Chapter 7: Advanced Theories of Covalent Bonding

7.2 Electron Pair Geometry versus Molecular Structure

Learning Outcomes

  • Explain the concepts of polar covalent bonds and molecular polarity

Electron-Pair Geometry versus Molecular Structure

It is important to note that electron-pair geometry around a central atom is not the same thing as its molecular structure. The electron-pair geometries shown in Figure 7.2.3 describe all regions where electrons are located, bonds as well as lone pairs. Molecular structure describes the location of the atoms, not the electrons.

A Lewis structure shows a carbon atom single bonded to four hydrogen atoms. This structure uses wedges and dashes to give it a three dimensional appearance.
Figure 7.2.1. The molecular structure of the methane molecule, [latex]\ce{CH4}[/latex], is shown with a tetrahedral arrangement of the hydrogen atoms.

We differentiate between these two situations by naming the geometry that includes all electron pairs the electron-pair geometry. The structure that includes only the placement of the atoms in the molecule is called the molecular structure. The electron-pair geometries will be the same as the molecular structures when there are no lone electron pairs around the central atom, but they will be different when there are lone pairs present on the central atom.

VSEPR structures like the one in Figure 7.2.1 are often drawn using the wedge and dash notation, in which solid lines represent bonds in the plane of the page, solid wedges represent bonds coming up out of the plane, and dashed lines represent bonds going down into the plane. For example, the methane molecule, [latex]\ce{CH4}[/latex], which is the major component of natural gas, has four bonding pairs of electrons around the central carbon atom; the electron-pair geometry is tetrahedral, as is the molecular structure (Figure 7.2.4). On the other hand, the ammonia molecule, [latex]\ce{NH3}[/latex], also has four electron pairs associated with the nitrogen atom, and thus has a tetrahedral electron-pair geometry. One of these regions, however, is a lone pair, which is not included in the molecular structure, and this lone pair influences the shape of the molecule (Figure 7.2.2).

Three images are shown and labeled, “a,” “b,” and “c.” Image a shows a nitrogen atom single bonded to three hydrogen atoms. There are four oval-shaped orbs that surround each hydrogen and one facing away from the rest of the molecule. These orbs are located in a tetrahedral arrangement. Image b shows a ball-and-stick model of the nitrogen single bonded to the three hydrogen atoms. Image c is the same as image a, but there are four curved, double headed arrows that circle the molecule and are labeled, “106.8 degrees.”
Figure 7.2.2. (a) The electron-pair geometry for the ammonia molecule is tetrahedral with one lone pair and three single bonds. (b) The trigonal pyramidal molecular structure is determined from the electron-pair geometry. (c) The actual bond angles deviate slightly from the idealized angles, because the lone pair takes up a larger region of space than do the single bonds, causing the HNH angle to be slightly smaller than 109.5°.

As seen in Figure 7.2.2, small distortions from the ideal angles in Figure 7.2.6 can result from differences in repulsion between various regions of electron density. VSEPR theory predicts these distortions by establishing an order of repulsions and an order of the amount of space occupied by different kinds of electron pairs. The order of electron-pair repulsions from greatest to least repulsion is:

lone pair-lone pair  >  lone pair-bonding pair  >  bonding pair-bonding pair

This order of repulsions determines the amount of space occupied by different regions of electrons. A lone pair of electrons occupies a larger region of space than the electrons in a triple bond; in turn, electrons in a triple bond occupy more space than those in a double bond, and so on. The order of sizes from largest to smallest is:

lone pair  >  triple bond  >  double bond  >  single bond

Consider formaldehyde, [latex]\ce{H2CO}[/latex], which is used as a preservative for biological and anatomical specimens (Figure 1). This molecule has regions of high electron density that consist of two single bonds and one double bond. The basic geometry is trigonal planar with 120° bond angles, but we see that the double bond causes slightly larger angles (121°), and the angle between the single bonds is slightly smaller (118°).

In the ammonia molecule, the three hydrogen atoms attached to the central nitrogen are not arranged in a flat, trigonal planar molecular structure, but rather in a three-dimensional trigonal pyramid (Figure 7.2.5) with the nitrogen atom at the apex and the three hydrogen atoms forming the base. The ideal bond angles in a trigonal pyramid are based on the tetrahedral electron pair geometry. Again, there are slight deviations from the ideal because lone pairs occupy larger regions of space than do bonding electrons. The [latex]\ce{H-N-H}[/latex] bond angles in [latex]\ce{NH3}[/latex] are slightly smaller than the 109.5° angle in a regular tetrahedron (Figure 7.2.3) because the lone pair-bonding pair repulsion is greater than the bonding pair-bonding pair repulsion (Figure 7.2.2). Figure 7.2.3 illustrates the ideal molecular structures, which are predicted based on the electron-pair geometries for various combinations of lone pairs and bonding pairs.
A table is shown that is comprised of six rows and six columns. The header row reads: “Number of Electron Pairs,” “Electron pair geometries; 0 lone pair,” “1 lone pair,” “2 lone pairs,” “3 lone pairs,” and “4 lone pairs.” The first column contains the numbers 2, 3, 4, 5, and 6. The first space in the second column contains a structure in which the letter E is single bonded to the letter X on each side. The angle of the bonds is labeled with a curved, double headed arrow and the value, “180 degrees.” The structure is labeled, “Linear.” The second space in the second column contains a structure in which the letter E is single bonded to the letter X on three sides. The angle between the bonds is labeled with a curved, double headed arrow and the value, “120 degrees.” The structure is labeled, “Trigonal planar.” The third space in the second column contains a structure in which the letter E is single bonded to the letter X four times. The angle between the bonds is labeled with a curved, double headed arrow and the value, “109 degrees.” The structure is labeled, “Tetrahedral.” The fourth space in the second column contains a structure in which the letter E is single bonded to the letter X on five sides. The angle between the bonds is labeled with a curved, double headed arrow and the values “90 and 120 degrees.” The structure is labeled, “Trigonal bipyramid.” The fifth space in the second column contains a structure in which the letter E is single bonded to the letter X on six sides. The angle between the bonds is labeled with a curved, double headed arrow and the value, “90 degrees.” The structure is labeled, “Octahedral.” The first space in the third column is empty while the second contains a structure in which the letter E is single bonded to the letter X on each side and has a lone pair of electrons. The angle between the bonds is labeled with a curved, double headed arrow and the value, “less than 120 degrees.” The structure is labeled, “Bent or angular.” The third space in the third column contains a structure in which the letter E is single bonded to the letter X three times and to a lone pair of electrons. It is labeled with a curved, double headed arrow and the value, “less than 109 degrees.” The structure is labeled, “Trigonal pyramid.” The fourth space in the third column contains a structure in which the letter E is single bonded to the letter X on four sides and has a lone pair of electrons. The bond angle is labeled with a curved, double headed arrow and the values, “less than 90 and less than 120 degrees.” The structure is labeled, “Sawhorse or seesaw.” The fifth space in the third column contains a structure in which the letter E is single bonded to the letter X on five sides and has a lone pair of electrons. The bond angle is labeled with a curved, double headed arrow and the value, “less than 90 degrees.” The structure is labeled, “Square pyramidal.” The first and second spaces in the fourth column are empty while the third contains a structure in which the letter E is single bonded to the letter X on each side and has two lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value, “less than less than 109 degrees.” The structure is labeled, “Bent or angular.” The fourth space in the fourth column contains a structure in which the letter E is single bonded to the letter X three times and to two lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value, “less than 90 degrees.” The structure is labeled, “T - shape.” The fifth space in the fourth column contains a structure in which the letter E is single bonded to the letter X on four sides and has two lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value “90 degrees.” The structure is labeled, “Square planar.” The first, second and third spaces in the fifth column are empty while the fourth contains a structure in which the letter E is single bonded to the letter X on each side and has three lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value, “180 degrees.” The structure is labeled, “Linear.” The fifth space in the fifth column contains a structure in which the letter E is single bonded to the letter X three times and to three lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value, “less than 90 degrees.” The structure is labeled, “T - shape.” The first, second, third, and fourth spaces in the sixth column are empty while the fifth contains a structure in which the letter E is single bonded to the letter X on each side and has four lone pairs of electrons. The bond angle is labeled with a curved, double headed arrow and the value “180 degrees.” The structure is labeled, “Linear.” All the structures use wedges and dashes to give them three dimensional appearances. According to VSEPR theory, the terminal atom locations (Xs in Figure 7.2.3) are equivalent within the linear, trigonal planar, and tetrahedral electron-pair geometries (the first three rows of the table). It does not matter which X is replaced with a lone pair, because the molecules can be rotated to convert positions. For trigonal bipyramidal electron-pair geometries, however, there are two distinct X positions, as shown in Figure 7.2.4: an axial position (if we hold a model of a trigonal bipyramid by the two axial positions, we have an axis around which we can rotate the model) and an equatorial position (three positions form an equator around the middle of the molecule). As shown in Figure 7.2.6, the axial position is surrounded by bond angles of 90°, whereas the equatorial position has more space available because of the 120° bond angles. In a trigonal bipyramidal electron-pair geometry, lone pairs always occupy equatorial positions because these more spacious positions can more easily accommodate the larger lone pairs.

Theoretically, we can come up with three possible arrangements for the three bonds and two lone pairs for the [latex]\ce{ClF3}[/latex] molecule (Figure 7.2.4). The stable structure is the one that puts the lone pairs in equatorial locations, giving a T-shaped molecular structure.
Four sets of images are shown and labeled, “a,” “b,” “c,” and “d.” Each image is separated by a dashed vertical line. Image a shows a six-faced, bi-pyramidal structure where the central vertical axis is labeled, “Axial,” and the horizontal plane is labeled, “Equatorial.” Image b shows a pair of diagrams in the same shape as image a, but in these diagrams, the left has a chlorine atom in the center while the right has a chlorine atom in the center, two fluorine atoms on the upper and lower ends, and one fluorine in the left horizontal position. Image c shows a pair of diagrams in the same shape as image a, but in these diagrams, the left has a chlorine atom in the center while the right has a chlorine atom in the center and three fluorine atoms in each horizontal position. Image d shows a pair of diagrams in the same shape as image a, but in these diagrams, the left has a chlorine atom in the center while the right has a chlorine atom in the center, two fluorine atoms in the horizontal positions, and one in the axial bottom position. Figure 7.2.4. (a) In a trigonal bipyramid, the two axial positions are located directly across from one another, whereas the three equatorial positions are located in a triangular arrangement. (b–d) The two lone pairs (red lines) in [latex]\ce{ClF3}[/latex] have several possible arrangements, but the T-shaped molecular structure (b) is the one actually observed, consistent with the larger lone pairs both occupying equatorial positions.

When a central atom has two lone electron pairs and four bonding regions, we have an octahedral electron-pair geometry. The two lone pairs are on opposite sides of the octahedron (180° apart), giving a square planar molecular structure that minimizes lone pair-lone pair repulsions (Figure 7.2.3).

Predicting Electron Pair Geometry and Molecular Structure

The following procedure uses VSEPR theory to determine the electron pair geometries and the molecular structures:

  1. Write the Lewis structure of the molecule or polyatomic ion.
  2. Count the number of regions of electron density (lone pairs and bonds) around the central atom. A single, double, or triple bond counts as one region of electron density.
  3. Identify the electron-pair geometry based on the number of regions of electron density: linear, trigonal planar, tetrahedral, trigonal bipyramidal, or octahedral (Figure 7.2.6, first column).
  4. Use the number of lone pairs to determine the molecular structure (Figure 7.2.6). If more than one arrangement of lone pairs and chemical bonds is possible, choose the one that will minimize repulsions, remembering that lone pairs occupy more space than multiple bonds, which occupy more space than single bonds. In trigonal bipyramidal arrangements, repulsion is minimized when every lone pair is in an equatorial position. In an octahedral arrangement with two lone pairs, repulsion is minimized when the lone pairs are on opposite sides of the central atom.

The following examples illustrate the use of VSEPR theory to predict the molecular structure of molecules or ions that have no lone pairs of electrons. In this case, the molecular structure is identical to the electron pair geometry.

Example 7.2.1: Predicting Electron-pair Geometry and Molecular Structure: [latex]\ce{CO2}[/latex] and [latex]\ce{BCl3}[/latex]

Predict the electron-pair geometry and molecular structure for each of the following:

  1. carbon dioxide, [latex]\ce{CO2}[/latex], a molecule produced by the combustion of fossil fuels
  2. boron trichloride, [latex]\ce{BCl3}[/latex], an important industrial chemical

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  1. We write the Lewis structure of [latex]\ce{CO2}[/latex] as:
    A Lewis structure shows a carbon atom double bonded on both the left and right sides to oxygen atoms that each have two lone pairs of electrons.
    This shows us two regions of high electron density around the carbon atom—each double bond counts as one region, and there are no lone pairs on the carbon atom. Using VSEPR theory, we predict that the two regions of electron density arrange themselves on opposite sides of the central atom with a bond angle of 180°. The electron-pair geometry and molecular structure are identical, and [latex]\ce{CO2}[/latex] molecules are linear.
  2. We write the Lewis structure of [latex]\ce{BCl3}[/latex] as:
    A Lewis structure depicts a boron atom that is single bonded to three chlorine atoms, each of which has three lone pairs of electrons.
    Thus we see that [latex]\ce{BCl3}[/latex] contains three bonds, and there are no lone pairs of electrons on boron. The arrangement of three regions of high electron density gives a trigonal planar electron-pair geometry. The [latex]\ce{B-Cl}[/latex] bonds lie in a plane with 120° angles between them. [latex]\ce{BCl3}[/latex] also has a trigonal planar molecular structure (Figure 7.2.8).

Figure 7.2.5 shows the electron-pair geometry and molecular structure of [latex]\ce{BCl3}[/latex] are both trigonal planar. Note that the VSEPR geometry indicates the correct bond angles (120°), unlike the Lewis structure shown above.

A Lewis structure depicts a boron atom that is single bonded to three chlorine atoms, each of which is oriented in the same flat plane. This figure uses dashes and wedges to give it a three-dimensional appearance.
Figure 7.2.5.

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Check Your Learning

Example 7.2.2: Predicting Electron-pair Geometry and Molecular Structure: Ammonium

Two of the top 50 chemicals produced in the United States, ammonium nitrate and ammonium sulfate, both used as fertilizers, contain the ammonium ion. Predict the electron-pair geometry and molecular structure of the [latex]\ce{NH4+}[/latex] cation.

[reveal-answer q=”222511″]Show Solution[/reveal-answer]
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We write the Lewis structure of [latex]\ce{NH4+}[/latex] as:

A Lewis structure depicts a nitrogen atom that is single bonded to four hydrogen atoms. The structure is surrounded by brackets and has a superscripted positive sign.

We can see that NH4+ contains four bonds from the nitrogen atom to hydrogen atoms and no lone pairs. We expect the four regions of high electron density to arrange themselves so that they point to the corners of a tetrahedron with the central nitrogen atom in the middle (Figure 7.2.6). Therefore, the electron pair geometry of [latex]\ce{NH4+}[/latex] is tetrahedral, and the molecular structure is also tetrahedral (Figure 9).

A Lewis structure depicts a nitrogen atom that is single bonded to four hydrogen atoms. The structure is surrounded by brackets and has a superscripted positive sign. This figure uses dashes and wedges to displays its three planes in a tetrahedral shape.
Figure 7.2.6. The ammonium ion displays a tetrahedral electron-pair geometry as well as a tetrahedral molecular structure.

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Check Your Learning

The next several examples illustrate the effect of lone pairs of electrons on molecular structure.

Example 7.2.3: Predicting Electron-pair Geometry and Molecular Structure: Lone Pairs on the Central Atom

Predict the electron-pair geometry and molecular structure of a water molecule.

[reveal-answer q=”63530″]Show Solution[/reveal-answer]
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The Lewis structure of [latex]\ce{H2O}[/latex] indicates that there are four regions of high electron density around the oxygen atom: two lone pairs and two chemical bonds:

A Lewis structure depicts an oxygen atom with two lone pairs of electrons single bonded to two hydrogen atoms.

We predict that these four regions are arranged in a tetrahedral fashion (Figure 10), as indicated in Figure 7.2.6. Thus, the electron-pair geometry is tetrahedral and the molecular structure is bent with an angle slightly less than 109.5°. In fact, the bond angle is 104.5°.

Two diagrams are shown and labeled, “a” and “b.” Diagram a shows an oxygen atom in the center of a four-sided pyramid shape. Diagram b shows the same image as diagram a, but this time there are hydrogen atoms located at two corners of the pyramid shape.
Figure 7.2.7. (a) [latex]\ce{H2O}[/latex] has four regions of electron density around the central atom, so it has a tetrahedral electron-pair geometry. (b) Two of the electron regions are lone pairs, so the molecular structure is bent.

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Check Your Learning

Example 7.2.4: Predicting Electron-pair Geometry and Molecular Structure: [latex]\ce{SF4}[/latex]

Sulfur tetrafluoride, [latex]\ce{SF4}[/latex], is extremely valuable for the preparation of fluorine-containing compounds used as herbicides (i.e., [latex]\ce{SF4}[/latex] is used as a fluorinating agent). Predict the electron-pair geometry and molecular structure of a [latex]\ce{SF4}[/latex] molecule.

[reveal-answer q=”418586″]Show Solution[/reveal-answer]
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The Lewis structure of [latex]\ce{SF4}[/latex] indicates five regions of electron density around the sulfur atom: one lone pair and four bonding pairs:

A Lewis diagram depicts a sulfur atom with one lone pair of electrons single bonded to four fluorine atoms, each with three lone pairs of electrons.

We expect these five regions to adopt a trigonal bipyramidal electron-pair geometry. To minimize lone pair repulsions, the lone pair occupies one of the equatorial positions. The molecular structure (Figure 11) is that of a seesaw (Figure 7.2.6).

Two diagrams are shown and labeled, “a” and “b.” Diagram a shows a sulfur atom in the center of a six-sided bi-pyramidal shape. Diagram b shows the same image as diagram a, but this time there are fluorine atoms located at four corners of the pyramid shape and they are connected to the sulfur atom by single lines.
Figure 7.2.8. (a) [latex]\ce{SF4}[/latex] has a trigonal bipyramidal arrangement of the five regions of electron density. (b) One of the regions is a lone pair, which results in a seesaw-shaped molecular structure.

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Check Your Learning

Example 7.2.5: Predicting Electron-pair Geometry and Molecular Structure: [latex]\ce{XeF4}[/latex]

Of all the noble gases, xenon is the most reactive, frequently reacting with elements such as oxygen and fluorine. Predict the electron-pair geometry and molecular structure of the [latex]\ce{XeF4}[/latex] molecule.

[reveal-answer q=”537122″]Show Solution[/reveal-answer]
[hidden-answer a=”537122″]

The Lewis structure of [latex]\ce{XeF4}[/latex] indicates six regions of high electron density around the xenon atom: two lone pairs and four bonds:

A Lewis structure depicts a xenon atom with two lone pairs of electrons that is single bonded to four fluorine atoms, each with three lone pairs of electrons.

These six regions adopt an octahedral arrangement (Figure 7.2.6), which is the electron-pair geometry. To minimize repulsions, the lone pairs should be on opposite sides of the central atom (Figure 12). The five atoms are all in the same plane and have a square planar molecular structure.

Two diagrams are shown and labeled, “a” and “b.” Diagram a shows a xenon atom in the center of an eight-sided octahedral shape. Diagram b shows the same image as diagram a, but this time there are fluorine atoms located at the four corners of the shape in the horizontal plane. They are connected to the xenon by single lines.
Figure 7.2.9. (a) [latex]\ce{XeF4}[/latex] adopts an octahedral arrangement with two lone pairs (red lines) and four bonds in the electron-pair geometry. (b) The molecular structure is square planar with the lone pairs directly across from one another.

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Check Your Learning

Key Concepts and Summary

Molecular structure, which refers only to the placement of atoms in a molecule and not the electrons, is equivalent to electron-pair geometry only when there are no lone electron pairs around the central atom.

Try It

  1. What are the electron-pair geometry and the molecular structure of each of the following molecules or ions?
    1. [latex]\ce{ClF5}[/latex] 
    2. [latex]\ce{ClO2-}[/latex]
    3. [latex]\ce{TeCl4^2-}[/latex]
    4. [latex]\ce{PCl3}[/latex] 
    5. [latex]\ce{SeF4}[/latex] 
    6. [latex]\text{PH2-}[/latex]
  2. Which of the following molecules and ions contain polar bonds? Which of these molecules and ions have dipole moments?
    1. [latex]\ce{ClF5}[/latex] 
    2. [latex]\ce{ClO2-}[/latex]
    3. [latex]\ce{TeCl4^2-}[/latex]
    4. [latex]\ce{PCl3}[/latex] 
    5. [latex]\ce{SeF4}[/latex] 
    6. [latex]\ce{PH2-}[/latex]
    7. [latex]\ce{XeF2}[/latex]

[reveal-answer q=”176329″]Show Selected Solutions[/reveal-answer]
[hidden-answer a=”176329″]

  1. The electron pair geometry and the molecular structure of each are as follows:
    1. electron-pair geometry: octahedral, molecular structure: square pyramidal
    2. electron-pair geometry: tetrahedral, molecular structure: bent
    3. electron-pair geometry: octahedral, molecular structure: square planar
    4. electron-pair geometry: tetrahedral, molecular structure: trigonal pyramidal
    5. electron-pair geometry: trigonal bypyramidal, molecular structure: seesaw
    6. electron-pair geometry: tetrahedral, molecular structure: bent (109°)
  2. All of these molecules and ions contain polar bonds. Only [latex]\ce{ClF5}[/latex], [latex]\ce{ClO2-},[/latex] [latex]\ce{PCl3}[/latex], [latex]\ce{SeF}[/latex], and [latex]\ce{PH2-}[/latex] have dipole moments.

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Glossary

axial position: location in a trigonal bipyramidal geometry in which there is another atom at a 180° angle and the equatorial positions are at a 90° angle

electron-pair geometry: arrangement around a central atom of all regions of electron density (bonds, lone pairs, or unpaired electrons)

equatorial position: one of the three positions in a trigonal bipyramidal geometry with 120° angles between them; the axial positions are located at a 90° angle

molecular structure: structure that includes only the placement of the atoms in the molecule

definition

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