Chapter 5 — Exercises

Thirty-five problems covering conformations, thermodynamics, and kinetics. ∗ = full solution in appendix.

Section A — Conformations of open-chain alkanes

5.1∗ Draw Newman projections of staggered and eclipsed ethane, looking down the C−C bond. Identify which is more stable and by how much.

5.2 Butane has four distinct conformations along the C2-C3 bond: anti, gauche, eclipsed (methyl-H), and eclipsed (methyl-methyl). Rank them by stability and state approximate energy differences.

5.3 Draw Newman projections of butane along C2-C3 for: (a) anti (b) gauche (c) eclipsed with methyl-methyl overlap

5.4∗ At room temperature, what fraction of butane is in the anti vs. gauche conformation? (Use $K_{eq} = e^{-\Delta G/RT}$, with $\Delta G = 0.9$ kcal/mol, T = 298 K, R = 1.987 × 10⁻³ kcal/(mol·K). Remember there are two gauche wells.)

5.5 Why is pentane more anti-dominant than butane at the same temperature? (Hint: multiple C-C bonds.)

5.6 (challenge) 2,3-dimethylbutane has two tertiary carbons connected by a C-C bond. Draw Newman projections along that bond for the staggered conformations. How many distinct staggered conformations are there? Rank them.

Section B — Cyclohexane and its substituents

5.7∗ Draw the two chair conformations of methylcyclohexane. Which is more stable, and by how much?

5.8 What is the A-value for a tert-butyl group? At equilibrium, approximately what fraction of tert-butylcyclohexane has the t-Bu axial?

5.9 (moderate) For 1,2-dimethylcyclohexane (cis isomer), draw both chair conformations. Identify which carbons are axial and which are equatorial in each chair. Are the two chairs equivalent in energy?

5.10 Compare the more-stable chair of cis-1,3-dimethylcyclohexane vs. trans-1,3-dimethylcyclohexane. Which isomer is more stable overall, and why?

5.11 (challenge) In glucose's β-pyranose form, all five substituents (four OH and one CH₂OH) are equatorial. Draw the chair. Why is this such a stable conformation?

5.12 Cyclopropane has angle strain. Estimate the strain energy per $CH_2$ based on the combustion enthalpy table in the chapter.

Section C — Thermodynamics

5.13∗ Using bond dissociation energies (approximate values in Chapter 2), estimate $\Delta H$ for the combustion of ethane: $$2\,CH_3CH_3 + 7\,O_2 \to 4\,CO_2 + 6\,H_2O$$

5.14 Compute $K_{eq}$ at 298 K for a reaction with $\Delta G = −2$ kcal/mol. Compute it for $\Delta G = −10$ kcal/mol.

5.15 (moderate) If the enthalpy of a reaction is −5 kcal/mol and the entropy change is −20 cal/(mol·K), is the reaction favorable at 298 K? At 500 K?

5.16 Rank the following by enthalpy of combustion per CH₂ (most negative first): cyclopropane, cyclobutane, cyclohexane. Explain.

Section D — Kinetics

5.17∗ A reaction has $E_a = 20$ kcal/mol and a rate constant of $10^{-3}$ s⁻¹ at 25 °C. What is the rate constant at 75 °C? (Use Arrhenius; R = 1.987 × 10⁻³ kcal/(mol·K).)

5.18 Sketch a reaction-coordinate diagram for an exothermic ($\Delta G < 0$) reaction with $E_a = 15$ kcal/mol. Label reactants, products, TS, $E_a$, $\Delta G$.

5.19 Sketch a diagram for an endothermic reaction ($\Delta G > 0$). Which way does the equilibrium lie?

5.20 (moderate) Using the Hammond postulate, predict whether the TS for a highly exothermic reaction is early or late. Does it look more like the reactants or the products?

5.21 (challenge) A two-step mechanism has two transition states (TS1 and TS2) and one intermediate. Sketch the diagram. Identify the rate-determining step (the one with the higher barrier).

Section E — Kinetic vs. thermodynamic control

5.22∗ Under kinetic control, the major product reflects what property? Under thermodynamic control, the major product reflects what property? Give a brief definition of each.

5.23 An $\alpha,\beta$-unsaturated enone can be attacked by a nucleophile at either the carbonyl (1,2-addition) or the β-carbon (1,4-addition). Kinetic control favors 1,2; thermodynamic control favors 1,4. Under what conditions would you use each? (Preview of Chapter 29.)

5.24 A reaction gives product A as 95% of the mixture when run at low temperature, but only 60% at high temperature. Interpret using kinetic vs. thermodynamic control.

Section F — Computational and biological

5.25 (computational) In Avogadro, build cyclohexane. Optimize (geometry minimum). View in chair. Rotate and measure a few internal bond angles to confirm they are all ~109.5°.

5.26 (computational) Build methylcyclohexane. Optimize. Check: is the methyl axial or equatorial? What is the reported energy?

5.27 (computational) Manually place the methyl in the axial position in Avogadro and re-optimize. Compare energies. You should see ~1.7 kcal/mol higher.

5.28 (biological) The steroid cholesterol is a molecule with four fused rings, of which three are six-membered cyclohexanes. Describe (without looking up) how this highly fused structure constrains the conformations of each ring.

5.29 (biological) Why is the chair conformation of $\beta$-D-glucose so important for its biological use? (Consider accessibility of the anomeric center, membrane crossing, and enzyme specificity.)

Section G — Cumulative challenges

5.30∗ A student computes the $\Delta G$ of a reaction as −15 kcal/mol, so it will happen. She tries to run the reaction at 25 °C. Nothing happens after 24 hours. Explain.

5.31 (challenge) A researcher reports that heating a reaction mixture from 25 °C to 60 °C increases the rate by a factor of 100. Estimate $E_a$ using the Arrhenius equation.

5.32 For the isomerization of cis- to trans-2-butene, $\Delta G \approx -1$ kcal/mol. At room temperature, about what fraction of 2-butene is trans (at equilibrium)?

5.33 (challenge) When is it reasonable to approximate $\Delta G \approx \Delta H$? When is the entropy term important?

Section H — Preview

5.34 Conformational analysis will return in Chapter 10 when we consider the geometry of the $S_{N}2$ transition state. Predict (without being told): for $S_{N}2$ on a secondary alkyl halide in a ring, will the reaction prefer axial or equatorial leaving-group geometry?

5.35 The 1,3-diaxial interaction of Chapter 5 is the same kind of steric repulsion that will govern E2 elimination stereochemistry in Chapter 12. Why might steric strain matter for transition-state energies too?

Preview of Chapter 6

Chapter 6 introduces IR and mass spectrometry. Bring your functional-group vocabulary from Chapter 4; IR identifies functional groups by their vibrations.