Molecular Orbitaltheory Homework Assignment for Chem II PDF

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Homework assignment for CHEM II for molecular orbital theory with all pages for the assignment. Professor Van Hoozen...

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MOLECULAR ORBITAL THEORY General Procedure for the construction of molecular orbitals: • • •

•

Construct molecular orbitals by forming linear combinations of all suitable valence atomic orbitals supplied by the atoms; N atomic orbitals result in N molecular orbitals. Accommodate the valence electrons subject to the constraint of the Pauli Exclusion Principle, that no more than two electrons may occupy a single orbital. If more than one molecular orbital of the same energy is available, add the electrons to each individual orbital before doubly occupying any one orbital (remember this minimizes electronelectron repulsions). And remember also Hund’s rule, that if the electrons occupy different degenerate orbitals (same energy), then they do so with parallel spins.

Homonuclear Diatomic Molecule: H2 In atoms, electrons occupy atomic orbitals, but in molecules they occupy similar molecular orbitals (MO) which surround the molecule. There are two molecular orbitals for diatomic hydrogen (Figure 1), which derive from the 1s atomic orbital from each hydrogen atom. The lower energy molecular orbital (labeled as σ1s in Figure 1) has greater electron density between the two nuclei. This is the bonding molecular orbital - and is of lower energy than the two 1s atomic orbitals of hydrogen atoms making this orbital more stable than two separated atomic hydrogen orbitals. The upper molecular orbital has a node in the electronic wave function and the electron density is low between the two positively charged nuclei. The energy of the upper orbital (labeled as σ*1s in Figure 1) is greater than that of the 1s atomic orbital and such an orbital is called an antibonding molecular orbital.

Figure 1-Molecular orbitals for hydrogen (H2)1

Homonuclear Diatomic Molecule: Period 2 Elements In period 2, atoms have four valence orbitals, one 2s and three 2p (Figure 2). If we consider the s and one of the p orbitals, the two orbitals can overlap end-to-end to form σ orbitals (Figure 3).

Figure 2 – Four valence orbitals for elements in period 21

Figure 3- Two p orbitals overlapping end-to-end to form a σ orbital: two p orbitals overlapping constructively (bonding σ orbital) and two p orbitals overlapping destructively (antibonding σ orbital)1

The remaining two 2p orbitals are perpendicular to each other with respect to the internuclear axis of the molecule and may overlap side-by-side forming π orbitals. This overlap may be constructive (Figure 4a) or destructive (Figure 4b) and results in a bonding and antibonding π orbital, respectively.

b)

a)

Figure 4-Two p orbitals overlapping side-by-side to form a π orbital. a) Two p orbitals overlapping constructively (bonding π orbital), b) Two p orbitals overlapping destructively (antibonding π orbital)1

The relative order of the σ and π orbitals in a molecule cannot be predicted and varies with the energy separation between the 2s and 2p orbital atoms. The explanation for the difference in the molecular orbitals for period 2 molecules comes from the energy difference between the 2s and 2px atomic orbitals, which is

relatively close for Li, Be, B, C, and N, and as a result the 2s orbitals are influenced by the 2p orbitals (Figure 5). This influence makes the bonding orbitals stronger than the pure 2p orbitals, and the antibonding orbitals weaker than those formed by 2s orbitals.

Figure 5-The variation of orbital energies for Period 2 homonuclear diatomic molecules from Li2 to F2.2

This process is called s p mixing. Due to s p mixing the relative order of the energy levels change, and the relative energy levels for B2, C2 and N2 (as well as Li2, Be2) have the following molecular energy level diagram seen to the left of the following image, while that for O2, F2 and Ne2 can be seen on the right:

Figure 6- The molecular orbital energy level diagram for Period 2 homonuclear diatomic molecules1

Bond Length and Bond Energy The bond order is a useful parameter for describing characteristics of bonds, such as length and strength. The bond order, b, in a diatomic molecule is defined as

𝑏 where n is the number of electrons in bonding orbitals and n* is the number of electrons in antibonding orbitals. Short bond lengths are indicated by a greater bond order between the atoms. Additionally, a strong bond is also indicated by a larger bond order; therefore, a high bond order is consistent with high dissociation energy. The electronic configuration agrees with experimental bond lengths and bond energies of homonuclear diatomic molecules of second-period elements. They are given in a table below. Note also that B2 and O2 are paramagnetic due to the unpaired electrons in the molecular orbitals. Other molecules in this group are diamagnetic and are pushed out of a magnetic field. Table 1 - Electronic configuration, bondlength (pm), and bond energy (kJ mol-1) of Period 2 homonuclear diatomic molecules

Electronic configuration Li-Li

σ2s2

Be..Be σ2s2 σ*2s2

Bondlength (pm) Bond energy (kJ mol-1) 267

110

exist?

exist?

B-B C=C

σ2s2 σ*2s2 π 2p2 σ2s2 σ*2s2 π2p4

159 124

290 602

N≡N

σ2s2 σ*2s2 π2p4 σ2p2

110

942

O=O F-F

σ2s2 σ*2s2 σ2p2 π2p4 π*2p2 σ2s2 σ*2s2 σ2p2 π2p4 π*2p4

121 142

494 155

Heteronuclear Diatomic Molecules A heteronuclear diatomic molecule is formed from atoms of two different elements, such as CO, HF and HCl. The electron distribution in these molecules is not symmetrical and results in a polar covalent bond. If the molecule is heteronuclear, the parent atomic orbitals will have different energy levels. Typically, the more electronegative atom will have lower energy atomic orbitals, which is seen in Figure 7 with the fluorine atom in hydrogen fluoride (HF). The more easily ionized (less electronegative) atom will have the atomic orbital level closer to E = 0 in the arrangement depicted to the right. A simple diatomic molecule such as hydrogen fluoride (Figure 7) has eight valence electrons which occupy four molecular orbitals. The two highest energy MO's are degenerate (same energy), are π type, and have no electron density associated with the hydrogen atom (i.e., they are Non-Bonding Orbitals, or NBO). In Lewis Theory, NBO are represented as two "Lone Pairs". Another important difference between hydrogen fluoride and previous molecules is that the electron density is not equally distributed about the molecule. There is a much greater electron density around the fluorine atom. This is because fluorine is an extremely electronegative element, and in each bonding molecular orbital, fluorine will take a greater share of the electron density. Reference List 1. Tro, N. J. Principles of Chemistry: A Molecular Approach, 3rd Edition; Pearson: 2016. 2. Duward, S. Inorganic Chemistry, 6th Edition.; W.H. Freeman & Company: 2014.

Figure 7-The molecular orbital energy level diagram for HF.2

Name: Anthony Parafati

Lab Section: ________________________

EXERCISES: Complete the following exercises. You must show all work to receive full credit. 1. How many molecular orbitals can be built from the valence shell orbitals in O2? 9 2. Give the ground state electron configuration (e.g., σ2s2 σ*2s2 π 2p2) for these molecules and deduce its bond order. Ground State Configuration H2+

Bond Order ½ = .5

σ1s1

O2-

3/2 = 1.5

σ2s2 σ*2s2 π 2px4 π 2py3

N2

6/2 = 3

σ2s2 σ*2s2 π 2px4 σ2py2 σ2pz2

3. Put the following species in order of increasing bond length by using molecular orbital diagrams and calculating their bond orders: F2-, F2, F2+ Molecular Orbital Diagram

Bond Order

F2-

10-9/2 = .5

F2

10-8/2 = 1

F2+

10-7/2 = 1.5

Shortest bond: ____F2-______ < _____F2_____ < ____F2+______ Longest bond 4. The superoxide ion, O2-, plays an important role in the ageing processes that take place in organisms. Judge whether O2- is likely to have larger or smaller dissociation energy than O2. Molecular Orbital Diagram O2-

Bond Order 3/2 = 1.5

O2

4/2 = 2

Does O2- have larger or smaller dissociation energy?: Smaller

5. The existence of compounds of the noble gases was once a great surprise and stimulated a great deal of theoretical work. Label the molecular orbital diagram for XeF (include atom chemical symbol, atomic orbitals, and molecular orbitals) and deduce its ground state electron configuration. Bond Order XeF 8-7/2 = .5

XeF+ 8-6/2 = 1

Is XeF likely to have a shorter bond length than XeF+? No, it would be longer___________________ 6. Draw the molecular orbital diagram shown to determine which of the following is paramagnetic. B22+, B2, C22-, B22- and N22+ Molecular Orbital Diagram

B22-

B2

C22-

B22+

N22+

Which molecule is paramagnetic? B2 is paramagnetic

7. Draw the Lewis structures and molecular orbital diagrams for CO and NO. What are their bond orders? Are the molecular orbital diagrams similar to their Lewis structures? Explain.

CO Lewis Structure

NO Lewis Structure

CO Bond Order

NO Bond Order

Yes, they are similar because the bond orders are close to each other.

CO Molecular Orbital Diagram

NO Molecular Orbital Diagram...