Chapter 3 — Exercises

Forty exercises. A $pK_a$ table (Appendix B) will be useful; print one and keep it at your workstation. ∗ marks problems with full solutions.

Section A — pKa vocabulary and basics

3.1∗ (routine) For each reaction, identify the Brønsted acid, Brønsted base, conjugate acid, and conjugate base: (a) $HCl + H_2O \rightleftharpoons H_3O^+ + Cl^-$ (b) $NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-$ (c) $CH_3CO_2H + NaOH \rightleftharpoons CH_3CO_2Na + H_2O$ (d) $CH_3NH_2 + HCl \rightleftharpoons CH_3NH_3^+ + Cl^-$

3.2 (routine) Write $pK_a = -\log_{10}K_a$. Compute the $K_a$ of each acid from its $pK_a$: (a) $HCl$ ($pK_a = -7$) (b) $HF$ ($pK_a = 3.2$) (c) acetic acid ($pK_a = 4.76$) (d) ammonium ($pK_a = 9.2$) (e) methanol ($pK_a = 15.5$)

3.3 (routine) Which of the following is a stronger acid? (Use the table in the chapter.) (a) acetic acid vs. ethanol (b) phenol vs. cyclohexanol (c) $HI$ vs. $HF$ (d) terminal alkyne vs. alkane (e) water vs. ammonia

Section B — The ARIO factors

3.4∗ (moderate) Rank in order of increasing acidity (lowest to highest $pK_a$): $CH_4$, $NH_3$, $H_2O$, $HF$. Explain using the Atom factor.

3.5 (moderate) Rank in order of increasing acidity: $HF$, $HCl$, $HBr$, $HI$. Explain using the Atom factor (size/polarizability).

3.6 (moderate) Propanoic acid, $CH_3CH_2CO_2H$, has $pK_a = 4.88$. 2-fluoropropanoic acid, $CH_3CHFCO_2H$, has $pK_a = 2.89$. Explain the difference.

3.7∗ (moderate) Arrange in order of increasing acidity: $CH_3CH_2CH_2CO_2H$, $ClCH_2CH_2CH_2CO_2H$, $CH_3CH_2CHClCO_2H$, $CH_3CHClCH_2CO_2H$. Explain using induction and distance.

3.8 (moderate) Compare the $pK_a$ of ethanol ($pK_a = 16$) and 2,2,2-trifluoroethanol ($pK_a = 12.5$). Explain.

3.9∗ (challenge) Acetylacetone (pentane-2,4-dione, $CH_3COCH_2COCH_3$) has $pK_a = 9$ at the central $CH_2$. Simple acetone ($CH_3COCH_3$) has $\alpha$-$pK_a \approx 20$. Account for the 11-unit difference.

3.10 (moderate) The ammonium cation $NH_4^+$ has $pK_a = 9.2$. Pyridinium (pyridine protonated on nitrogen) has $pK_a = 5.2$. Explain why pyridinium is more acidic than an ammonium.

3.11∗ (challenge) Rank the following in order of increasing acidity: methanol, phenol, acetic acid, 2,4,6-trinitrophenol (picric acid), trifluoroacetic acid. Justify with ARIO.

3.12 (challenge) The imide $N-H$ of phthalimide has $pK_a = 8.3$. Simple amines have $pK_a$ (of $N-H$) around 36–40. What accounts for the huge difference?

Section C — Equilibrium direction

3.13∗ (routine) For each reaction, predict whether the equilibrium favors forward or reverse, and compute $K_{eq}$: (a) $CH_3CO_2H + CH_3O^- \rightleftharpoons CH_3CO_2^- + CH_3OH$ ($pK_a$ of acetic acid = 4.76; $pK_a$ of methanol = 15.5) (b) $NH_4^+ + HO^- \rightleftharpoons NH_3 + H_2O$ ($pK_a$ of ammonium = 9.2; $pK_a$ of water = 15.7) (c) $CH_3OH + NaNH_2 \rightleftharpoons CH_3O^- Na^+ + NH_3$ ($pK_a$ of methanol = 15.5; $pK_a$ of ammonia = 38)

3.14 (moderate) Hydroxide deprotonates carboxylic acids completely, and easily deprotonates phenols. Can it deprotonate a terminal alkyne ($pK_a = 25$) effectively? Why or why not? What base would you use instead?

3.15 (moderate) Why is bicarbonate ($HCO_3^-$) a useful base to dissolve carboxylic acids in water, but not effective for dissolving phenols? (Consider the $pK_a$ of carbonic acid, ~6.35.)

3.16∗ (challenge) You need to selectively deprotonate a carboxylic acid in a molecule that also contains an alcohol (OH). What base would you use? Why is this chemoselective?

Section D — Choosing the right base

3.17 (routine) For each substrate, choose one or more appropriate bases to effect deprotonation quantitatively: (a) acetic acid ($pK_a = 4.76$) (b) phenol ($pK_a = 10$) (c) terminal alkyne ($pK_a = 25$) (d) ketone $\alpha$-carbon ($pK_a = 20$) (e) alkane ($pK_a = 50$)

3.18 (moderate) LDA (lithium diisopropylamide) is a very bulky, strong base with $pK_{aH}$ = 36. Why is it the classic reagent for making kinetic enolates from ketones? (Preview Chapter 27.)

3.19 (moderate) A student wants to deprotonate an ester to make its enolate. Hydroxide doesn't work (why not — $pK_a$ considerations), but LDA does. What $K_{eq}$ does LDA give for this deprotonation if ester $\alpha$-$pK_a = 25$?

3.20 (challenge) Sodium hydride ($NaH$) is the textbook reagent for deprotonating alcohols. The relevant reaction is $R-OH + NaH \to R-O^- Na^+ + H_2$. Why does this work essentially quantitatively regardless of the alcohol's exact $pK_a$ (as long as it is a normal alcohol)?

Section E — Lewis acids and bases

3.21 (routine) Classify each species as a Lewis acid, a Lewis base, or both: (a) $BF_3$ (b) $NH_3$ (c) $H_2O$ (d) $AlCl_3$ (e) $CH_3^-$ (f) $CH_3^+$ (g) benzene (h) $Fe^{3+}$

3.22∗ (moderate) For each reaction, identify the Lewis acid and Lewis base, and draw a curved arrow showing the electron-pair donation: (a) $BF_3 + :NH_3 \to F_3B{-}NH_3$ (b) $AlCl_3 + :OEt_2 \to Cl_3Al{-}OEt_2$ (c) carbocation $+ :Cl^- \to R{-}Cl$

3.23 (moderate) Transition metal cations like $Cu^{2+}$ and $Fe^{2+}$ are common Lewis acids in biochemistry. Give one example of an amino acid side chain that could act as a Lewis base to coordinate such a metal.

Section F — Nucleophilicity and leaving-group ability

3.24∗ (moderate) Rank the following as nucleophiles (toward an alkyl halide in a polar aprotic solvent): $F^-$, $Cl^-$, $Br^-$, $I^-$, $HO^-$, $CH_3O^-$, $NH_3$. Justify using $pK_{aH}$.

3.25 (moderate) Rank the following as leaving groups: $F^-$, $Cl^-$, $Br^-$, $I^-$, $HO^-$, $CH_3O^-$, $CH_3CO_2^-$, $H_2O$, $TsO^-$. Justify using $pK_a$ of the conjugate acid.

3.26 (challenge) An alcohol ($R-OH$) does not undergo $S_N$ reactions directly because $OH^-$ is a terrible leaving group. Name two ways to chemically convert an alcohol into a good leaving group (preview of Chapters 10–11).

Section G — Integrative problems

3.27∗ (moderate) For aspirin (acetylsalicylic acid, see Figure 1.1): (a) Identify every acidic proton. (b) Estimate the $pK_a$ of each using the table in the chapter. (c) Which is most acidic? Why?

3.28 (moderate) For ibuprofen: (a) Identify the acidic carboxylic-acid proton. (b) Estimate its $pK_a$. (c) At the stomach pH of ~1–2, what percentage of ibuprofen is protonated? What about at intestinal pH (~6–7)? (d) Discuss the significance: where in the digestive tract is ibuprofen absorbed, and why?

3.29 (challenge) For thalidomide (Figure 1.2): (a) Identify the most acidic proton. (b) Why is this particular proton so acidic? (Consider resonance into the neighboring carbonyls.) (c) Estimate the $pK_a$.

3.30 (challenge) A peptide contains the amino acids lysine ($\epsilon$-amino $pK_a \approx 10.5$), aspartate ($COOH$ $pK_a \approx 3.9$), and histidine (imidazolium $pK_a \approx 6.0$). Draw the fully protonated form at pH 1, and the fully deprotonated form at pH 12. What is the charge state of each amino acid's side chain at pH 7?

Section H — Computational and spectroscopy connections

3.31 (computational) In Avogadro or a similar program, build acetic acid and compute its electrostatic potential map. Where is the most negative region? Where is the most positive? Does this match your expectation from Chapter 2's polarity analysis?

3.32 (computational) Repeat problem 3.31 for phenol. Compare the maps.

3.33 (challenge) Infrared spectroscopy (Chapter 6) can detect whether a molecule is protonated or deprotonated. A carboxylic acid's $C=O$ stretch is around 1710 $cm^{-1}$; a carboxylate anion shows two bands, around 1560 and 1400 $cm^{-1}$ (symmetric and asymmetric stretches of the delocalized $CO_2^-$ group). Why does the carboxylate's $C=O$ frequency decrease? (Hint: think about bond order in each form.)

Section I — Preview problems

3.34 (challenge) When $CH_3CH_2Br$ reacts with $CH_3O^-$ in methanol, the major product is $CH_3OCH_2CH_3$ ($S_N2$ substitution). If we instead react with $NH_3$ in excess, the product is $CH_3CH_2NH_2$. Explain why $NH_3$ (neutral) is a reasonable nucleophile despite hydroxide ($HO^-$, anionic) being a stronger nucleophile.

3.35 (challenge) An organic chemist wants to convert an alkyl chloride to an alkyl iodide. The Finkelstein reaction does this using $NaI$ in acetone. Using the $pK_a$ framework, predict which direction the equilibrium lies. What drives the reaction forward in practice? (Hint: solubility of products vs. reactants.)

3.36 (challenge) Explain in your own words why the amide $N-H$ of a secondary amide ($R-C(=O)-NHR'$) has $pK_a \approx 17$ — very similar to an alcohol, and much more acidic than a simple amine's $N-H$ ($pK_a$ ~36). What structural feature of an amide makes its $N-H$ so much more acidic?

3.37 (challenge) A student claims that ammonia is a stronger base than water because ammonia's $pK_{aH}$ is 9.2 while water's is $-1.7$. Explain why this reasoning is sound and what it means for the direction of the reaction $NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-$.

3.38 (challenge, biological) The Henderson-Hasselbalch equation for weak acids: $$pH = pK_a + \log \frac{[A^-]}{[HA]}$$ For a drug with carboxylic acid $pK_a = 4$, what is the ratio of ionized (deprotonated) to neutral form in blood plasma (pH 7.4)? What about in the stomach (pH 2)? Why does this matter for drug absorption?

3.39 (challenge) Why is ethanol a stronger acid than $tert$-butanol ($pK_a$ 16 vs. 17) in solution, even though in the gas phase $tert$-butoxide is more stable than ethoxide? (Solvation effects.)

3.40 (challenge) Your lab partner proposes that nitric acid ($HNO_3$, $pK_a \approx -1.4$) should be a better leaving group than acetate ($pK_a$ of AcOH = 4.76). Evaluate the claim. Then, thinking about organic chemistry, why are nitro groups (which include a formal negative oxygen) almost never leaving groups in practice?

Preview of Chapter 4

Chapter 4 is the functional-groups vocabulary chapter. Bring the $pK_a$ intuition with you — you will use it to predict the properties of every functional group you learn.