Chapter 9

(a) An \(\mathrm{AB}_{2}\) molecule is linear. How many nonbonding electron pairs are around the A atom from this information? (b) How many nonbonding electrons surround the Xe in \(\mathrm{XeF}_{2} ?(\mathbf{c})\) Is \(\mathrm{XeF}_{2}\) linear?

(a) Boron trichloride \(\left(\mathrm{BCl}_{3}\right)\) and the carbonate ion \(\left(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\right)\) are both described as trigonal. What does this indicate about their bond angles? (b) The \(\mathrm{PCl}_{3}\) molecule is trigonal pyramidal, while \(\mathrm{ICl}_{3}\) is T-shaped. Which of these molecules is flat?

How does a trigonal pyramid differ from a tetrahedron so far as molecular geometry is concerned?

Describe the bond angles to be found in each of the following molecular structures: (a) trigonal planar, (b) tetrahedral, (c) Octahedral, (d) linear.

(a) An \(\mathrm{AB}_{6}\) molecule has no lone pairs of electrons on the \(\mathrm{A}\) atom. What is its molecular geometry? (b) An \(\mathrm{AB}_{4}\) molecule has two lone pairs of electrons on the A atom (in addition to the four B atoms). What is the electron-domain geometry around the A atom? (c) For the \(\mathrm{AB}_{4}\) molecule in part (b), predict the molecular geometry.

Would you expect the nonbonding electron-pair domain in \(\mathrm{NCl}_{3}\) to be greater or smaller in size than the corresponding one in \(\mathrm{PCl}_{3}\)?

In which of these molecules or ions does the presence of nonbonding electron pairs produce an effect on molecular shape? (a) \(\mathrm{CO}_{2},(\mathbf{b}) \mathrm{CH}_{2} \mathrm{Br}_{2},(\mathbf{c}) \mathrm{OF}_{2},\) (d) \(\mathrm{BCl}_{3}\), (e) \(\mathrm{SF}_{6}\).

In which of the following molecules can you confidently predict the bond angles about the central atom, and for which would you be a bit uncertain? Explain in each case. (a) \(\mathrm{H}_{2} \mathrm{~S}\) (b) \(\mathrm{BCl}_{3}\) (c) \(\mathrm{CH}_{3} \mathrm{I}\) (d) \(\mathrm{CBr}_{4}\) (e) \(\mathrm{TeBr}_{4}\)

How many nonbonding electron pairs are there in each of the following molecules: \((\mathbf{a}) \mathrm{N}\left(\mathrm{CH}_{3}\right)_{3},\) (b) CO, (c) \(\mathrm{BF}_{3},\) (d) \(\mathrm{SO}_{2} ?\)

How many electron domains are surrounding the central atoms which adopt the following geometries? (a) linear (b) trigonal planar (c) trigonal pyramidal (d) trigonal bipyramidal.

Give the electron-domain and molecular geometries of a molecule that has the following electron domains on its central atom: (a) four bonding domains and no nonbonding domains, (b) three bonding domains and two nonbonding domains, (c) five bonding domains and one nonbonding domain, (d) four bonding domains and two nonbonding domains.

What are the electron-domain and molecular geometries of a molecule that has the following electron domains on its central atom? (a) Three bonding domains and no nonbonding domains, (b) three bonding domains and one nonbonding domain, (c) two bonding domains and two nonbonding domains.

Give the electron-domain and molecular geometries for the following molecules and ions: \((\mathbf{a}) \mathrm{BeF}_{2},(\mathbf{b}) \mathrm{AsCl}_{5},(\mathbf{c}) \mathrm{NO}_{2}^{-},\) (d) \(\mathrm{CS}_{2}\), (e) \(\mathrm{SF}_{4}\) (f) \(\mathrm{BrF}_{5}\).

Draw the Lewis structure for each of the following molecules or ions, and predict their electron-domain and molecular geometries: \((\mathbf{a}) \mathrm{AsF}_{3},(\mathbf{b}) \mathrm{CH}_{3}^{+},(\mathbf{c}) \mathrm{BrF}_{3},(\mathbf{d}) \mathrm{ClO}_{3}^{-},(\mathbf{e}) \mathrm{XeF}_{2},\) (f) \(\mathrm{BrO}_{2}^{-}\).

Ammonia, \(\mathrm{NH}_{3}\), reacts with incredibly strong bases to produce the amide ion, \(\mathrm{NH}_{2}^{-}\). Ammonia can also react with acids to produce the ammonium ion, \(\mathrm{NH}_{4}^{+}\). (a) Which species (amide ion, ammonia, or ammonium ion) has the largest \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angle? \((\mathbf{b})\) Which species has the smallest \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angle?

In which of the following \(\mathrm{AF}_{n}\) molecules or ions is there more than one \(\mathrm{F}-\mathrm{A}-\mathrm{F}\) bond angle: \(\mathrm{PF}_{6}^{-}, \mathrm{SbF}_{5}, \mathrm{SF}_{4}\) ?

(a) Explain why \(\mathrm{BrF}_{4}^{-}\) is square planar, whereas \(\mathrm{BF}_{4}^{-}\) is tetrahedral. (b) How would you expect the \(\mathrm{H}-\mathrm{X}-\mathrm{H}\) bond angle to vary in the series \(\mathrm{H}_{2} \mathrm{O}, \mathrm{H}_{2} \mathrm{~S}, \mathrm{H}_{2}\) Se? Explain. (Hint: The size of an electron pair domain depends in part on the electronegativity of the central atom.)

What is the distinction between a bond dipole and a molecular dipole moment?

Consider a molecule with formula \(\mathrm{AX}_{2}\). Supposing the \(\mathrm{A}-\mathrm{X}\) bond is polar, how would you expect the dipole moment of the \(\mathrm{AX}_{2}\) molecule to change as the \(\mathrm{X}-\mathrm{A}-\mathrm{X}\) bond angle decreases from \(180^{\circ}\) to \(100^{\circ}\) ?

(a) Does \(\mathrm{CS}_{2}\) have a dipole moment? If so, in which direction does the net dipole point? (b) Does \(\mathrm{SO}_{2}\) have a dipole moment? If so, in which direction does the net dipole point?

(a) The \(\mathrm{PH}_{3}\) molecule is polar. Does this offer experimental proof that the molecule cannot be planar? Explain. (b) It turns out that ozone, \(\mathrm{O}_{3}\), has a small dipole moment. How is this possible, given that all the atoms are the same?

(a) Is the molecule \(\mathrm{BF}_{3}\) polar or nonpolar? (b) If you react \(\mathrm{BF}_{3}\) to make the ion \(\mathrm{BF}_{3}{\underline{\phantom{xx}}}^{2-}\), is this ion planar? (c) Does the molecule \(\mathrm{BF}_{2} \mathrm{Cl}\) have a dipole moment?

(a) Consider the following two molecules: \(\mathrm{PCl}_{3}\) and \(\mathrm{BCl}_{3}\). Which molecule has a nonzero dipole moment? (b) Consider the following two molecules: \(\mathrm{XeF}_{4}\) and \(\mathrm{SF}_{4}\). Which molecule has a zero dipole moment?

Predict whether each of the following molecules is polar or nonpolar: (a) IF, (b) \(\mathrm{CS}_{2}\) (c) \(\mathrm{SO}_{3}\) (d) \(\mathrm{PCl}_{3}\), (e) \(\mathrm{SF}_{6}\) (f) \(\mathrm{IF}_{5}\).

Predict whether each of the following molecules is polar or nonpolar: \((\mathbf{a}) \mathrm{CCl}_{4},(\mathbf{b}) \mathrm{NH}_{3},(\mathbf{c}) \mathrm{SF}_{4},(\mathbf{d}) \mathrm{XeF}_{4},\) (e) \(\mathrm{CH}_{3} \mathrm{Br}\) (f) \(\mathrm{GaH}_{3}\)

Dichloroethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}_{2}\right)\) has three forms (isomers), each of which is a different substance. (a) Draw Lewis structures of the three isomers, all of which have a carbon-carbon double bond. (b) Which of these isomers has a zero dipole moment? (c) How many isomeric forms can chloroethylene, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), have? Would they be expected to have dipole moments?

Dihydroxybenzene, \(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}_{2}\), exists in three forms (isomers) called ortho, meta, and para: Which of these has a nonzero dipole moment?

For each statement, indicate whether it is true or false. (a) In order to make a covalent bond, the orbitals on each atom in the bond must overlap. (b) A \(p\) orbital on one atom cannot make a bond to an \(s\) orbital on another atom. (c) Lone pairs of electrons on an atom in a molecule influence the shape of a molecule. \((\mathbf{d})\) The \(1 s\) orbital has a nodal plane. \((\mathbf{e})\) The \(2 p\) orbital has a nodal plane.

Draw sketches illustrating the overlap between the following orbitals on two atoms: (a) the \(2 s\) orbital on each atom, (b) the \(2 p_{z}\) orbital on each atom (assume both atoms are on the \(z\) -axis), \((\mathbf{c})\) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

For each statement, indicate whether it is true or false. (a) The greater the orbital overlap in a bond, the weaker the bond. (b) The greater the orbital overlap in a bond, the shorter the bond. \((\mathbf{c})\) To create a hybrid orbital, you could use the \(s\) orbital on one atom with a \(p\) orbital on another atom. (d) Nonbonding electron pairs cannot occupy a hybrid orbital.

How would you expect the extent of overlap of the bonding atomic orbitals to vary in the series IF, ICl, IBr, and \(\mathrm{I}_{2}\) ? Explain your answer.

Consider the molecule \(\mathrm{BF}_{3} .\) (a) What is the electron configuration of an isolated B atom? (b) What is the electron configuration of an isolated \(\mathrm{F}\) atom? (c) What hybrid orbitals should be constructed on the \(\mathrm{B}\) atom to make the \(\mathrm{B}-\mathrm{F}\) bonds in \(\mathrm{BF}_{3} ?(\mathbf{d})\) What valence orbitals, if any, remain unhybridized on the \(\mathrm{B}\) atom in \(\mathrm{BF}_{3}\) ?

Indicate the hybridization of the central atom in (a) \(\mathrm{H}_{2} \mathrm{~S}\), (b) \(\mathrm{SeF}_{6}\) (c) \(\mathrm{P}(\mathrm{OH})_{3},\) (d) \(\mathrm{AlI}_{3} .\)

What is the hybridization of the central atom in (a) \(\mathrm{PBr}_{5}\), (b) \(\mathrm{CH}_{2} \mathrm{O},(\mathbf{c}) \mathrm{O}_{3},\) (d) \(\mathrm{NO}_{2} ?\)

(a) Which geometry and central atom hybridization would you expect in the series \(\mathrm{BH}_{4}^{-}, \mathrm{CH}_{4}, \mathrm{NH}_{4}^{+} ?(\mathbf{b})\) What would you expect for the magnitude and direction of the bond dipoles in this series? (c) Write the formulas for the analogous species of the elements of period 3 ; would you expect them to have the same hybridization at the central atom?

(a) Draw a picture showing how two \(p\) orbitals on two different atoms can be combined to make a \(\sigma\) bond. (b) Sketch a \(\pi\) bond that is constructed from \(p\) orbitals. (c) Which is generally stronger, a \(\sigma\) bond or a \(\pi\) bond? Explain. (d) Can two \(s\) orbitals combine to form a \(\pi\) bond? Explain.

The oxygen atoms in \(\mathrm{O}_{2}\) participate in multiple bonding, whereas those in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2},\) do not. (a) Draw Lewis structures for both molecules. (b) What is the hybridization of the oxygen atoms in each molecule? (c) Which molecule has the stronger \(\mathrm{O}-\mathrm{O}\) bond?

Vinyl chloride, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), is a gas that is used to form the important polymer called polyvinyl chloride (PVC). Its Lewis structure is (a) What is the total number of valence electrons in the vinyl chloride molecule? (b) How many valence electrons are used to make \(\sigma\) bonds in the molecule? (c) How many valence electrons are used to make \(\pi\) bonds in the molecule? (d) How many valence electrons remain in nonbonding pairs in the molecule? (e) What is the hybridization at each carbon atom in the molecule?

Consider the Lewis structure for acetic acid, which is known as vinegar: (a) What are the approximate bond angles about each of the two carbon atoms, and what are the hybridizations of the orbitals on each of them? (b) What are the hybridizations of the orbitals on the two oxygen atoms, and what are the approximate bond angles at the oxygen that is connected to carbon and hydrogen? (c) What is the total number of \(\sigma\) bonds in the entire molecule, and what is the total number of \(\pi\) bonds?

(a) What is the difference between a localized \(\pi\) bond and a delocalized one? (b) How can you determine whether a molecule or ion will exhibit delocalized \(\pi\) bonding? (c) Is the \(\pi\) bond in \(\mathrm{NO}_{2}^{-}\) localized or delocalized?

(a) Write a single Lewis structure for \(\mathrm{N}_{2} \mathrm{O}\), and determine the hybridization of the central \(\mathrm{N}\) atom. (b) Are there other possible Lewis structures for the molecule? (c) Would you expect \(\mathrm{N}_{2} \mathrm{O}\) to exhibit delocalized \(\pi\) bonding?

In the sulphate ion, \(\mathrm{SO}_{4}{\underline{\phantom{xx}}}^{2-}\), the sulphur atom is the central atom with the other 4 oxygen atoms attached to it. (a) Draw a Lewis structure for the sulphate ion. (b) What hybridization is exhibited by the \(S\) atom? (c) Are there multiple equivalent resonance structures for the ion? (d) How many electrons are in the \(\pi\) system of the ion?

What hybridization do you expect for the atom that is underlined in each of the following species? (a) \(\underline{\mathrm{I}} \mathrm{O}_{2}^{-} ;(\mathbf{b}) \underline{\mathrm{N}} \mathrm{H}_{4}^{+} ;(\mathbf{c}) \mathrm{SC} \mathrm{N}^{-}\) (d) \(\underline{\mathrm{Br}} \mathrm{Cl}_{3}\)

(a) What is the difference between hybrid orbitals and molecular orbitals? (b) How many electrons can be placed into each MO of a molecule? (c) Can antibonding molecular orbitals have electrons in them?

(a) If you combine two atomic orbitals on two different atoms to make a new orbital, is this a hybrid orbital or a molecular orbital? (b) If you combine two atomic orbitals on one atom to make a new orbital, is this a hybrid orbital or a molecular orbital? (c) Does the Pauli exclusion principle (Section 6.7 ) apply to MOs? Explain.

(a) Sketch the molecular orbitals of the \(\mathrm{H}_{2}^{-}\) ion and draw its energy-level diagram. (b) Write the electron configuration of the ion in terms of its MOs. (c) Calculate the bond order in \(\mathrm{H}_{2}^{-}\). (d) Suppose that the ion is excited by light, so that an electron moves from a lower- energy to a higher-energy molecular orbital. Would you expect the excited- state \(\mathrm{H}_{2}^{-}\) ion to be stable? (e) Which of the following statements about part (d) is correct: (i) The light excites an electron from a bonding orbital to an antibonding orbital, (ii) The light excites an electron from an antibonding orbital to a bonding orbital, or (iii) In the excited state there are more bonding electrons than antibonding electrons?

Indicate whether each statement is true or false. (a) \(p\) orbitals can only make \(\sigma\) or \(\sigma^{*}\) molecular orbitals. (b) The probability is always \(0 \%\) for finding an electron in an antibonding orbital. (c) Molecules containing electrons that occupy antibonding orbitals must be unstable. (d) Electrons cannot occupy a nonbonding orbital.

(a) What are the relationships among bond order, bond length, and bond energy? (b) According to molecular orbital theory, would either \(\mathrm{Be}_{2}\) or \(\mathrm{Be}_{2}^{+}\) be expected to exist? Explain.

Explain the following: \((\mathbf{a})\) The peroxide ion, \(\mathrm{O}_{2}^{2-},\) has a longer bond length than the superoxide ion, \(\mathrm{O}_{2}^{-}\). (b) The magnetic properties of \(\mathrm{B}_{2}\) are consistent with the \(\pi_{2 p}\) MOs being lower in energy than the \(\sigma_{2 p}\) MO. (c) The \(\mathrm{O}_{2}^{2+}\) ion has a stronger \(\mathrm{O}-\mathrm{O}\) bond than \(\mathrm{O}_{2}\) itself.

How would we describe a substance that contains only paired electrons and is weakly repelled by a magnetic field? Which of the following ions would you expect to possess similar characteristics: \(\mathrm{H}_{2}^{-}, \mathrm{Ne}_{2}^{+}, \mathrm{F}_{2}, \mathrm{O}_{2}^{2+} ?\)