Chemistry
Rate of reaction in case of Electrophilic Addition Reaction via Classical Carbocation
Step-by-step chemistry solution: Rate of reaction in case of Electrophilic Addition Reaction via Classical Carbocation
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1. What the question is really asking
We have two alkenes
| Alkene | Structure | Substitution of the C=C bond |
|---|---|---|
| propene | CH₂=CH‑CH₃ | monosubstituted (one alkyl group attached to the double bond) |
| but‑2‑ene | CH₃‑CH=CH‑CH₃ | disubstituted (two alkyl groups attached to the double bond) |
Both are allowed to undergo an electrophilic addition that proceeds through a classical carbocation intermediate (e.g., addition of H⁺/X⁻, HBr, HCl, H₂SO₄, etc.).
The problem asks: Which alkene reacts faster, and why? In other words, we must decide which substrate has the higher rate constant for the rate‑determining step of the electrophilic addition.
2. Step‑by‑step reasoning
2.1 General mechanism for electrophilic addition to alkenes
π‑bond (nucleophile) + electrophile (E⁺) → π‑complex (transition state) → carbocation intermediate → nucleophilic attack → product
- The rate‑determining step (RDS) is almost always the initial attack of the electrophile on the π‑bond.
- The RDS is therefore governed by how nucleophilic (electron‑rich) the double bond is and by how easily it can stabilize the incipient positive charge that develops in the transition state.
Both of these factors are strongly correlated with alkene substitution:
| Substitution | Electron‑donating effect of alkyl groups (inductive + hyperconjugation) | Ability to delocalise/ stabilize a developing positive charge |
|---|---|---|
| 0 (ethylene) | none | very poor |
| 1 (monosubstituted) | modest (one alkyl donor) | modest |
| 2 (disubstituted) | larger (two donors) | better |
| 3 (trisubstituted) | even larger | even better |
| 4 (tetrasubstituted) | maximal | maximal |
Hence, more substituted alkenes are both better nucleophiles and give more stabilized carbocation‑like transition states.
2.2 Apply the rule to the two substrates
| Alkene | Substitution at C=C | Expected nucleophilicity | Expected carbocation stability |
|---|---|---|---|
| Propene | 1‑alkyl (monosubstituted) | Lower (only one donating alkyl) | Less stable (primary‑like) |
| But‑2‑ene | 2‑alkyl (disubstituted) | Higher (two donating alkyls) | More stable (secondary‑like) |
Thus the transition state for the electrophilic attack on but‑2‑ene is lower in energy than that for propene, leading to a larger rate constant.
2.3 What about “α‑hydrogens” (the 6 α‑H vs 5 α‑H argument)?
The number of α‑hydrogens (hydrogens on the carbon bearing the positive charge in the final carbocation) is not a controlling factor for the rate of the addition.
- The stability of the carbocation is dominated by hyperconjugation from adjacent C–H and C–C σ‑bonds, not by the count of α‑hydrogens alone.
- A disubstituted carbocation (as formed from but‑2‑ene) has two alkyl groups that donate electron density via hyperconjugation, which outweighs the small numerical difference in α‑hydrogen count.
Consequently, the “more α‑hydrogens = more stable carbocation” argument is an oversimplification and does not reverse the substitution trend.
2.4 Quantitative perspective (optional)
Kinetic studies on the addition of HBr to alkenes give approximate relative rate constants (k) at 25 °C:
| Alkene (R‑CH=CH‑R’) | k (relative to ethylene = 1) |
|---|---|
| Ethylene | 1 |
| Propene (CH₂=CH‑CH₃) | ≈ 5–6 |
| trans‑But‑2‑ene (CH₃‑CH=CH‑CH₃) | ≈ 15–20 |
| 2‑Methyl‑2‑butene (tert‑butyl‑substituted) | ≈ 30–40 |
These numbers illustrate the 2‑fold–3‑fold increase in rate when moving from a monosubstituted to a disubstituted alkene.
2.5 Final answer
But‑2‑ene reacts faster than propene in electrophilic addition reactions that proceed through a classical carbocation. The higher rate is due to the greater substitution of the double bond, which makes the π‑bond more nucleophilic and stabilises the developing positive charge in the transition state.
3. Short “Common Mistakes” checklist
| Mistake | Why it’s wrong | How to avoid it |
|---|---|---|
| Thinking “more α‑hydrogens = faster reaction.” | α‑Hydrogen count does not dictate the energy of the RDS; substitution does. | Focus on substitution level (mono‑, di‑, tri‑) when comparing alkenes. |
| Confusing product stability with reaction rate. | A more stable product does not guarantee a faster reaction; the RDS is what matters. | Identify the rate‑determining step (electrophile attack) and examine the transition‑state stabilization. |
| Ignoring hyperconjugation from alkyl groups. | Alkyl groups donate electron density via σ‑C–H and σ‑C–C bonds, lowering activation energy. | Remember: each alkyl substituent contributes roughly 1–2 kcal mol⁻¹ to carbocation/transition‑state stabilization. |
| Assuming that “primary > secondary > tertiary” always applies. | That hierarchy is for carbocation stability after formation; in electrophilic addition the RDS depends on how well the alkene can support a developing charge, which follows the same order but is applied to the alkene, not the product. | Apply the substitution rule directly to the alkene’s double bond. |
| Neglecting solvent or acid strength. | In some special cases (e.g., very weak acids, highly polar solvents) the mechanism may shift to a concerted pathway. | The problem explicitly states “classical carbocation” → assume the usual acid‑catalysed mechanism. |
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