Chapter 2 — Exercises

Forty problems. All drawing. Use a pencil — not a screen — for the mechanism and structure problems. An ∗ marks problems with worked solutions in Appendix Answers to Selected Exercises.

Section A — Atomic structure and valence

2.1∗ (routine) Write the ground-state electron configuration of each atom: (a) C (b) N (c) O (d) F (e) Cl (f) Si (g) S (h) P

2.2 (routine) How many valence electrons does each atom contribute to a molecule? (a) C (b) N (c) O (d) F (e) H (f) S

2.3 (moderate) Silicon is directly below carbon on the periodic table. List three ways silicon and carbon are chemically similar, and three ways they are different. Use specific structural or energetic data from the chapter.

2.4 (routine) Draw a sketch (by hand, on paper) of: (a) a $1s$ orbital (b) a $2s$ orbital (including the radial node) (c) a $2p$ orbital along the x-axis (d) a $2p$ orbital along the z-axis

Section B — Lewis structures

2.5∗ (routine) Draw the complete Lewis structure of each molecule, showing all bonds, lone pairs, and formal charges: (a) $H_2O$ (b) $NH_3$ (c) $CH_3Cl$ (d) $HCN$ (e) $CO_2$ (f) $N_2$ (g) $CH_3OH$ (h) $CH_3NH_2$

2.6 (moderate) Draw the Lewis structure of each ion: (a) $OH^-$ (b) $H_3O^+$ (c) $CN^-$ (d) $NH_4^+$ (e) $NO_2^-$ (f) $BF_4^-$

2.7 (moderate) For each of the following, draw the Lewis structure and identify every atom that carries a formal charge: (a) nitromethane, $CH_3NO_2$ (b) methyl isocyanide, $CH_3NC$ (c) the hydronium ion, $H_3O^+$ (d) the methyl cation, $CH_3^+$ (e) the methyl anion, $CH_3^-$

2.8∗ (moderate) A student draws the Lewis structure of $CO_2$ as $O-C-O$ with single bonds and three lone pairs on each oxygen. Identify everything wrong with this structure and correct it.

2.9 (challenge) The molecule $SF_6$ has six fluorines around a central sulfur. The octet rule is satisfied at every fluorine, but the sulfur appears to have 12 electrons around it. Why is this allowed? (Hint: think about what shells are available to third-row elements but not to second-row elements.)

2.10 (moderate) For each structure, count the total valence electrons and verify the Lewis structure is correct (or correct it): (a) $H_2CO_3$ (carbonic acid) (b) $H_2C=CH_2$ (ethylene) (c) $CH_3CO_2H$ (acetic acid) (d) $CH_3CONH_2$ (acetamide)

Section C — Skeletal formulas

2.11∗ (routine) Convert each condensed formula to a skeletal formula: (a) $CH_3CH_2CH_2CH_3$ (b) $CH_3CH(OH)CH_3$ (c) $CH_3COCH_3$ (d) $CH_3CH=CHCH_3$

2.12 (moderate) Convert each skeletal formula to a condensed formula and write the molecular formula:

(Describe hexane — six-carbon zig-zag; 1-butanol — four-carbon zig-zag with OH on the terminal carbon; cyclohexane — six-membered ring; benzene — six-membered ring with alternating double bonds.)

2.13 (moderate) How many hydrogens are implied at each labeled carbon in the following skeletal formula? (Label the carbons 1–5 along a chain of five carbons with a branch of one carbon on C2 and an $OH$ on C3.)

2.14 (routine) Draw skeletal formulas for: (a) 2-methylpentane (b) 3-ethyl-2-methylhexane (c) 1,3-cyclohexadiene (d) ethyl acetate, $CH_3CO_2CH_2CH_3$

Section D — Hybridization and geometry

2.15∗ (routine) Assign the hybridization of every non-hydrogen atom: (a) methane, $CH_4$ (b) ethylene, $CH_2=CH_2$ (c) acetylene, $HC \equiv CH$ (d) formaldehyde, $H_2CO$ (e) hydrogen cyanide, $HCN$ (f) methanol, $CH_3OH$ (g) dimethyl ether, $CH_3OCH_3$ (h) methylamine, $CH_3NH_2$

2.16 (moderate) For benzene ($C_6H_6$): (a) What is the hybridization of each carbon? (b) How many $\sigma$ bonds and how many $\pi$ bonds does benzene contain? (c) Describe the geometry of the ring.

2.17 (moderate) For each atom in acetone, $(CH_3)_2C=O$: (a) Assign hybridization. (b) Predict the geometry (tetrahedral, trigonal planar, etc.). (c) Predict the approximate bond angles.

2.18∗ (moderate) The nitrogen atom in ammonia, $NH_3$, has steric number 4 but the molecule is not tetrahedral in the usual sense. Explain why, and state the actual molecular geometry.

2.19 (challenge) Explain why the $H-N-H$ angle in $NH_3$ (107°) is slightly smaller than the tetrahedral 109.5°, while the $H-C-H$ angle in $CH_4$ is exactly 109.5°.

2.20 (challenge) Which of the following molecules have a net (non-zero) dipole moment, and in which direction does it point? (a) $CO_2$ (b) $H_2O$ (c) $CH_4$ (d) $CH_3Cl$ (e) $CCl_4$ (f) $CHCl_3$ (chloroform)

Section E — Resonance

2.21∗ (routine) Draw all important resonance structures of each ion: (a) the acetate anion, $CH_3CO_2^-$ (b) the methoxide anion, $CH_3O^-$ (how many are needed?) (c) the enolate of acetone (d) the nitrate anion, $NO_3^-$

2.22 (moderate) Acetamide, $CH_3CONH_2$, has two important resonance structures: one with a $C=O$ double bond and a neutral $NH_2$, and one with a $C=N$ double bond, a negatively charged oxygen, and a positively charged nitrogen. Draw both.

2.23 (moderate) Which resonance structure in problem 2.22 contributes more to the actual structure of acetamide? Justify your answer using the rules from Section 2.6.

2.24∗ (challenge) A student draws two "resonance structures" of butane — one as the normal $CH_3CH_2CH_2CH_3$ and another as $CH_3CH_2CH(CH_3)$ (2-methylpropane). Explain why these are NOT resonance structures.

2.25 (challenge) The amide $C-N$ bond in acetamide is about 1.33 Å long — intermediate between a typical $C-N$ single bond (1.47 Å) and a typical $C=N$ double bond (1.28 Å). Explain this observation using resonance.

Section F — Electronegativity and polarity

2.26 (routine) Predict the direction of the bond dipole (which atom is $\delta^+$ and which is $\delta^-$) for each bond: (a) $C-H$ (b) $C-O$ (c) $C-N$ (d) $C-Cl$ (e) $O-H$ (f) $N-H$ (g) $C-Li$ (yes, lithium — this will be important in Chapter 10) (h) $C-Mg$

2.27∗ (moderate) In the molecule $CH_3OH$, which atom is most electrophilic (highest $\delta^+$)? Which is most nucleophilic (highest $\delta^-$ or most available lone pair)?

2.28 (moderate) A student argues that because the $C-F$ bond is the most polar of all $C-X$ bonds (where $X$ is a halogen), fluoroalkanes should be the most reactive alkyl halides. Yet in practice, fluoroalkanes are the least reactive toward nucleophiles. What else, besides bond polarity, affects reactivity? (You are previewing Chapter 10.)

Section G — Molecular orbital theory

2.29 (moderate) Sketch the molecular orbital diagram for $H_2$. Label the HOMO and the LUMO.

2.30∗ (moderate) Sketch the molecular orbital diagram for $He_2$ (hypothetical). Predict the bond order and state whether the molecule is stable.

2.31 (challenge) The nitrogen molecule $N_2$ has a triple bond. Explain, in terms of molecular orbital theory (without drawing the full diagram), why $N_2$ has a bond order of 3.

2.32 (computational) In Avogadro, build ethylene ($CH_2=CH_2$). Optimize the geometry. Display the HOMO and the LUMO. Describe (in words) what each looks like in three dimensions. Take a screenshot for each.

2.33 (challenge, computational) In Avogadro, build formaldehyde ($H_2CO$). Optimize, display the HOMO and LUMO. Where is the electron density on the HOMO? On the LUMO? Based on this, predict which end of the molecule a nucleophile would attack if it were to add across the $C=O$. (You are anticipating Chapter 25.)

Section H — Integrative problems

2.34∗ (moderate) For aspirin (acetylsalicylic acid, structure in Chapter 1, Figure 1.1): (a) Count the total number of atoms, the number of each element. (b) Assign hybridization to every non-hydrogen atom. (c) Identify every polar bond. (d) Predict which atom is most electrophilic. (Hint: look at the two ester $C$'s.)

2.35 (moderate) For thalidomide (Chapter 1, Figure 1.2): (a) Assign hybridization to every heteroatom (N and O). (b) Which nitrogens carry a lone pair? Which oxygens? (c) Which atom do you predict is the most basic (best proton acceptor)? (Anticipating Chapter 3.)

2.36 (challenge) Draw the two major resonance structures of the nitro group ($-NO_2$, as in nitrobenzene). Explain how the two oxygens of the nitro group are equivalent in the molecule's actual structure even though they appear inequivalent in either individual resonance structure.

2.37 (challenge) The carbonate dianion, $CO_3^{2-}$, has three resonance structures. Draw all three and explain why the three $C-O$ bonds in carbonate are experimentally equivalent in length (1.28 Å).

2.38 (challenge) When $H_2O$ bonds with $H^+$ to form $H_3O^+$, the newly formed $O-H$ bond is chemically identical to the two existing $O-H$ bonds — rotations around the central axis make them interchangeable. Draw the Lewis structure of $H_3O^+$ and verify by electron bookkeeping that all three $O-H$ bonds are equivalent.

2.39 (challenge) Silicon can form $sp^3$-hybridized bonds just as carbon can, as in silane, $SiH_4$. Yet biology does not use silicon as a backbone. Using data from Table 2.1 (bond strengths) and concepts from this chapter, give three specific reasons why silicon is a poor replacement for carbon in biology.

2.40 (challenge) A student has just drawn a Lewis structure of a molecule and computed a formal charge of $+2$ on a single carbon. What are the most likely errors the student has made? List three things to check.

Preview of Chapter 3

Chapter 3 builds the $pK_a$ framework. Every prediction in that chapter will use the electronegativity, resonance, and hybridization ideas from this chapter. Practice those three skills until they are automatic before proceeding.