Chapter 4

What are molecular orbitals? How do they compare with atomic orbitals? Can you tell by the shape of the bonding and antibonding orbitals which is lower in energy? Explain.

Explain the difference between the \(\sigma\) and \(\pi\) MOs for homonuclear diatomic molecules. How are bonding and antibonding orbitals different? Why are there two \(\pi\) MOs and one \(\sigma\) MO? Why are the \(\pi\) MOs degenerate?

Which of the following would you expect to be more favorable energetically? Explain. a. an \(\mathrm{H}_{2}\) molecule in which enough energy is added to excite one electron from the bonding to the antibonding MO b. two separate \(\mathrm{H}\) atoms

Arrange the following molecules from most to least polar and explain your order: \(\mathrm{CH}_{4}, \mathrm{CF}_{2} \mathrm{Cl}_{2}, \mathrm{CF}_{2} \mathrm{H}_{2}, \mathrm{CCl}_{4},\) and \(\mathrm{CCl}_{2} \mathrm{H}_{2}\).

Which is the more correct statement: "The methane molecule \(\left(\mathrm{CH}_{4}\right)\) is a tetrahedral molecule because it is \(s p^{3}\) hybridized" or "The methane molecule \(\left(\mathrm{CH}_{4}\right)\) is \(s p^{3}\) hybridized because it is a tetrahedral molecule"? What, if anything, is the difference between these two statements?

Compare and contrast the MO model with the local electron model. When is each useful?

What are the relationships among bond order, bond energy, and bond length? Which of these quantities can be measured?

Which of the following statements is/are true? Correct the false statements. a. The molecules \(\operatorname{SeS}_{3}, \operatorname{SeS}_{2}, \operatorname{PCl}_{5}, \operatorname{TeCl}_{4},\) ICl \(_{3}\), and \(\mathrm{XeCl}_{2}\) all exhibit at least one bond angle which is approximately \(120^{\circ} .\) b. The bond angle in \(\mathrm{SO}_{2}\) should be similar to the bond angle in \(\mathrm{CS}_{2}\) or \(\mathrm{SCl}_{2}\) c. Of the compounds \(\mathrm{CF}_{4}, \mathrm{KrF}_{4},\) and \(\mathrm{SeF}_{4},\) only \(\mathrm{SeF}_{4}\) exhibits an overall dipole moment (is polar). d. Central atoms in a molecule adopt a geometry of the bonded atoms and lone pairs about the central atom in order to maximize electron repulsions.

Give one example of a compound having a linear molecular structure that has an overall dipole moment (is polar) and one example that does not have an overall dipole moment (is nonpolar). Do the same for molecules that have trigonal planar and tetrahedral molecular structures.

In the hybrid orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbitals form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.

In the molecular orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbitals form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.

Why are \(d\) orbitals sometimes used to form hybrid orbitals? Which period of elements does not use \(d\) orbitals for hybridization? If necessary, which \(d\) orbitals \((3 d, 4 d, 5 d, \text { or } 6 d)\) would sulfur use to form hybrid orbitals requiring \(d\) atomic orbitals? Answer the same question for arsenic and for iodine.

The atoms in a single bond can rotate about the internuclear axis without breaking the bond. The atoms in a double and triple bond cannot rotate about the internuclear axis unless the bond is broken. Why?

Compare and contrast bonding molecular orbitals with antibonding molecular orbitals.

Why does the molecular orbital model do a better job in explaining the bonding in \(\mathrm{NO}^{-}\) and \(\mathrm{NO}\) than the hybrid orbital model?

The three NO bonds in \(\mathrm{NO}_{3}^{-}\) are all equivalent in length and strength. How is this explained even though any valid Lewis structure for \(\mathrm{NO}_{3}^{-}\) has one double bond and two single bonds to nitrogen?

Predict the molecular structure (including bond angles) for each of the following. a. \(\mathrm{PCl}_{3}\) b. \(\mathrm{SCl}_{2}\) c. \(\mathrm{SiF}_{4}\)

Predict the molecular structure (including bond angles) for each of the following. (See Exercises 25 and \(26 .\) ) a. \(\mathrm{XeCl}_{2}\) b. ICl \(_{3}\) c. TeF \(_{4}\) d. \(\mathrm{PCl}_{5}\)

Predict the molecular structure (including bond angles) for each of the following. (See Exercises 25 and \(26 .\) ) a. ICls b. \(\mathrm{XeCl}_{4}\) c. \(\mathrm{SeCl}_{6}\)

Write Lewis structures and predict the molecular structures of the following. (See Exercises 25 and \(26 .\) ) a. \(\mathrm{OCl}_{2}, \mathrm{KrF}_{2}, \mathrm{BeH}_{2}, \mathrm{SO}_{2}\) b. \(\mathrm{SO}_{3}, \mathrm{NF}_{3}, \mathrm{IF}_{3}\) c. \(\mathrm{CF}_{4}, \mathrm{SeF}_{4}, \mathrm{KrF}_{4}\) d. IF \(_{5}, \mathrm{AsF}_{5}\) Which of these compounds are polar?

Write Lewis structures and predict whether each of the following is polar or nonpolar. a. HOCN (exists as HO-CN) b. cos c. \(\mathrm{XeF}_{2}\) d. \(\mathrm{CF}_{2} \mathrm{Cl}_{2}\) e. \(\operatorname{SeF}_{6}\) f. \(\mathrm{H}_{2} \mathrm{CO}(\mathrm{C}\) is the central atom.)

Two different compounds have the formula \(\mathrm{XeF}_{2} \mathrm{Cl}_{2}\). Write Lewis structures for these two compounds, and describe how measurement of dipole moments might be used to distinguish between them.

Use the localized electron model to describe the bonding in \(\mathrm{H}_{2} \mathrm{O}\).

Use the localized electron model to describe the bonding in \(\mathrm{CCl}_{4}\).

Use the localized electron model to describe the bonding in \(\mathrm{H}_{2} \mathrm{CO}\) (carbon is the central atom).

For each of the following molecules, write the Lewis structure(s), predict the molecular structure (including bond angles), give the expected hybrid orbitals of the central atom, and predict the overall polarity. a. \(\mathrm{CF}_{4}\) b. \(\mathrm{NF}_{3}\) c. \(\mathrm{OF}_{2}\) d. \(B F_{3}\) e. \(\mathbf{B e H}_{2}\) f. \(\operatorname{TeF}_{4}\) g. \(\mathrm{AsF}_{5}\) h. \(\mathrm{KrF}_{2}\) i. \(\quad \mathrm{KrF}_{4}\) j. \(\operatorname{SeF}_{6}\) k. IF \(_{5}\) l. IF \(_{3}\)

For each of the following molecules or ions that contain sulfur, write the Lewis structure(s), predict the molecular structure (including bond angles), and give the expected hybrid orbitals for sulfur. a. \(\mathrm{SO}_{2}\) b. \(\mathrm{SO}_{3}\) c. \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\left[\begin{array}{c}\mathrm{Q} \\\ \mathrm{S}-\mathrm{S}-\mathrm{O} \\ \mathrm{O}\end{array}\right]^{2-}\) d. \( \mathrm{S}_{2} \mathrm{O}_{8}^{2-}\left[\begin{array}{cc}\mathrm{Q} & \mathrm{Q} \\\ \mathrm{O}-\mathrm{S}-\mathrm{O}-\mathrm{O}-\mathrm{S}-\mathrm{O} \\\ \mathrm{O} & \mathrm{O}\end{array}\right]^{2-}\) e. \(\mathrm{SO}_{3}^{2-}\) f. \(\mathrm{SO}_{4}^{2-}\) g. \(\mathrm{SF}_{2}\) h. \(\mathrm{SF}_{4}\) i. \(\mathrm{SF}_{6}\) j. \(\mathbf{F}_{3} \mathbf{S}-\mathbf{S F}\) k. \(\mathrm{SF}_{5}^{+}\)

Why must all six atoms in \(\mathrm{C}_{2} \mathrm{H}_{4}\) lie in the same plane?

The allene molecule has the following Lewis structure: Must all hydrogen atoms lie the same plane? If not, what is their spatial relationship? Explain.

Biacetyl and acetoin are added to margarine to make it taste more like butter. Complete the Lewis structures, predict values for all \(\mathrm{C}-\mathrm{C}-\mathrm{O}\) bond angles, and give the hybridization of the carbon atoms in these two compounds. Must the four carbon atoms and two oxygen atoms in biacetyl lie in the same plane? How many \(\sigma\) bonds and how many \(\pi\) bonds are there in biacetyl and acetoin?

Many important compounds in the chemical industry are derivatives of ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right) .\) Two of them are acrylonitrile and methyl methacrylate. Complete the Lewis structures, showing all lone pairs. Give approximate values for bond angles \(a\) through \(f\). Give the hybridization of all carbon atoms. In acrylonitrile, how many of the atoms in the molecule must lie in the same plane? How many \(\sigma\) bonds and how many \(\pi\) bonds are there in methyl methacrylate and acrylonitrile?

Consider the following molecular orbitals formed from the combination of two hydrogen \(1 s\) orbitals: a. Which is the bonding molecular orbital and which is the antibonding molecular orbital? Explain how you can tell by looking at their shapes. b. Which of the two molecular orbitals is lower in energy? Why is this true?

Which of the following are predicted by the molecular orbital model to be stable diatomic species? a. \(\mathrm{H}_{2}^{+}, \mathrm{H}_{2}, \mathrm{H}_{2}^{-}, \mathrm{H}_{2}^{2-}\) b. \(\mathrm{He}_{2}^{2+}, \mathrm{He}_{2}^{+}, \mathrm{He}_{2}\)

Which of the following are predicted by the molecular orbital model to be stable diatomic species? a. \(\mathrm{N}_{2}^{2-}, \mathrm{O}_{2}^{2-}, \mathrm{F}_{2}^{2-}\) b. \(\mathrm{Be}_{2}, \mathrm{B}_{2}, \mathrm{Ne}_{2}\)

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? a. \(\mathrm{Li}_{2}\) b. \(C_{2}\) c. \(S_{2}\)

Consider the following electron configuration: $$\left(\sigma_{3 s}\right)^{2}\left(\sigma_{3 s}^{* *}\right)^{2}\left(\sigma_{3 p}\right)^{2}\left(\pi_{3 p}\right)^{4}\left(\pi_{3 p}^{*}\right)^{4}$$ Give four species that, in theory, would have this electron configuration.

Using molecular orbital theory, explain why the removal of one electron in \(\mathrm{O}_{2}\) strengthens bonding, while the removal of one electron in \(\mathrm{N}_{2}\) weakens bonding.

Using the molecular orbital model to describe the bonding in \(\mathrm{F}_{2}^{+}, \mathrm{F}_{2},\) and \(\mathrm{F}_{2}^{-},\) predict the bond orders and the relative bond lengths for these three species. How many unpaired electrons are present in each species?

The transport of \(\mathrm{O}_{2}\) in the blood is carried out by hemoglobin. Carbon monoxide can interfere with oxygen transport because hemoglobin has a stronger affinity for CO than for \(\mathrm{O}_{2}\). If \(\mathrm{CO}\) is present, normal uptake of \(\mathrm{O}_{2}\) is prevented, depriving the body of needed oxygen. Using the molecular orbital model, write the electron configurations for CO and for \(\mathbf{O}_{2} .\) From your configurations, give two property differences between CO and \(\mathbf{O}_{2}\)

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy. a. CO b. \(\mathrm{CO}^{+}\) c. \(\mathrm{CO}^{2+}\)

Using the molecular orbital model, write electron configurations for the following diatomic species and calculate the bond orders. Which ones are paramagnetic? Place the species in order of increasing bond length and bond energy. a. \(\mathrm{CN}^{+}\) b. CN c. \(\mathrm{CN}^{-}\)

In which of the following diatomic molecules would the bond strength be expected to weaken as an electron is removed? a. \(\mathrm{H}_{2}\) b. \(B_{2}\) c. \(C_{2}^{2-}\) d. OF

In terms of the molecular orbital model, which species in each of the following two pairs will most likely be the one to gain an electron? Explain. a. CN or NO b. \(\mathrm{O}_{2}^{2+}\) or \(\mathrm{N}_{2}^{2+}\)

Show how two \(2 p\) atomic orbitals can combine to form a \(\sigma\) or a \(\pi\) molecular orbital.

Show how a hydrogen \(1 s\) atomic orbital and a fluorine \(2 p\) atomic orbital overlap to form bonding and antibonding molecular orbitals in the hydrogen fluoride molecule. Are these molecular orbitals \(\sigma\) or \(\pi\) molecular orbitals?

The diatomic molecule OH exists in the gas phase. The bond length and bond energy have been measured to be \(97.06 \mathrm{pm}\) and \(424.7 \mathrm{kJ} / \mathrm{mol},\) respectively. Assume that the OH molecule is analogous to the HF molecule discussed in the chapter and that molecular orbitals result from the overlap of a lowerenergy \(p_{z}\) orbital from oxygen with the higher- energy \(1 s\) orbital of hydrogen (the \(\mathrm{O}-\mathrm{H}\) bond lies along the \(z\) -axis). a. Which of the two molecular orbitals will have the greater hydrogen 1s character? b. Can the \(2 p_{x}\) orbital of oxygen form molecular orbitals with the \(1 s\) orbital of hydrogen? Explain. c. Knowing that only the \(2 p\) orbitals of oxygen will interact significantly with the \(1 s\) orbital of hydrogen, complete the molecular orbital energy- level diagram for OH. Place the correct number of electrons in the energy levels. d. Estimate the bond order for OH. e. Predict whether the bond order of \(\mathrm{OH}^{+}\) will be greater than, less than, or the same as that of OH. Explain.

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) can be produced from the reaction of calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) with water. Use both the localized electron and molecular orbital models to describe the bonding in the acetylide anion \(\left(\mathrm{C}_{2}^{2-}\right)\).

Describe the bonding in \(\mathrm{NO}^{+}, \mathrm{NO}^{-},\) and \(\mathrm{NO},\) using both the localized electron and molecular orbital models. Account for any discrepancies between the two models.

Describe the bonding in the \(\mathrm{O}_{3}\) molecule and the \(\mathrm{NO}_{2}^{-}\) ion, using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in these two species?

Describe the bonding in the \(\mathrm{CO}_{3}^{2-}\) ion using the localized electron model. How would the molecular orbital model describe the \(\pi\) bonding in this species?