Chapter 5 — Alkanes, Conformations, and an Introduction to Thermodynamics and Kinetics

"The rate of a reaction does not tell you whether it happens. The thermodynamics tells you whether it can. The kinetics tells you whether it does." — chemistry aphorism

Chapter 4 gave you the vocabulary. This chapter gives you the energetics: how much energy is in a bond, how molecules choose among possible 3D arrangements, and how fast reactions run. These ideas — energetics of conformations, enthalpy of reactions, activation energy — underpin every mechanism you will meet in the rest of the book.

By the end of the chapter you should be able to:

• Draw and interpret Newman projections for any alkane.
• Predict the most-stable conformation of any alkane chain and any cyclohexane derivative.
• Compute the approximate enthalpy of a reaction from bond energies.
• Interpret a reaction-coordinate diagram — identify reactants, products, transition states, activation energy.
• Apply the Hammond postulate to predict transition-state structure.
• Distinguish thermodynamic from kinetic control.

5.1 Alkanes: the simplest carbon framework

Alkanes are hydrocarbons with only single bonds (saturated). General formula $C_nH_{2n+2}$ for open chains; $C_nH_{2n}$ for cycloalkanes. Every carbon is $sp^3$. Every bond angle is approximately $109.5°$.

Alkanes are the least reactive class of organic molecules. Their $C-C$ and $C-H$ bonds are strong (83 and 105 kcal/mol) and essentially nonpolar. At room temperature they do not react with most acids, bases, oxidizing agents, or reducing agents in common use. The major useful reaction of alkanes is combustion, and that requires a spark or high temperature.

That makes alkanes the ideal starting point for thinking about molecular energetics. Nothing is going on chemically — just the atoms sitting there, interacting through $\sigma$ bonds and through non-bonded interactions. The only thing that varies is the 3D arrangement of atoms. And even that modest variation turns out to have energetic consequences that show up later, in every reaction of every other chapter.

The homologous series

Consecutive members of a family like the alkanes are called a homologous series. Each member differs from the next by one $CH_2$ unit. Properties change systematically with chain length — boiling point goes up, melting point (eventually) goes up, solubility in water goes down.

The pattern is familiar: at room temperature, $C_1$ to $C_4$ are gases; $C_5$ to ~$C_{17}$ are liquids; heavier alkanes are solids. This is the scale on which the fuel industry operates — natural gas is mostly $CH_4$, gasoline is predominantly $C_5$–$C_{12}$, diesel is $C_{12}$–$C_{22}$ (Chapter 4 case study 2).

5.2 Conformations of ethane

Now for the first big idea of the chapter: molecules rotate.

Ethane ($CH_3-CH_3$) has a single $C-C$ bond. The two methyl groups can rotate relative to each other around that bond. If you built ethane in Avogadro in Chapter 1 and rotated it, you saw this directly.

Two extreme arrangements:

• Staggered conformation. Looking down the $C-C$ axis, the hydrogens on the front carbon are positioned between the hydrogens on the back carbon — maximally separated.
• Eclipsed conformation. Hydrogens on the front carbon are aligned with hydrogens on the back carbon — overlapping when viewed end-on.

These two arrangements are different conformations — different 3D shapes that a molecule can adopt by rotation around single bonds, without breaking any bonds. A given molecule spends its time interconverting among its possible conformations.

The Newman projection

To draw conformations efficiently, chemists use Newman projections. Sighting along the bond in question, the front carbon is shown as a dot (with three bonds radiating out) and the back carbon is shown as a circle behind it (with three bonds emerging from the rim).

Figure 5.1 — Newman projections of ethane. Looking down the $C-C$ bond, the front carbon (with its three H's) is shown as a dot with three bonds; the back carbon (with its three H's) is shown as a circle. Left: the staggered conformation, with H's of the back carbon positioned in between the H's of the front carbon. Right: the eclipsed conformation, with front and back H's lined up. The dihedral angle between a front H and the nearest back H is 60° for staggered and 0° for eclipsed.

Torsional strain and rotation barriers

The staggered conformation of ethane is about 3 kcal/mol more stable than the eclipsed conformation. Why?

The explanation is called torsional strain (or "Pitzer strain"). In the eclipsed conformation, the $C-H$ bonding electrons on the front carbon are spatially close to the $C-H$ bonding electrons on the back carbon. Electron-electron repulsion — combined with a subtler hyperconjugative effect — makes this arrangement less stable than when the bonds are staggered apart.

Three kilocalories per mole is not much. At room temperature, $RT \approx 0.6$ kcal/mol — so molecules routinely have enough thermal energy to cross a 3-kcal/mol barrier. Ethane is therefore rapidly interconverting between its staggered and eclipsed forms at any instant. But the staggered form is populated more often (by a Boltzmann factor of $e^{3/0.6} \approx 150$), so on average, most ethane molecules are in or near the staggered configuration at any given instant.

This small number — 3 kcal/mol — is the archetype of what will eventually control reaction rates, selectivities, and product ratios throughout the book. Small energy differences, multiplied by Boltzmann factors, become large population differences.

5.3 Conformations of butane

Butane ($CH_3CH_2CH_2CH_3$) has multiple $C-C$ bonds to rotate around, but the most informative is the central $C2-C3$ bond. Four distinct conformations (and the barriers between them):

• Anti — the two methyl groups on opposite sides (180° apart). Most stable.
• Gauche — methyls at 60° to each other (staggered, but methyls close). About 0.9 kcal/mol less stable than anti.
• Eclipsed (methyl-H) — methyls at 120° to each other. About 3.6 kcal/mol higher than anti.
• Eclipsed (methyl-methyl) — methyls at 0° to each other. About 5.7 kcal/mol higher than anti — the most unstable conformation.

Figure 5.2 — Conformational energy of butane as a function of the $C2-C3$ dihedral angle. The anti conformation (180°) is most stable; two equivalent gauche conformations (60° and 300°) are 0.9 kcal/mol higher; eclipsed conformations (0°, 120°, 240°) are substantially higher. The maximum — methyl eclipsing methyl — sits at about 5.7 kcal/mol.

New contributor: the methyl-methyl gauche interaction introduces steric strain — two groups that are close to each other in space repelling each other through van der Waals contact. Steric strain will return in every chapter from here on: in $S_N2$ rates (bulky substrates react slowly), in aldol selectivity (bulky groups sort), in drug-receptor binding (shapes match or do not).

The 0.9 kcal/mol gauche-vs-anti difference means that at room temperature, butane is approximately 72% anti and 28% gauche (split between two equivalent gauche forms). Not overwhelming, but a real preference.

5.4 Cyclohexane — where conformational analysis pays off

Cyclic alkanes add a new complication. The ring closes on itself, which constrains which conformations are accessible. And depending on the ring size, there can be angle strain (bond angles forced away from their ideal 109.5°) and torsional strain (bonds forced into eclipsing relationships).

• Cyclopropane (three-membered ring): huge angle strain (60° bond angles vs. ideal 109.5°) and full eclipsing of adjacent $C-H$ bonds. Strain energy about 27 kcal/mol. Ring-opening reactions dominate cyclopropane chemistry.
• Cyclobutane (four): still significant angle strain (88°); ring is slightly puckered to relieve some torsional strain. Strain energy ~26 kcal/mol.
• Cyclopentane (five): minimal angle strain (approximately 104° when puckered into an envelope shape). Strain ~6 kcal/mol.
• Cyclohexane (six): essentially strain-free. This is the single most important ring size in organic chemistry. Many natural products, many drugs, and all of the sugars (as their cyclic pyranose forms) contain cyclohexane-like six-membered rings.

The chair conformation

Cyclohexane is not flat. A flat hexagonal ring of six $sp^3$ carbons would have 120° internal angles — not 109.5° — and every $C-H$ bond would eclipse its neighbor. A pucker is necessary.

The energetically preferred shape is the chair conformation: the ring puckers such that three alternate carbons are "up" and three alternate carbons are "down," making a chair-like shape. In the chair, every internal angle is 109.5° (no angle strain) and every adjacent $C-H$ is staggered (no torsional strain). Cyclohexane in the chair conformation is as happy as an $sp^3$ carbon can be.

Figure 5.3 — The chair conformation of cyclohexane. Six carbons with alternating up-down puckering. Each carbon has two hydrogens: one pointing along the axis perpendicular to the average plane of the ring (axial, dark), and one pointing outward, roughly in the plane (equatorial, light). Three axials point up; three point down. Three equatorials point "up" on average; three point "down." Every bond angle is ~109.5° and every adjacent C-H is staggered — minimum strain.

Axial and equatorial positions

On a chair cyclohexane, each carbon has two hydrogens. One points roughly perpendicular to the average plane of the ring (straight up or straight down, alternating) — this is an axial hydrogen. The other points outward, roughly in the plane of the ring — this is an equatorial hydrogen.

When a substituent is placed on a cyclohexane (instead of a hydrogen), it can be either axial or equatorial — and the two possibilities are different in energy.

The ring flip

A chair cyclohexane can interconvert to another chair conformation by a series of bond rotations (the "ring flip"). The flip goes through various twist-boat and boat intermediates at higher energy, with a total barrier of about 10.5 kcal/mol. At room temperature this is fast — the ring flips approximately 100,000 times per second.

After a ring flip, every axial substituent has become equatorial, and every equatorial substituent has become axial. The chair "inverts" like turning a glove inside out.

For a simple cyclohexane (all six carbons identical), the two chair forms are equivalent in energy and the flip is thermodynamically neutral. For a substituted cyclohexane, one chair form is usually more stable than the other, because axial substituents are more strained than equatorial ones.

Why equatorial is better: the 1,3-diaxial interaction

When a substituent is axial, it is on the same side of the ring as two other axial hydrogens — the ones on C3 and C5 relative to the substituent's C1. These three axial bonds are close in space — each pair about 2.5 Å apart for simple hydrogens. A substituent bigger than hydrogen (a methyl, for example) crowds into those hydrogens: the 1,3-diaxial interaction.

For a methyl group, the 1,3-diaxial strain amounts to about 1.7 kcal/mol per interaction, and there are two such interactions (one with each H at the 3 and 5 positions), for a total of ~1.7 kcal/mol preference for equatorial.

In the more useful form, for a substituent with A-value (a tabulated measure of the axial-to-equatorial energy penalty):

At equilibrium, the chair with the substituent equatorial dominates. For t-butyl, the preference is so strong (4.9 kcal/mol = $K_{eq} \approx 4000$) that a t-butylcyclohexane exists essentially entirely in the equatorial-t-butyl chair.

Worked Problem 5.1 — Two substituents on a cyclohexane

Predict the more stable chair of cis-1,3-dimethylcyclohexane.

In the cis isomer, the two methyls are on the same face of the ring. In one chair, both methyls are equatorial. In the other chair, both are axial. The all-equatorial chair is lower in energy by 2 × 1.7 = 3.4 kcal/mol. Predominant form: both-equatorial.

Contrast: in trans-1,3-dimethylcyclohexane, one methyl is axial and one is equatorial in either chair. The two chairs are equivalent (both have one ax and one eq methyl). No preference.

Chapter 7 returns to cis/trans with the full stereochemistry framework. For now, notice that the chair analysis lets you predict which 3D arrangement dominates.

Biological Connection 5.1 — Cyclohexane chairs in biology

Glucose and fructose and almost every common sugar exist primarily in their cyclic (pyranose or furanose) forms. For glucose, the pyranose form is a six-membered ring with an oxygen in place of one of the carbons. The ring adopts a chair conformation. In the most stable chair of $\beta$-D-glucose, all five substituents — four hydroxyls and the $CH_2OH$ arm — are equatorial. This is why $\beta$-D-glucose is so exceptionally stable and why it is the form nature chose as its preferred biological sugar: it is, geometrically, the most relaxed possible arrangement of a six-membered-ring carbohydrate. Evolution saw to it.

Chapter 32 returns to this in depth.

5.5 Thermodynamics: ΔG, ΔH, ΔS

The energetic reasoning we have been doing — comparing conformations — uses the same tools as the thermodynamics of reactions. Recall from general chemistry:

$$\Delta G = \Delta H - T \Delta S$$

• $\Delta G$ is the Gibbs free energy change of a process.
• $\Delta H$ is the enthalpy change (heat released or absorbed at constant pressure).
• $\Delta S$ is the entropy change (change in disorder or multiplicity of microstates).
• $T$ is temperature in Kelvin.

A reaction is thermodynamically favorable when $\Delta G < 0$. The equilibrium constant is related to $\Delta G$ by:

$$\Delta G = -RT \ln K_{eq}$$

or equivalently $K_{eq} = e^{-\Delta G / RT}$.

At room temperature (298 K), $RT \approx 0.59$ kcal/mol. A $\Delta G$ of 1 kcal/mol corresponds to $K_{eq} \approx 5$ (not overwhelming). A $\Delta G$ of 6 kcal/mol corresponds to $K_{eq} \approx 10^4$ (essentially irreversible). A $\Delta G$ of −10 kcal/mol corresponds to $K_{eq} \approx 10^7$.

Useful rules of thumb: - Every 1.4 kcal/mol of $\Delta G$ changes $K_{eq}$ by a factor of 10. - Every 2.8 kcal/mol changes $K_{eq}$ by a factor of 100.

Bond dissociation energies and enthalpy of reactions

The enthalpy change of a reaction can be estimated by bond bookkeeping:

$$\Delta H_{rxn} \approx \Sigma \text{BDE (bonds broken)} - \Sigma \text{BDE (bonds formed)}$$

This is an approximation — it ignores strain energy changes, solvation differences, and more subtle effects — but it gets you within 5–10 kcal/mol for most reactions, which is often close enough to know whether a reaction is enthalpically favorable or not.

Worked Problem 5.2 — Combustion of methane

$$CH_4 + 2\,O_2 \to CO_2 + 2\,H_2O$$

Bonds broken: four $C-H$ bonds (4 × 105 = 420 kcal/mol) + two $O=O$ bonds (2 × 119 = 238). Total = 658 kcal/mol.

Bonds formed: two $C=O$ bonds (2 × 192 = 384) + four $O-H$ bonds (4 × 119 = 476). Total = 860 kcal/mol.

$\Delta H_{rxn} \approx 658 - 860 = -202$ kcal/mol. Combustion releases about 202 kcal/mol of energy. The actual value is −213 kcal/mol — the bond-bookkeeping estimate is off by only 5%.

This is why methane is a good fuel: large negative $\Delta H$ means a lot of heat released per mole burned.

Most combustion reactions have similar order-of-magnitude enthalpies. The useful chemistry of alkanes is, essentially, combustion — which is why alkanes are the feedstocks for fuels.

Heats of combustion as a measure of strain

The enthalpy of combustion ($\Delta H_{comb}$) per $CH_2$ unit should be constant for a homologous series if every $CH_2$ is energetically identical. It is not quite constant: small deviations reveal strain.

For cycloalkanes, $\Delta H_{comb} / CH_2$ (per methylene):

Cyclohexane is the least strained, as expected. Cyclopropane and cyclobutane are the most strained — the combustion enthalpy reveals exactly how much (≈27 kcal/mol for cyclopropane, in rough agreement with earlier estimates).

5.6 Kinetics: rates, activation energies, and the transition state

Thermodynamics says whether a reaction can happen. Kinetics says whether it does happen on a useful timescale.

A reaction's rate is proportional to the concentrations of its reactants, with an exponential dependence on temperature. For a simple reaction $A + B \to$ products:

$$rate = k[A][B]$$

where $k$ is the rate constant. The rate constant depends on temperature according to the Arrhenius equation:

$$k = A e^{-E_a / RT}$$

or equivalently $\ln k = \ln A - E_a / RT$.

• $A$ is the pre-exponential factor (related to collision frequency).
• $E_a$ is the activation energy — the minimum energy needed to surmount the reaction barrier.
• The exponential dependence on $E_a/RT$ is what gives reactions their extreme temperature sensitivity.

At room temperature, $RT \approx 0.59$ kcal/mol. A reaction with $E_a = 10$ kcal/mol has $e^{-10/0.59} \approx e^{-17}$, a very small fraction of molecules with enough energy — but still enough that the reaction happens at a measurable rate if the concentrations are reasonable. A reaction with $E_a = 50$ kcal/mol has virtually no molecules with enough energy at room temperature and is effectively forbidden unless heated.

Rule of thumb for $E_a$ and rate

• $E_a = 15$ kcal/mol: reaction is fast at room temperature (seconds to minutes).
• $E_a = 20$ kcal/mol: reaction is moderate at room temperature (hours to days).
• $E_a = 25$ kcal/mol: reaction requires heat (refluxing solvent, maybe 80 °C).
• $E_a = 35$ kcal/mol: reaction requires substantial heat (high-boiling solvent).
• $E_a = 50$ kcal/mol: the reaction effectively does not happen at ordinary temperatures.

A rough rule: every 10 °C increase in temperature doubles the reaction rate (for typical $E_a$ in the 15–25 kcal/mol range).

The reaction-coordinate diagram

Figure 5.4 — A reaction-coordinate diagram. The x-axis is a schematic "progress" through the reaction; the y-axis is energy. Reactants sit on the left; products on the right. The maximum — the transition state (TS) — is the top of the barrier. The height of the barrier above the reactants is the activation energy ($E_a$). The vertical drop from reactants to products is $\Delta G$ of the reaction. If $\Delta G < 0$, the reaction is exothermic/exergonic; it runs downhill.

The transition state is not a real molecule. It is the highest-energy configuration along the reaction path — a single geometry that exists for about a vibrational period (around $10^{-13}$ s) before collapsing into either reactants or products. The transition state is usually drawn with partial bonds (dashed lines) where the bonds are in transition.

The Hammond postulate

The Hammond postulate (George Hammond, 1955) gives you a rule for guessing what the transition state looks like:

The transition state resembles in structure whichever is closer to it in energy — reactant or product.

In practice:

• Exothermic reactions (product below reactant) have "early" transition states that resemble reactants.
• Endothermic reactions (product above reactant) have "late" transition states that resemble products.
• Highly exothermic reactions have TSs that look almost exactly like reactants.

Why this matters: when we analyze mechanisms, we often ask "which TS is lower in energy?" The Hammond postulate says to look at the product-like intermediate if the step is endothermic — the one whose electronics are closer to the TS. This rule will be central in Chapter 15 (why Markovnikov addition happens) and throughout the rest of the book.

Thermodynamic vs. kinetic control

Two different regimes for how product ratios are decided:

• Thermodynamic control: the reaction is reversible; products equilibrate. Major product is the most stable one.
• Kinetic control: the reaction is effectively irreversible; products reflect transition-state energies, not product stabilities. Major product is the one formed via the lowest-$E_a$ pathway.

Reactions run at low temperature tend to be kinetically controlled (not enough energy to reverse). Reactions run at high temperature tend to be thermodynamically controlled (enough energy to reverse and re-equilibrate). This distinction will come back in Chapter 19 (Diels-Alder adducts), Chapter 27 (enolates), and elsewhere.

Computational Exercise 5.1

Build cyclohexane in Avogadro and optimize. Observe the chair shape. Use the measure-bond-angle tool to confirm the bond angles are all ~110°.

Now build methylcyclohexane. Optimize. Take a screenshot. Is the methyl axial or equatorial in the optimized structure? (It should be equatorial — the force field's minimum.)

Now manually rotate the methyl into the axial position (select the methyl, apply a rotation, re-optimize). Compare the energies reported. You should see roughly 1.7 kcal/mol higher energy for axial methyl — the A-value.

Common Mistake 5.1

Students often conflate $E_a$ with $\Delta G$. They are independent:

• $\Delta G$ tells you whether the reaction is thermodynamically favorable.
• $E_a$ tells you how fast the reaction proceeds.

A reaction can be extremely favorable ($\Delta G = -50$ kcal/mol) but have a huge activation barrier ($E_a = 50$ kcal/mol) and run at essentially zero rate at room temperature. Example: hydrogen + oxygen at room temperature.

Always check both when evaluating a reaction.

5.7 Summary and connections

What you have learned:

1. Alkanes are the simplest and least reactive class of organic compounds. Their chemistry is almost entirely about 3D arrangement and energetics, which makes them the ideal entry point to conformational analysis and thermodynamics.

2. Conformations are different 3D arrangements accessible by bond rotation. Staggered is more stable than eclipsed by ~3 kcal/mol (ethane) because of torsional strain. Anti is more stable than gauche by ~0.9 kcal/mol (butane) because of steric strain.

3. Cyclohexane in the chair conformation is strain-free. Substituents prefer the equatorial position because axial groups encounter 1,3-diaxial interactions. The A-value quantifies how much.

4. Thermodynamics ($\Delta G = \Delta H - T\Delta S$) tells you whether a reaction can happen. $\Delta G < 0$ = favorable. $K_{eq} = e^{-\Delta G/RT}$; every 1.4 kcal/mol of $\Delta G$ corresponds to a factor of 10 in $K_{eq}$.

5. Kinetics (Arrhenius equation) tells you how fast. $E_a$ in the 15-25 kcal/mol range is the sweet spot for laboratory reactions at normal temperatures. Transition states are the highest-energy points on the reaction path; Hammond's postulate says they resemble whichever of reactants or products is closer to them in energy.

6. Thermodynamic vs. kinetic control is about whether the reaction equilibrates (major product reflects stability) or does not (major product reflects activation-energy ordering). An organic chemist who understands this distinction can often change the product ratio by changing the temperature.

Chapter 6 — the last chapter of Part I — introduces spectroscopy: infrared and mass spectrometry. Tools for identifying molecules by their vibrations (IR) and their mass fragments (MS). From there onward, every chapter uses spectra as diagnostic tools in parallel with mechanisms.

The habit to leave with: When you see any new reaction, ask both "is $\Delta G$ negative?" (thermodynamically favorable?) and "is $E_a$ low enough for this temperature?" (kinetically accessible?). Every successful reaction satisfies both. Failing to separate the two is the single most common analytical error in first-semester orgo.