does the SF4 molecule adopt a seesaw geometry, while the CH4 molecule is tetrahedral?

### Problems

1. Using the VSEPR method, predict the molecular geometries of the following molecules:
1. SF2
2. PBr3
3. AlCl3
4. TeCl4
5. HCN
2. Predict the molecular geometries of the following ions:
1. NO3
2. ICl2
3. ClO3
4. PO43−
5. SeCl3
3. Predict the H-As-H bond angle in AsH3. Predict the H-B-H bond angle in BH3. Explain the difference.
4. What are the molecular geometry and the bond angle for XeF2?
5. In the XeOF4 molecule, the central xenon atom has a double bond to the oxygen atom and single bonds to the four fluorine atoms. Predict the geometry of this molecule.

## Points to Consider

The electronegativity of an atom describes its ability to attract shared electrons. Nonmetal atoms generally have high electronegativities, while metals generally have low electronegativities.

• How can electronegativity be used to predict whether a bond between two atoms will be ionic or covalent?
• Is the sharing of electrons in a covalent bond always equal, or can the sharing be dominated by one of the atoms? How would this affect the properties of the molecule?

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