Chapter 9

The molecule shown here is difluoromethane \(\left(\mathrm{CH}_{2} \mathrm{~F}_{2}\right)\), which is used as a refrigerant called \(R-32\). (a) Based on the structure, how many electron domains surround the \(\mathrm{C}\) atom in this molecule? (b) Would the molecule have a nonzero dipole moment? (c) If the molecule is polar, which of the following describes the direction of the overall dipole moment vector in the molecule: (i) from the carbon atom toward a fluorine atom, (ii) from the carbon atom to a point midway between the fluorine atoms, (iii) from the carbon atom to a point midway between the hydrogen atoms, or (iv) From the carbon atom toward a hydrogen atom? [Sections \(9.2\) and 9.3]

The orbital diagram that follows presents the final step in the formation of hybrid orbitals by a silicon atom. (a) Which of the following best describes what took place before the step pictured in the diagram: (i) Two 3 p electrons became unpaired, (ii) An electron was promoted from the \(2 p\) orbital to the \(3 s\) orbital, or (iii) An electron was promoted from the \(3 s\) orbital to the \(3 p\) orbital? (b) What type of hybrid orbital is produced in this hybridization? [Section 9.5]

The following is part of a molecular orbital energy-level diagram for MOs constructed from \(1 s\) atomic orbitals. (a) What labels do we use for the two MOs shown? (b) For which of the following molecules or ions could this be the energy-level diagram: \(\mathrm{H}_{2}, \mathrm{He}_{2}, \mathrm{H}_{2}{\underline{\phantom{xx}}}^{+}, \mathrm{He}_{2}{\underline{\phantom{xx}}}^{+}\), or \(\mathrm{H}_{2}{\underline{\phantom{xx}}}^{-}\)? (c) What is the bond order of the molecule or ion? (d) If an electron is added to the system, into which of the MOs will it be added? [Section 9.7]

For each of these contour representations of molecular orbitals, identify (a) the atomic orbitals (s or \(p\) ) used to construct the MO (b) the type of MO ( \(\sigma\) or \(\pi\) ), (c) whether the MO is bonding or antibonding, and (d) the locations of nodal planes. [Sections \(9.7\) and 9.8]

The diagram that follows shows the highest-energy occupied MOs of a neutral molecule \(\mathrm{CX},\) where element \(\mathrm{X}\) is in the same row of the periodic table as C. (a) Based on the number of electrons, can you determine the identity of \(X ?\) (b) Would the molecule be diamagnetic or paramagnetic? (c) Consider the \(\pi_{2 p}\) MOs of the molecule. Would you expect them to have a greater atomic orbital contribution from \(\mathrm{C}\), have a greater atomic orbital contribution from \(X\), or be an equal mixture of atomic orbitals from the two atoms? [Section 9.8\(]\) $$ \begin{array}{l|l|l|} \cline { 2 - 3 } \sigma_{2 p} & \multicolumn{1}{c} {1} \\ \cline { 2 - 3 } \pi_{2 p} & 1 \downarrow & 1 \downarrow \\ \hline \end{array} $$

\mathrm{An} \mathrm{} \mathrm{AB}_{2}\( molecule is described as linear, and the \)\mathrm{A}-\mathrm{B}\( bond length is known. (a) Does this information completely describe the geometry of the molecule? (b) Can you tell how many nonbonding pairs of electrons are around the \)A$ atom from this information?

(a) Methane \(\left(\mathrm{CH}_{4}\right)\) and the perchlorate ion \(\left(\mathrm{ClO}_{4}{\underline{\phantom{xx}}}^{-}\right)\)are both described as tetrahedral. What does this indicate about their bond angles? (b) The \(\mathrm{NH}_{3}\) molecule is trigonal pyramidal, while \(\mathrm{BF}_{3}\) is trigonal planar. 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) How does one determine the number of electron domains in a molecule or ion? (b) What is the difference between a bonding electron domain and a nonbonding electron domain?

Would you expect the nonbonding electron-pair domain in \(\mathrm{NH}_{3}\) to be greater or less in size than for the corresponding one in \(\mathrm{PH}_{3}\) ?

In which of these molecules or ions does the presence of nonbonding electron pairs produce an effect on molecular shape? (a) \(\mathrm{SiH}_{4}\), (b) \(\mathrm{PF}_{3}\), (c) \(\mathrm{HBr}\), (d) \(\mathrm{HCN}\), (e) \(\mathrm{SO}_{2}\).

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) \(\mathrm{H}_{2} \mathrm{~S}_{\text {, }}\) (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: (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~S}\), (b) \(\mathrm{HCN}\), (c) \(\mathrm{H}_{2} \mathrm{C}_{2}\), (d) \(\mathrm{CH}_{3} \mathrm{~F}\) ?

Describe the characteristic electron-domain geometry of each of the following numbers of electron domains about a central atom: (a) 3 , (b) 4 , (c) 5, (d) 6 .

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: (a) \(\mathrm{HCN}\), (b) \(\mathrm{SO}_{3}^{2-}\), (c) \(\mathrm{SF}_{4}\), (d) \(\mathrm{PF}_{6}^{-}\), (e) \(\mathrm{NH}_{3} \mathrm{Cl}^{+}\), (f) \(\mathrm{N}_{3}^{-}\).

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

The three species \(\mathrm{NH}_{2}^{-}, \mathrm{NH}_{3}\), and \(\mathrm{NH}_{4}{\underline{\phantom{xx}}}^{+}\)have \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angles of \(105^{\circ}, 107^{\circ}\), and \(109^{\circ}\), respectively. Explain this variation in bond angles.

In which of the following \(\mathrm{AF}_{n}\) molecules or ions is there more than one \(\mathrm{F}-\mathrm{A}-\mathrm{F}\) bond angle: \(\mathrm{SiF}_{4}, \mathrm{PF}_{5}, \mathrm{SF}_{4}, \mathrm{AsF}_{3}\) ?

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

(a) Explain why the following ions have different bond angles: \(\mathrm{ClO}_{2}^{-}\)and \(\mathrm{NO}_{2}^{-}\). Predict the bond angle in each case. (b) Explain why the \(\mathrm{XeF}_{2}\) molecule is linear.

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

Consider a molecule with formula \(\mathrm{AX}_{3}\). Supposing the \(\mathrm{A}-\mathrm{X}\) bond is polar, how would you expect the dipole moment of the \(\mathrm{AX}_{3}\) molecule to change as the \(\mathrm{X}-\mathrm{A}-\mathrm{X}\) bond angle increases from \(100^{\circ}\) to \(120^{\circ}\) ?

(a) Does \(\mathrm{SCl}_{2}\) have a dipole moment? If so, in which direction does the net dipole point? (b) Does \(\mathrm{BeCl}_{2}\) 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) What conditions must be met if a molecule with polar bonds is nonpolar? (b) What geometries will signify nonpolar molecules for \(\mathrm{AB}_{2}, \mathrm{AB}_{3}\), and \(\mathrm{AB}_{4}\) geometries?

Predict whether each of the following molecules is polar or nonpolar: (a) \(\mathrm{IF}_{3}\) (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: (a) \(\mathrm{CCl}_{4}\), (b) \(\mathrm{NH}_{3}\), (c) \(\mathrm{SF}_{4}\), (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?

(a) What is meant by the term orbital overlap? (b) Describe what a chemical bond is in terms of electron density between two atoms.

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), (c) the \(2 s\) orbital on one atom and the \(2 p_{z}\) orbital on the other atom.

Consider the bonding in an \(\mathrm{MgH}_{2}\) molecule. (a) Draw a Lewis structure for the molecule, and predict its molecular geometry. (b) What hybridization scheme is used in \(\mathrm{MgH}_{2}\) ? (c) Sketch one of the two-electron bonds between an \(\mathrm{Mg}\) hybrid orbital and an \(\mathrm{H} 1 \mathrm{~s}\) atomic orbital.

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

(a) Starting with the orbital diagram of a boron atom, describe the steps needed to construct hybrid orbitals appropriate to describe the bonding in \(\mathrm{BF}_{3}\). (b) What is the name given to the hybrid orbitals constructed in (a)? (c) Sketch the large lobes of the hybrid orbitals constructed in part (a). (d) Are any valence atomic orbitals of B left unhybridized? If so, how are they oriented relative to the hybrid orbitals?

(a) Starting with the orbital diagram of a sulfur atom, describe the steps needed to construct hybrid orbitals appropriate to describe the bonding in \(\mathrm{SF}_{2}\). (b) What is the name given to the hybrid orbitals constructed in (a)? (c) Sketch the large lobes of these hybrid orbitals. (d) Would the hybridization scheme in part (a) be appropriate for \(\mathrm{SF}_{4}\) ? Explain.

Indicate the hybridization of the central atom in (a) \(\mathrm{BCl}_{3}\), (b) \(\mathrm{AlCl}_{4}^{-}\), (c) \(\mathrm{CS}_{2}\), (d) \(\mathrm{GeH}_{4}\) -

What is the hybridization of the central atom in (a) \(\mathrm{SiCl}_{4}\), (b) \(\mathrm{HCN}^{\text {, }}\) (c) \(\mathrm{SO}_{3}\), (d) \(\mathrm{TeCl}_{2}\).

Shown here are three pairs of hybrid orbitals, with each set at a characteristic angle. For each pair, determine the type of hybridization, if any, that could lead to hybrid orbitals at the specified angle.

(a) Which geometry and central atom hybridization would you expect in the series \(\mathrm{BH}_{4}^{-}, \mathrm{CH}_{4}, \mathrm{NH}_{4}^{+}\)? (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.

(a) If the valence atomic orbitals of an atom are sp hybridized, how many unhybridized \(p\) orbitals remain in the valence shell? How many \(\pi\) bonds can the atom form? (b) Imagine that you could hold two atoms that are bonded together, twist them, and not change the bond length. Would it be easier to twist (rotate) around a single \(\sigma\) bond or around a double ( \(\sigma\) plus \(\pi\) ) bond, or would they be the same?

(a) Draw Lewis structures for ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\), ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\), and acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\). (b) What is the hybridization of the carbon atoms in each molecule? (c) Predict which molecules, if any, are planar. (d) How many \(\sigma\) and \(\pi\) bonds are there in each molecule?

The nitrogen atoms in \(N_{2}\) participate in multiple bonding, whereas those in hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\), do not. (a) Draw Lewis structures for both molecules. (b) What is the hybridization of the nitrogen atoms in each molecule? (c) Which molecule has the stronger \(\mathrm{N}-\mathrm{N}\) bond?

Propylene, \(\mathrm{C}_{3} \mathrm{H}_{6}\), is a gas that is used to form the important polymer called polypropylene. Its Lewis structure is (a) What is the total number of valence electrons in the propylene 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?

Ethyl acetate, \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\), is a fragrant substance used both as a solvent and as an aroma enhancer. Its Lewis structure is (a) What is the hybridization at each of the carbon atoms of the molecule? (b) What is the total number of valence electrons in ethyl acetate? (c) How many of the valence electrons are used to make \(\sigma\) bonds in the molecule? (d) How many valence electrons are used to make \(\pi\) bonds? (e) How many valence electrons remain in nonbonding pairs in the molecule?

Consider the Lewis structure for glycine, the simplest amino acid: (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 oxygens and the nitrogen atom, and what are the approximate bond angles at the nitrogen? (c) What is the total number of \(\sigma\) bonds in the entire molecule, and what is the total number of \(\pi\) bonds?

Acetylsalicylic acid, better known as aspirin, has the Lewis structure (a) What are the approximate values of the bond angles labeled 1,2 , and 3 ? (b) What hybrid orbitals are used about the central atom of each of these angles? (c) How many \(\sigma\) bonds are in the molecule?

(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 \(\mathrm{NO}_{2}{\underline{\phantom{xx}}}^{-}\)localized or delocalized?