Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10.

Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals
Chapter 10

Bond Theory In this chapter we will discuss the geometries of molecules in terms of their electronic structure. We will also explore two theories of chemical bonding: valence bond theory and molecular orbital theory. Molecular geometry is the general shape of a molecule, as determined by the relative positions of the atomic nuclei. 2

The Valence-Shell Electron Pair Repulsion Model
The valence-shell electron pair repulsion (VSEPR) model predicts the shapes of molecules and ions by assuming that the valence shell electron pairs are arranged as far from one another as possible. To predict the relative positions of atoms around a given atom using the VSEPR model, you first note the arrangement of the electron pairs around that central atom. 2

Predicting Molecular Geometry
The following rules and figures will help discern electron pair arrangements. Draw the Lewis structure Determine how many electrons pairs are around the central atom. Count a multiple bond as one pair. Arrange the electrons pairs. 2

Arrangement of Electron Pairs About an Atom
Linear 3 pairs Trigonal planar 4 pairs Tetrahedral 5 pairs Trigonal bipyramidal 6 pairs Octahedral

Valence shell electron pair repulsion (VSEPR) model:
Predict the geometry of the molecule from the electrostatic repulsions between the electron (bonding and nonbonding) pairs. Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear B

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

Arrangement of electron pairs
VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear trigonal planar trigonal planar AB3 3

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral trigonal bipyramidal trigonal bipyramidal AB5 5

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB2 2 linear linear AB3 3 trigonal planar AB4 4 tetrahedral tetrahedral AB5 5 trigonal bipyramidal AB6 6 octahedral octahedral

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

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal planar trigonal planar AB3 3 trigonal planar AB2E 2 1 bent

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB4 4 tetrahedral tetrahedral trigonal pyramidal AB3E 3 1 tetrahedral

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB4 4 tetrahedral tetrahedral AB3E 3 1 tetrahedral trigonal pyramidal AB2E2 2 2 tetrahedral bent H O

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 trigonal
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 trigonal bipyramidal distorted tetrahedron AB4E 4 1

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1 trigonal bipyramidal distorted tetrahedron trigonal bipyramidal AB3E2 3 2 T-shaped Cl F

VSEPR trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1
Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry trigonal bipyramidal trigonal bipyramidal AB5 5 AB4E 4 1 trigonal bipyramidal distorted tetrahedron AB3E2 3 2 trigonal bipyramidal T-shaped trigonal bipyramidal AB2E3 2 3 linear I

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB6 6 octahedral square pyramidal Br F AB5E 5 1 octahedral

VSEPR Class # of atoms bonded to central atom # lone pairs on central atom Arrangement of electron pairs Molecular Geometry AB6 6 octahedral AB5E 5 1 octahedral square pyramidal square planar Xe F AB4E2 4 2 octahedral

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 distorted tetrahedron bent

Two electron pairs (linear arrangement). : You have two double bonds, or two electron groups about the carbon atom. Thus, according to the VSEPR model, the bonds are arranged linearly, and the molecular shape of carbon dioxide is linear. Bond angle is 180o. 2

Three electron pairs (trigonal planar arrangement). Cl C : O The three groups of electron pairs are arranged in a trigonal plane. Thus, the molecular shape of COCl2 is trigonal planar. Bond angle is 120o. 2

Three electron pairs (trigonal planar arrangement). O : Ozone has three electron groups about the central oxygen. One group is a lone pair. These groups have a trigonal planar arrangement. 2

Three electron pairs (trigonal planar arrangement). O : Since one of the groups is a lone pair, the molecular geometry is described as bent or angular. 2

Three electron pairs (trigonal planar arrangement). O : Note that the electron pair arrangement includes the lone pairs, but the molecular geometry refers to the spatial arrangement of just the atoms. 2

Four electron pairs (tetrahedral arrangement). : :Cl: H N : : O H : : :Cl C Cl: : : :Cl: : Four electron pairs about the central atom lead to three different molecular geometries. 2

Four electron pairs (tetrahedral arrangement). : :Cl: H N : : O H C :Cl : : Cl: :Cl: : tetrahedral 2

Four electron pairs (tetrahedral arrangement). : :Cl: H N : : O H C :Cl : : Cl: :Cl: : tetrahedral trigonal pyramid 2

Four electron pairs (tetrahedral arrangement). : :Cl: : H N : C O :Cl : : : Cl: H :Cl: H : tetrahedral trigonal pyramid bent 2

Five electron pairs (trigonal bipyramidal arrangement). : F : : F : : F P This structure results in both 90o and 120o bond angles. 2

Other molecular geometries are possible when one or more of the electron pairs is a lone pair. SF4 ClF3 XeF2 Let’s try their Lewis structures. 2

Other molecular geometries are possible when one or more of the electron pairs is a lone pair. F ClF3 XeF2 F : S F F see-saw 2

Other molecular geometries are possible when one or more of the electron pairs is a lone pair. S F : Cl F : XeF2 see-saw T-shape 2

Other molecular geometries are possible when one or more of the electron pairs is a lone pair. S F : Cl F : F : Xe : : F see-saw T-shape linear 2

Six electron pairs (octahedral arrangement). :F: : :F : F: : S : F: : :F :F: : This octahedral arrangement results in 90o bond angles. 2

Six electron pairs (octahedral arrangement). IF5 XeF4 Six electron pairs also lead to other molecular geometries. 2

Six electron pairs (octahedral arrangement). F F F XeF4 I F F : square pyramid 2

Six electron pairs (octahedral arrangement). : I F : F F Xe F F : square pyramid square planar 2

Dipole Moment and Molecular Geometry
The dipole moment is a measure of the degree of charge separation in a molecule. We can view the polarity of individual bonds within a molecule as vector quantities. Thus, molecules that are perfectly symmetric have a zero dipole moment. These molecules are considered nonpolar. d- d+ 2

Dipole Moments and Polar Molecules
H F electron rich region electron poor region d+ d- m = Q x r Q is the charge r is the distance between charges 1 D = 3.36 x C m

Dipole Moment and Molecular Geometry
Molecules that exhibit any asymmetry in the arrangement of electron pairs would have a nonzero dipole moment. These molecules are considered polar. d- d+ H N : d+ d- 2

Which of the following molecules have a dipole moment?
H2O, CO2, SO2, and CH4 O H S O dipole moment polar molecule dipole moment polar molecule C H C O no dipole moment nonpolar molecule no dipole moment nonpolar molecule

Does BF3 have a dipole moment?

Does CH2Cl2 have a dipole moment?

Chemistry In Action: Microwave Ovens

Valence Bond Theory Valence bond theory is an approximate theory to explain the covalent bond from a quantum mechanical view. According to this theory, a bond forms between two atoms when the following conditions are met. Two atomic orbitals “overlap” The total number of electrons in both orbitals is no more than two. 2

Sharing of two electrons between the two atoms.
How does Lewis theory explain the bonds in H2 and F2? Sharing of two electrons between the two atoms. Bond Dissociation Energy Bond Length H2 F2 436.4 kJ/mole 150.6 kJ/mole 74 pm 142 pm Overlap Of 2 1s 2 2p Valence bond theory – bonds are formed by sharing of e- from overlapping atomic orbitals.

Change in Potential Energy of Two Hydrogen Atoms
as a Function of Their Distance of Separation

Change in electron density as two hydrogen atoms approach each other.

Valence Bond Theory and NH3
N – 1s22s22p3 3 H – 1s1 If the bonds form from overlap of 3 2p orbitals on nitrogen with the 1s orbital on each hydrogen atom, what would the molecular geometry of NH3 be? If use the 3 2p orbitals predict 900 Actual H-N-H bond angle is 107.30

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 Hybrid orbitals are orbitals used to describe bonding that are obtained by taking combinations of atomic orbitals of an isolated atom. In this case, a set of hybrids are constructed from one “s” orbital and three “p” orbitals, so they are called sp3 hybrid orbitals. The four sp3 hybrid orbitals take the shape of a tetrahedron. 2

You can represent the hybridization of carbon in CH4 as follows.
sp3 1s sp3 1s Energy C-H bonds 1s C atom (ground state) C atom (hybridized state) C atom (in CH4) 2

Formation of sp3 Hybrid Orbitals

Predict correct bond angle

Formation of sp Hybrid Orbitals

Formation of sp2 Hybrid Orbitals

How do I predict the hybridization of the central atom?
Draw the Lewis structure of the molecule. Count the number of lone pairs AND the number of atoms bonded to the central atom # 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

Hybrid Orbitals Note that there is a relationship between the type of hybrid orbitals and the geometric arrangement of those orbitals. Thus, if you know the geometric arrangement, you know what hybrid orbitals to use in the bonding description. 2

Geometric Arrangements
Hybrid Orbitals Hybrid Orbitals Geometric Arrangements Number of Orbitals Example sp Linear 2 Be in BeF2 sp2 Trigonal planar 3 B in BF3 sp3 Tetrahedral 4 C in CH4 sp3d Trigonal bipyramidal 5 P in PCl5 sp3d2 Octahedral 6 S in SF6 2

Hybrid Orbitals To obtain the bonding description of any atom in a molecule, you proceed as follows: Write the Lewis electron-dot formula for the molecule. From the Lewis formula, use the VSEPR theory to determine the arrangement of electron pairs around the atom. 2

Hybrid Orbitals To obtain the bonding description of any atom in a molecule, you proceed as follows: From the geometric arrangement of the electron pairs, obtain the hybridization type (see Table 10.2). Assign valence electrons to the hybrid orbitals of this atom one at a time, pairing only when necessary. 2

Hybrid Orbitals To obtain the bonding description of any atom in a molecule, you proceed as follows: Form bonds to this atom by overlapping singly occupied orbitals of other atoms with the singly occupied hybrid orbitals of this atom. 2

A Problem to Consider Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. From the Lewis formula for a molecule, determine its geometry about the central atom using the VSEPR model. 2

A Problem to Consider Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. The Lewis formula for H2O is 2

A Problem to Consider Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. From this geometry, determine the hybrid orbitals on this atom, assigning its valence electrons to these orbitals one at a time. 2

A Problem to Consider Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. Note that there are four pairs of electrons about the oxygen atom. According to the VSEPR model, these are directed tetrahedrally, and from the previous table you see that you should use sp3 hybrid orbitals. 2

A Problem to Consider Describe the bonding in H2O according to valence bond theory. Assume that the molecular geometry is the same as given by the VSEPR model. Each O-H bond is formed by the overlap of a 1s orbital of a hydrogen atom with one of the singly occupied sp3 hybrid orbitals of the oxygen atom. 2

You can represent the bonding to the oxygen atom in H2O as follows:
sp3 1s sp3 1s Energy lone pairs O-H bonds 1s O atom (ground state) O atom (hybridized state) O atom (in H2O) 2

A Problem to Consider Describe the bonding in XeF4 using hybrid orbitals. From the Lewis formula for a molecule, determine its geometry about the central atom using the VSEPR model. 2

A Problem to Consider Describe the bonding in XeF4 using hybrid orbitals. The Lewis formula of XeF4 is 2

A Problem to Consider Describe the bonding in XeF4 using hybrid orbitals. From this geometry, determine the hybrid orbitals on this atom, assigning its valence electrons to these orbitals one at a time. 2

A Problem to Consider Describe the bonding in XeF4 using hybrid orbitals. The xenon atom has four single bonds and two lone pairs. It will require six orbitals to describe the bonding. This suggests that you use sp3d2 hybrid orbitals on xenon. 2

A Problem to Consider Describe the bonding in XeF4 using hybrid orbitals. Each Xe-F bond is formed by the overlap of a xenon sp3d2 hybrid orbital with a singly occupied fluorine 2p orbital. You can summarize this as follows: 2

5d 5p 5s Xe atom (ground state) 2

Xe atom (hybridized state)
sp3d2 Xe atom (hybridized state) 2

5d sp3d2 lone pairs Xe-F bonds Xe atom (in XeF4) 2

Multiple Bonding According to valence bond theory, one hybrid orbital is needed for each bond (whether a single or multiple) and for each lone pair. For example, consider the molecule ethene. 2

Multiple Bonding Each carbon atom is bonded to three other atoms and no lone pairs, which indicates the need for three hybrid orbitals. This implies sp2 hybridization. The third 2p orbital is left unhybridized and lies perpendicular to the plane of the trigonal sp2 hybrids. The following slide represents the sp2 hybridization of the carbon atoms. 2

2p 2p sp2 2s Energy 1s 1s C atom (ground state) C atom (hybridized)
(unhybridized) 2p 2p sp2 2s Energy 1s 1s C atom (ground state) C atom (hybridized) 2

Multiple Bonding To describe the multiple bonding in ethene, we must first distinguish between two kinds of bonds. A s (sigma) bond is a “head-to-head” overlap of orbitals with a cylindrical shape about the bond axis. This occurs when two “s” orbitals overlap or “p” orbitals overlap along their axis. A p (pi) bond is a “side-to-side” overlap of parallel “p” orbitals, creating an electron distribution above and below the bond axis. 2

Multiple Bonding Now imagine that the atoms of ethene move into position. Two of the sp2 hybrid orbitals of each carbon overlap with the 1s orbitals of the hydrogens. The remaining sp2 hybrid orbital on each carbon overlap to form a s bond. 2

Multiple Bonding The remaining “unhybridized” 2p orbitals on each of the carbon atoms overlap side-to-side forming a p bond. You therefore describe the carbon-carbon double bond as one s bond and one p bond. 2

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

Describe the bonding in CH2O.
C – 3 bonded atoms, 0 lone pairs C – sp2

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

Experiments show O2 is paramagnetic
No unpaired e- Should be diamagnetic Molecular orbital theory – bonds are formed from interaction of atomic orbitals to form molecular orbitals.

Molecular Orbital Theory
Molecular orbital theory is a theory of the electronic structure of molecules in terms of molecular orbitals, which may spread over several atoms or the entire molecule. As atoms approach each other and their atomic orbitals overlap, molecular orbitals are formed. In the quantum mechanical view, both a bonding and an antibonding molecular orbital are formed. 2

Molecular Orbital Theory
For example, when two hydrogen atoms bond, a s1s (bonding) molecular orbital is formed as well as a s1s* (antibonding) molecular orbital. The following slide illustrates the relative energies of the molecular orbitals compared to the original atomic orbitals. Because the energy of the two electrons is lower than the energy of the individual atoms, the molecule is stable. 2

H atom H2 molecule H atom s1s* 1s 1s s1s

Energy levels of bonding and antibonding molecular orbitals in hydrogen (H2).
A bonding molecular orbital has lower energy and greater stability than the atomic orbitals from which it was formed. An antibonding molecular orbital has higher energy and lower stability than the atomic orbitals from which it was formed.

Two Possible Interactions Between Two Equivalent p Orbitals

The arrows show the occupation of molecular orbitals by the valence electrons in N2.

Molecular Orbital (MO) Configurations
The number of molecular orbitals (MOs) formed is always equal to the number of atomic orbitals combined. The more stable the bonding MO, the less stable the corresponding antibonding MO. The filling of MOs proceeds from low to high energies. Each MO can accommodate up to two electrons. Use Hund’s rule when adding electrons to MOs of the same energy. The number of electrons in the MOs is equal to the sum of all the electrons on the bonding atoms.

Bond Order The term bond order refers to the number of bonds that exist between two atoms. The bond order of a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals, nb, and the number of electrons in antibonding orbitals, na. 2

( ) - bond order = 1 2 Number of electrons in bonding MOs
Number of electrons in antibonding MOs ( - ) bond order 1

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

Electron density above and below the plane of the benzene molecule.

Chemistry In Action: Buckyball Anyone?

Vesper in class exercise

WORKED EXAMPLES

Worked Example 10.1a

Worked Example 10.2

Worked Example 10.3a

Worked Example 10.3b

Worked Example 10.4

Worked Example 10.5

Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10.

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Chemical Bonding II: Molecular Geometry and Hybridization of Atomic Orbitals Chapter 10.

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