Chemistry: Atoms First Julia Burdge & Jason Overby

Chemistry: Atoms First Julia Burdge & Jason Overby
Chapter 7 Molecular Geometry and Bonding Theories Homework 7, 9, 11, 13, 19, 21, 35, 37, 39 43, 45, 47, 49, 79 and 83 Kent L. McCorkle Cosumnes River College Sacramento, CA Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Valence Bond (VB) Theory
Deals with the overlap of the atomic orbitals (AO) of the participation atoms to form a chemical bond. Due to the overlapping, electrons are localized in the bond region However, the atomic orbitals for bonding may not be "pure" atomic orbitals directly from the solution of the Schrodinger Equation. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an AO with the proper character for the bonding is called hybridization. The resulting atomic orbitals are called hybridized atomic orbitals or simply hybrid orbitals.

Valence Shell Electron Pair Repulsion Theory
Valence Shell Electron Pair Repulsion (VSEPR) theory allows the Chemist to predict the 3-dimensional shape of molecules from knowledge of their Lewis Dot structure. In VSEPR theory, the position of bound atoms (ligands) and electron pairs are described relative to a central atom. Once the ligands and lone pair electrons are positioned, the resulting geometrical shape presented by the atoms only (ignoring lone pairs) is used to describe the molecule. The VSEPR theory is based on the desire of electrons to be as far Apart from each other as possible in a molecule

Linear Molecules There are only two places in the valence shell of the central atom in BeF2 where electrons can be found. Repulsion between these pairs of electrons can be minimized by arranging them so that they point in opposite directions. Thus, the VSEPR theory predicts that BeF2 should be a linear molecule, with a 180o angle between the two Be-F bonds. Electron domains = 2 VSEPER Notation = AX2

0 lone pairs on central atom 2 atoms bonded to central atom
Cl Be 0 lone pairs on central atom 2 atoms bonded to central atom

Trigonal Planar Molecules
There are three places on the central atom in boron trifluoride (BF3) where valence electrons can be found. Repulsion between these electrons can be minimized by arranging them toward the corners of an equilateral triangle. The VSEPR theory therefore predicts a trigonal planar geometry for the BF3 molecule, with a F-B-F bond angle of 120o. Electron Domains = 3 VSEPR Notation AX3

Bent (Angular) Electron Domains = 3 VSEPR Notation AX2E
There are three regions of electron density two bonding regions and and lone pair region Electron Domains = 3 VSEPR Notation AX2E

Tetrahedral Molecules
BeF2 and BF3 are both two-dimensional molecules, in which the atoms lie in the same plane. If we place the same restriction on methane (CH4), we would get a square-planar geometry in which the H-C-H bond angle is 90o. If we let this system expand into three dimensions, however, we end up with a tetrahedral molecule in which the H-C-H bond angle is 109o Electron Domains = 4 VSEPR Notation AX4

Trigonal Pyramidal Electron Domains = 4 VSEPR Notation = AX2E
Has four regions of electron density. Three bonding regions and one lone pair Region. In the trigonal pyramidal structure the H-N-H angle is less than 109° because the lone pair likes to spread out as much as possible Electron Domains = 4 VSEPR Notation = AX2E

Bent (Angular) Electron Domains = 4 VSEPR Notation = AX2E2
Has four regions of electron density. Two bonding regions and two lone pair Region. In the trigonal pyramidal structure the H-O-H angle is even less than 109° than the trigonal pyramidal because the two lone pair like to spread out as much as possible Electron Domains = 4 VSEPR Notation = AX2E2

Trigonal Bipyramidal Molecules
Repulsion between the five pairs of valence electrons on the phosphorus atom in PF5 can be minimized by distributing these electrons toward the corners of a trigonal bipyramidal. Three of the positions in a trigonal bipyramidal are labeled equatorial because they lie along the equator of the molecule. The other two are axial because they lie along an axis perpendicular to the equatorial plane. The angle between the three equatorial positions is 120o, while the angle between an axial and an equatorial position is 90o. Electron Domains = 5 VSEPR Notation = AX5

See-Saw Electron Domains = 5 VSEPR Notation = AX4E
Because if you turn it side-ways it looks like a see saw. It has five regions of electron density. four bonding regions and one lone pair region. In the see-saw structure the lone pair is found in the equatorial plane because the lone pair likes to spread out as much as possible Electron Domains = 5 VSEPR Notation = AX4E

T- Shaped Electron Domains = 5 VSEPR Notation = AX3E2
Because it looks like a T. Has five regions of electron density. three bonding regions and 2 lone pair regions. In the T-Shped structure the lone pairs are found in the equatorial plane because the lone pairs likes to spread out as much as possible Electron Domains = 5 VSEPR Notation = AX3E2

Linear Electron Domains = 5 VSEPR Notation = AX2E3
Because all the molecules are in a line with the bond angle being 180°. Has five regions of electron density, two bonding regions and three lone pair regions. Electron Domains = 5 VSEPR Notation = AX2E3

Octahedral Molecules There are six places on the central atom in SF6 where valence electrons can be found. The repulsion between these electrons can be minimized by distributing them toward the corners of an octahedron. The term octahedron literally means "eight sides," but it is the six corners, or vertices, that interest us. To imagine the geometry of an SF6 molecule, locate fluorine atoms on opposite sides of the sulfur atom along the X, Y, and Z axes of an XYZ coordinate system. Electron Domains = 6 Octahedral VSEPR notation = AX6 Square Pyramidal VSEPR notation = AX5E Square Planar: VSEPR notation = AX4E2

Applying the VSEPR Theory
Draw a plausible Lewis Structure Determine the number of electron pairs around the central atom Identify the electrons and bonding pairs (X) or lone pairs (E) Write the VSEPR Notation for the Molecule Match the shape with the name

Valence shell electron pair repulsion (VSEPR) model:
Predict the geometry of the molecule from the electrostatic repulsions between the electron (bonding and nonbonding) pairs. Steric # Class # of bonding # of lone pair arrangement Molecular electrons of e- pairs Shape linear B linear 2 AB2 2 trigonal planar trigonal planar 3 AB3 3 trigonal planar bent 3 AB2E 2 1

VSEPR Cont…….. Steric # Class # of bonding # of lone pair arrangement Molecular electrons of e- pairs Shape tetrahedral tetrahedral 4 AB4 4 trigonal pyramidal tetrahedral 4 AB3E 3 1 tetrahedral bent H O 4 AB2E2 2 2

bonding-pair vs. bonding
pair repulsion lone-pair vs. lone pair repulsion lone-pair vs. bonding >

VSEPR Cont…….. Steric # Class # of bonding # of lone pair arrangement Molecular electrons of e- pairs Shape trigonal bipyramidal trigonal bipyramidal 5 AB5 5 trigonal bipyramidal See- saw AB4E 1 5 4

VSEPR Cont…….. Steric # Class # of bonding # of lone pair arrangement Molecular electrons of e- pairs Shape trigonal bipyramidal T-shaped Cl F 2 AB3E2 3 5 trigonal bipyramidal linear I 5 AB2E3 2 3

VSEPR Cont…….. Steric # Class # of bonding # of lone pair arrangement Molecular electrons of e- pairs Shape octahedral octahedral 6 6 AB6 octahedral square pyramidal Br F AB5E 5 1 6 square planar Xe F octahedral 6 4 2 AB4E2

Predicting Molecular Geometry
Draw Lewis structure for molecule. Count number of lone pairs on the central atom and number of atoms bonded to the central atom. Use VSEPR to predict the geometry of the molecule. What are the molecular geometries of SO2 and SF4? S F S O AB4E AB2E See-Saw bent

ABx Molecular Geometry 7.1
Molecular shape can be predicted by using the valence-shell electron-pair repulsion (VSEPR) model. A is the central atom surrounded by x B atoms. x can have integer values of 2 to 6. ABx

2 electron domains (on central atom)
The VSEPR Model The basis of the VSEPR model is that electrons repel each other. Electrons are found in various domains. Lone pairs Single bonds Double bonds Triple bonds 1 single bond 1 double bond 1 lone pair 3 single bonds 1 lone pair 2 double bonds 2 electron domains (on central atom) 3 electron domains (on central atom) 4 electron domains (on central atom)

Electron-Domain Geometry and Molecular Geometry
The basis of the VSEPR model is that electrons repel each other. Electrons will arrange themselves to be as far apart as possible. Arrangements minimize repulsive interactions. 2 electron domains Linear 3 electron domains Trigonal planar

4 electron domains Tetrahedral 5 electron domains Trigonal bipyramidal 6 electron domains Octahedral

The electron domain geometry is the arrangement of electron domains around the central atom. The molecular geometry is the arrangement of bonded atoms. In an ABx molecule, a bond angle is the angle between two adjacent A-B bonds. Linear Trigonal planar 180° 120° Trigonal bipyramidal Octahedral Tetrahedral 90° 109.5° 120° 90°

AB5 molecules contain two different bond angles between adjacent bonds. Axial positions; perpendicular to the trigonal plane 90° Equatorial positions; three bonds arranged in a trigonal plane. 120° Trigonal bipyramidal

When the central atom in an ABx molecule bears one or more lone pairs, the electron-domain geometry and the molecular geometry are no longer the same. O •• = −

The steps to determine the electron-domain and molecular geometries are as follows: Step 1: Draw the Lewis structure of the molecule or polyatomic ion. Step 2: Count the number of electron domains on the central atom. Step 3: Determine the electron-domain geometry by applying the VSEPR model. Step 4: Determine the molecular geometry by considering the positions of the atoms only.

Worked Example 7.1 Determine the shapes of (a) SO3 and (b) ICl4-.
Strategy Use Lewis structures and the VSEPR model to determine first the electron-domain geometry and then the molecular geometry (shape). (a) The Lewis structure of SO3 is: There are three electron domains on the central atom: one double bond and two single bonds. (b) The Lewis structure of ICl4- is: There are six electron domains on the central atom in ICl4-: four single bonds and two lone pairs.

Worked Example 7.1 (cont.) Solution
(a) According to the VSEPR model, three electron domains will be arranged in a trigonal plane. Since there are no lone pairs on the central atom in SO3, the molecular geometry is the same as the electron-domain geometry. Therefore, the shape of SO3 is trigonal planar. (b) Six electron domains will be arranged in an octahedron. Two lone pairs on an octahedron will be located on opposite sides of the central atom, making the shape of ICl4- square planar. Think About It Compare these results with the information in Figure 7.2 and Table 7.2. Make sure that you can draw Lewis structures correctly. Without a correct Lewis structure, you will be unable to determine the shape of a molecule.

Deviation from Ideal Bond Angles
Some electron domains are better than others at repelling neighboring domains. Lone pairs take up more space than bonded pairs of electrons. Multiple bonds repel more strongly than single bonds.

Geometry of Molecules with More Than One Central Atom
The geometry of more complex molecules can be determined by treating them as though they have multiple central atoms. Central O atom No. of electron domains: 4 Electron-domain geometry: tetrahedral Molecular geometry: bent Central C atom No. of electron domains: 4 Electron-domain geometry: tetrahedral Molecular geometry: tetrahedral

Worked Example 7.2 Acetic acid, the substance that gives vinegar its characteristic smell and sour taste, is sometimes used in combination with corticosteroids to treat certain types of ear infections. Its Lewis structure is Determine the molecular geometry about each of the central atoms, and determine the approximate value of each of the bond angles in the molecule. Which if any of the bond angles would you expect to be smaller than the ideal values? Strategy The leftmost C atom is surrounded by four electron domains: one C−C bond and three C−H bonds. The middle C atom is surrounded by three electron domains: one C−C bond, one C−O bond, and one C=O bond. The O atom is surrounded by four electron domains: one O−C bond, one O−H bond, and two lone pairs.

Worked Example 7.2 (cont.) Solution The electron-domain geometry of the leftmost C is tetrahedral. Because all four electron domains are bonds, the molecular geometry of this part of the molecule is also tetrahedral. The electron-domain geometry of the middle C is trigonal planar. Again, because all the domains are bonds, the molecular geometry is also trigonal planar. The electron-domain geometry of the O atom is tetrahedral. Because two of the domains are lone pairs, the molecular geometry about the O atom is bent.

Worked Example 7.2 (cont.) Solution (cont.) Bond angles are determined using electron-domain geometry. Therefore, the approximate bond angles about the leftmost C are 109.5°C, those about the middle C are 120°, and those about the O are 109.5°. The angle between the two single bonds on the middle carbon will be less than 120° because the double bond repels the single bonds more strongly than they repel each other. Likewise, the bond angle between the two bonds on the O will be less than 109.5° because the lone pairs on O repel the single bonds more strongly than they repel each other and push the two bonding pairs closer together. The angles are labeled as follows: ~109.5° >120° <120° <109.5° Think About It Compare these answers with the information in Figure 7.2 and Table 7.2

Molecular Geometry and Polarity
7.2 Molecular polarity is one of the most important consequences of molecular geometry. A diatomic molecule is polar when the electronegativites of the two atoms are different. Comp: Replace with Middle panel of new Fig 6.3 H− F •• H− F •• δ+ δ−

The polarity of a molecule made up of three or more atoms depends on: (1) the polarity of the individual bonds (2) the molecular geometry Carbon dioxide, CO2 The bonds in CO2 are polar but the molecule is nonpolar.

The polarity of a molecule made up of three or more atoms depends on: (1) the polarity of the individual bonds (2) the molecular geometry Water, H2O The bonds in H2O are polar and the molecule is polar.

The polarity of a molecule made up of three or more atoms depends on: (1) the polarity of the individual bonds (2) the molecular geometry Boron trifluoride, BF3 The bonds in BF3 are polar but the molecule is nonpolar.

Worked Example 7.3 (a) Determine whether PCl5 is polar.
Strategy Draw the Lewis structure, use the VSEPR model to determine its molecular geometry, and then determine whether the individual bond dipoles cancel. (a) The Lewis structure of PCl5 is With five identical electron domains around the central atom, the electron-domain and molecular geometries are trigonal bipyramidal. The equatorial bond dipoles will cancel one another, just as in the case of BF3, and the axial bond dipoles will also cancel each other. Solution PCl5 is nonpolar.

Worked Example 7.3 (b) Determine whether (b) H2CO (C double bonded to O) is polar. Strategy Draw the Lewis structure, use the VSEPR model to determine its molecular geometry, and then determine whether the individual bond dipoles cancel. (b) The Lewis structure of H2CO is The bond dipoles, although symmetrically distributed around the C atom, are not identical and therefore will not sum to zero. Think About It Make sure that your Lewis structures are correct and that you count electron domains on the central atom carefully. This will give you the correct electron-domain and molecular geometries. Molecular polarity depends on both the individual bond dipoles and the molecular geometries. Solution H2CO is polar.

Dipole moments can be used to distinguish between structural isomers. trans-dichloroethylene nonpolar cis-dichloroethylene polar

Valence Bond Theory 7.3 According to valence bond theory, atoms share electrons when atomic orbitals overlap. A bond forms when single occupied atomic orbitals on two atoms overlap. The two electrons shared in the region of orbital overlap must be of opposite spin. Formation of a bond results in a lower potential energy for the system.

Valence Bond Theory The H−H bond in H2 forms when the singly occupied 1s orbitals of the two H atoms overlap:

Valence Bond Theory The F−F bond in F2 forms when the singly occupied 2p orbitals of the two F atoms overlap:

Valence Bond Theory The H−F bond in HF forms when the singly occupied 1s orbital on the H atom overlaps with the single occupied 2p orbital of the F atom:

Hybridization – mixing of two or more atomic orbitals to form a new set of hybrid orbitals.
Mix at least 2 nonequivalent atomic orbitals (e.g. s and p). Hybrid orbitals have very different shape from original atomic orbitals. Number of hybrid orbitals is equal to number of pure atomic orbitals used in the hybridization process. Covalent bonds are formed by: Overlap of hybrid orbitals with atomic orbitals Overlap of hybrid orbitals with other hybrid orbitals

Hybrid Orbitals Leaving out the math, we can say that an imaginary mixing process converts a set of atomic orbitals to a new set of hybrid atomic orbitals or hybrid orbitals. At this level, we consider the following hybrid orbitals: sp sp2 sp3 sp3d sp3d2

Formation of sp Hybrid Orbitals

The sp Hybrid Atomic Orbitals
The sp hybrid atomic orbitals are possible states of electron in an atom, especially when it is bonded to others. These electron states have half 2s and half 2p characters. From a mathematical view point, there are two ways to combine the 2s and 2p atomic orbitals: sp1 = 2s + 2p (yellow) sp2 = 2s - 2p (green) These energy states (sp1 and sp2) have a region of high electron probability each, and the two atomic orbitals are located opposite to each other, centered on the atom. The sp hybrid orbitals are represented by this photograph. A molecule that is sp hybridized has a steric number of 2 meaning that it has 2 regions of electron density either as bonds or lone pairs. H-Be-H s-sp bond Be is sp hybridized so the bond between H and Be is a s-sp bond

Formation of sp2 Hybrid Orbitals

The sp2 Hybrid Orbitals F B F F : : : sp2-sp3 bond : : : : : :
The energy states of the valence electrons in atoms of the second period are in the 2s and 2p orbitals. If we mix two of the 2p orbitals with a 2s orbital, we end up with three sp2 hybridized orbitals. These three orbitals lie on a plane, and they point to the vertices of a equilateral triangle as shown here. When the central atom has a steric number of 3 it makes use of sp2 hybridized orbitals, and has a trigonal shape. BF3 is such a molecule: : : F : sp2-sp3 bond B : : F : F : : :

The sp3 Hybrid Orbitals . . . . O H H s-sp3 bond
Mixing one s and all three p atomic orbitals produces a set of four equivalent sp3 hybrid atomic orbitals. The four sp3 hybrid orbitals points towards the vertices of a tetrahedron, as shown here in this photograph. When sp3 hybrid orbitals are used for the central atom in the formation of molecule, the molecule is said to have the shape of a tetrahedron and a steric number of 4 and has the molecular geometry of a tetrahedron. The typical molecule is CH4, in which the 1s orbital of a H atom overlap with one of the sp3 hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH4 molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO44-, SO42-, As are the cases with sp2, hybrid orbitals, one or two of the sp3 hybrid orbitals may be occupied by non-bonding electrons. Water and ammonia are such molecules. . . . . O H H s-sp3 bond

Predict correct bond angle

The sp3d Hybrid Orbitals
The five dsp3 hybrid orbitals resulted when one 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of five dsp3 hybrid orbitals the steric number of the molecule is 5 and it has the molecular geometry of a trigonal bipyramidal. For example, PClF4 displayed here forms such a structure. Some of the sp3d hybrid orbitals may be occupied by electron pairs. The shapes of these molecules are interesting. In TeCl4, only one of the hybrid dsp3 orbitals is occupied by a lone pair. This structure may be represented by TeCl4E, where E represents a lone pair of electrons. Two lone pairs occupy two such orbitals in the molecule BrF3, or BrF3E2.

The sp3d2 hybrid orbitals
The six sp3d2 hybrid orbitals resulted when two 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of six sp3d2 hybrid orbitals for bonds or lone pairs it has a steric number of 6 and has the molecular geometry of an octahedron.

Number of Electron Domains
Hybridization 2 sp 3 sp2 4 sp3 5 sp3d 6 sp3d2

How do I predict the hybridization of the central atom?
Count the number of lone pairs AND the number of atoms bonded to the central atom (This is also called the steric number) # of Lone Pairs + # of Bonded Atoms Hybridization Examples 2 sp BeCl2 3 sp2 BF3 4 sp3 CH4, NH3, H2O 5 sp3d PCl5 6 sp3d2 SF6

Hybridization in Molecules Containing Multiple Bonds
7.5 Valence bond theory and hybridization can be used to describe the bonding in molecules containing double and triple bonds. Each carbon has three electron domains: 2 single bonds 1 double bond Expect sp2 hybridization ethylene (C2H4)

A sigma (σ) bond forms when sp2 hybrid orbitals on the C atoms overlap. In a sigma bond, the shared electron density lies directly along the internuclear axis.

The ethylene molecule contains five sigma bonds: 1 between the two carbon atoms (sp2 and sp2 overlap) 4 between the C and H atoms (sp2 and 1s overlap)

Multiple Bonds Any single bond between atoms is termed a sigma (s) bonds Multiple bonds are termed pi (p) bonds s bond p bond

Sigma bonds form between hybridized orbitals
p or d orbitals must be free to form multiple bonds

p-bonds form from the side by side overlap of adjacent
p orbitals above and below the sigma plane

Pi bond (p) – electron density above and below plane of nuclei
Pi bond (p) – electron density above and below plane of nuclei of the bonding atoms Sigma bond (s) – electron density between the 2 atoms

A localized p bond can form through side-by-side overlap between a
d and a p orbital. As with other p bonds, electron density is concentrated between the nuclei, above and below the intermolecular axis. All four oxygen atoms are equivalent, so six resonance structures are needed to represent the p bonding of the sulfate anion. These structures indicate that delocalized orbitals span the entire anion.

Resonance and Multiple Double Bonds

Delocalized molecular orbitals are not confined between two adjacent bonding atoms, but actually extend over three or more atoms.

Resonance structures like ozone or
benzene (right) have overlapping p orbitals that all lie in the same plane

Triple Bonds Pz Pz Px Px Px Pz
Acetylene has a triple bond between the two carbons. The sigma Bond is sp hybridized leaving two p orbitals to overlap Pz Pz Px Px Px Pz

Sigma (s) and Pi Bonds (p)
1 sigma bond Single bond Double bond 1 sigma bond and 1 pi bond Triple bond 1 sigma bond and 2 pi bonds How many s and p bonds are in the acetic acid (vinegar) molecule CH3COOH? C H O s bonds = 6 + 1 = 7 p bonds = 1

Chemistry: Atoms First Julia Burdge & Jason Overby

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