Difficulty: Intermediate | Prerequisites: CHEM 2301 Ch. 5 Parts 1-2 (reaction types, polar reactions, nucleophiles/electrophiles), orbital hybridisation (sp2, sp3).
Carbocations are among the most important reactive intermediates in organic chemistry. They appear whenever a leaving group departs or whenever a bond breaks heterolytically to leave a carbon with only six electrons. Understanding which carbocations are stable (and why) lets you predict whether a rearrangement will occur, which product will form, and how fast the reaction will go. Energy diagrams tie all of this together by showing you the energetic landscape of a reaction: where the transition states are, where intermediates sit, and which step is rate-determining. If you can read an energy diagram and rank carbocation stability, you have the tools to reason through most of the mechanisms in this course.
Carbocations are positively charged, sp2-hybridised carbons with an empty p orbital. More substituted carbocations are more stable (3° > 2° > 1° > methyl) because of hyperconjugation from adjacent C-H bonds. Carbocations rearrange via hydride shifts or methyl shifts to reach a more stable form. Energy diagrams show activation energy (ΔG‡), overall energy change (ΔG), transition states, and intermediates, with the largest energy barrier determining the reaction rate.
Carbocation
A positively charged carbon with only six valence electrons and an empty p orbital. Carbocations are sp2-hybridised and planar. Think of it as: a carbon that is desperately short of electrons and will react with anything electron-rich nearby.
Hyperconjugation
The stabilising interaction between the filled C-H (or C-C) sigma bonding orbitals on adjacent carbons and the empty p orbital of the carbocation. More adjacent C-H bonds means more hyperconjugation and greater stability. In simple terms, neighbouring bonds donate a little electron density into the empty orbital, partially satisfying the positive charge.
Hydride shift (1,2-H shift)
A rearrangement in which a hydrogen atom and its bonding electrons migrate from an adjacent carbon to the carbocation centre, producing a more stable carbocation. Think of it as: the H (with both electrons) hops one carbon over to where the positive charge is.
Methyl shift (1,2-alkyl shift)
A rearrangement in which a methyl (or alkyl) group and its bonding electrons migrate to the carbocation centre. Less favourable than a hydride shift and occurs only when no adjacent hydrogen is available to shift. In simple terms, a CH₃ group slides over to stabilise the positive charge when there is no H to move instead.
Activation energy (ΔG‡)
The energy difference between the starting materials and the highest-energy transition state. Directly related to the rate of the reaction: a larger ΔG‡ means a slower reaction. Think of it as: the height of the hill the reaction must climb.
Transition state (TS)
The highest-energy point along a single reaction step. Bonds are partially formed and partially broken. A transition state cannot be isolated. In simple terms, the unstable peak of the energy hill, where the molecule is caught mid-transformation.
Reaction intermediate
A species that forms between two steps of a multi-step reaction. Less stable than reactants or products, but sits in an energy minimum (a valley between two transition-state peaks). Can sometimes be detected but is transient. Think of it as: a brief rest stop in the valley between two hills.
ΔG (Gibbs free energy change)
The difference in energy between the starting materials and the products. A negative ΔG means the reaction is exergonic (products are lower in energy). A positive ΔG means endergonic. In simple terms, tells you whether the reaction releases or absorbs energy overall.
Rate-determining step
The slowest step in a multi-step reaction, corresponding to the highest-energy transition state (the largest energy barrier). The overall rate of the reaction cannot exceed the rate of this step. Think of it as: the bottleneck that controls how fast the whole reaction goes.
Carbocations are sp2-hybridised, planar, and carry a formal positive charge. Their stability follows the substitution pattern:
Methyl cation (CH₃⁺): least stable
Primary (1°): one alkyl group attached to the positive carbon
Secondary (2°): two alkyl groups
Tertiary (3°): three alkyl groups, most stable
Stability order: methyl < 1° < 2° < 3°. More substituted carbocations are more stable.
The empty p orbital on the carbocation centre can overlap with filled C-H (or C-C) sigma bonds on adjacent carbons. This donation of electron density partially fills the empty orbital and spreads the positive charge over a larger area. More adjacent C-H bonds (more substitution) means more hyperconjugation and greater stabilisation.
A carbocation will only rearrange to form a product that is more stable than the starting material. Two types:
(A) Hydride shift (1,2-H shift): A hydrogen on the carbon adjacent to the carbocation migrates with its bonding electrons to the positively charged carbon. This converts a less stable carbocation into a more stable one (e.g. 2° → 3°). Hydride shifts are the more common rearrangement.
(B) Methyl shift (1,2-alkyl shift): When no adjacent hydrogen is available to shift, a methyl (or other alkyl) group migrates instead. Less favourable than a hydride shift. Example: a 1° carbocation with no adjacent H to shift can undergo a methyl shift to become a 3° carbocation.
Key rules:
A carbocation rearranges only if the product carbocation is more stable.
Hydride shifts are preferred over methyl shifts.
Methyl shifts occur only when no hydrogen is available on the adjacent carbon.
An energy diagram plots free energy (y-axis) against reaction progress (x-axis) and shows every transition state and intermediate along the way.
Transition states sit at energy maxima (hilltops). They represent the point at which bonds are partially broken and partially formed.
Intermediates sit at energy minima between transition states (valleys). They are real species but short-lived.
ΔG‡ (activation energy) is measured from the starting materials to the highest-energy transition state. It determines the rate: larger barrier means slower reaction.
ΔG (overall energy change) is measured from starting materials to products. Negative ΔG means the products are lower in energy (exergonic); positive ΔG means higher (endergonic).
Rate-determining step: In a multi-step reaction, the step with the largest energy barrier (highest transition state relative to its preceding minimum) is rate-determining. The largest barrier determines the overall reaction rate.
Example from lecture: the addition of HBr to ethylene is a two-step reaction. Step 1 forms a carbocation intermediate (higher-energy transition state, rate-determining). Step 2 is the nucleophilic attack of Br⁻ on the carbocation (lower barrier). The energy diagram shows two humps with a valley (the intermediate) between them.
Carbocation rearrangements are not just textbook curiosities. In petroleum refining, acid-catalysed isomerisation of straight-chain alkanes into branched alkanes (which burn more efficiently) proceeds through carbocation intermediates that rearrange to the most stable form. Energy diagrams are the standard tool chemical engineers use to compare catalysed and uncatalysed reaction pathways when designing industrial processes.
Students often think ΔG‡ (activation energy) and ΔG (overall energy change) are the same thing. They are not. ΔG‡ tells you about rate (how fast). ΔG tells you about thermodynamics (how favourable). A reaction can have a large ΔG‡ (slow) but a very negative ΔG (strongly favoured).
A common error is assuming that carbocations always rearrange. They rearrange only when the product carbocation is more stable than the starting one. A 3° carbocation has nowhere better to go.
Students sometimes confuse intermediates with transition states. An intermediate sits in an energy minimum and can (in principle) be detected. A transition state sits at an energy maximum and cannot be isolated.
Many students forget that a hydride shift moves H⁻ (a hydrogen with both bonding electrons), not H⁺. The proton does not jump on its own.
⚠️ You must be able to rank carbocation stability: methyl < 1° < 2° < 3°. Expect this on every exam (LOs 5g, 5h).
⚠️ Be able to predict whether a carbocation will rearrange, and if so, whether by hydride shift or methyl shift.
⚠️ Know that a hydride shift is always preferred over a methyl shift when both are possible.
⚠️ Be able to read and draw energy diagrams: label the transition states, intermediates, ΔG‡, and ΔG. Identify the rate-determining step as the one with the largest barrier (LOs 5f).
⚠️ On an energy diagram, the rate-determining step corresponds to the highest transition state measured from the starting materials, not the tallest individual hump.
Rank in order of increasing stability: tertiary carbocation, methyl cation, secondary carbocation, primary carbocation. Methyl < primary < secondary < tertiary.
True or false: A carbocation is sp3-hybridised. False. A carbocation is sp2-hybridised with an empty p orbital.
Fill in the blank: Hyperconjugation stabilises a carbocation by donating electron density from adjacent ______ into the empty p orbital. C-H (or C-C) sigma bonds.
True or false: The rate-determining step is the step with the smallest activation energy barrier. False. It is the step with the largest activation energy barrier.
Fill in the blank: A reaction intermediate sits at an energy ______ on an energy diagram, while a transition state sits at an energy ______. Minimum; maximum.
Q: Rank the following carbocations from least to most stable: (CH₃)₃C⁺, CH₃CH₂⁺, (CH₃)₂CH⁺, CH₃⁺.
A: CH₃⁺ (methyl, least stable) < CH₃CH₂⁺ (1°) < (CH₃)₂CH⁺ (2°) < (CH₃)₃C⁺ (3°, most stable).
Q: A secondary carbocation sits adjacent to a carbon bearing three hydrogens. Will a rearrangement occur, and if so, what type?
A: A hydride shift is possible if it produces a more stable (tertiary) carbocation. Since a hydrogen is available on the adjacent carbon, a 1,2-hydride shift would occur in preference to a methyl shift.
Q: Explain why a methyl shift from a primary carbocation to form a tertiary carbocation is observed, but a methyl shift from a secondary carbocation to form another secondary carbocation is not.
A: A carbocation rearranges only to form a more stable carbocation. A 1° to 3° shift is a large stability gain, so it proceeds. A 2° to 2° shift offers no stability improvement, so there is no driving force for the rearrangement.
Q: On an energy diagram for a two-step reaction, the first transition state is higher in energy than the second. Which step is rate-determining?
A: Step 1 is rate-determining because its transition state represents the largest energy barrier measured from the starting materials. The overall rate cannot exceed the rate of the slowest step.
Q: A reaction has ΔG‡ = 85 kJ/mol and ΔG = -40 kJ/mol. Is this reaction fast or slow? Is it exergonic or endergonic?
A: The relatively large ΔG‡ suggests a moderate-to-slow reaction (the barrier is substantial). The negative ΔG means the reaction is exergonic: products are lower in energy than starting materials, so the reaction is thermodynamically favourable.
Carbocation stability is the foundation for understanding Markovnikov's rule in alkene addition reactions (coming up next). The energy diagram framework applies to every reaction you will study for the rest of the course, including SN1/SN2 and E1/E2, where the number of steps and the shape of the diagram differ but the principles (ΔG‡ controls rate, ΔG controls thermodynamic favourability) stay the same. Rearrangements will reappear in any reaction that passes through a carbocation intermediate, so recognising when a shift can occur is a skill you will use repeatedly.
Carbocation, carbocation stability, carbocation rearrangement, hydride shift, 1,2-hydride shift, methyl shift, 1,2-alkyl shift, hyperconjugation, sp2, empty p orbital, tertiary carbocation, secondary carbocation, primary carbocation, methyl cation, activation energy, ΔG‡, delta G double dagger, transition state, reaction intermediate, energy diagram, reaction coordinate diagram, rate-determining step, rate-limiting step, exergonic, endergonic, ΔG, Gibbs free energy, CHEM 2301, organic chemistry I, Chapter 5, LOs 5f, 5g, 5h