$Tertiary > Secondary > Primary > CH_3^+$
Carbocation Stability Explained by Hyperconjugation
This question asks us to identify the stability trend of carbocations that is best explained by hyperconjugation. A carbocation is a molecule containing a positively charged carbon atom.
Understanding Hyperconjugation Theory
Hyperconjugation is a key concept in organic chemistry used to explain the stability of molecules, particularly those with charged centers like carbocations or species with adjacent pi bonds.
- It involves the delocalization of electrons from adjacent sigma bonds (usually C-H or C-C bonds) into an adjacent empty or partially filled p-orbital.
- In the case of carbocations, the empty p-orbital is on the positively charged carbon.
- This overlap allows the positive charge to spread out or be delocalized over a larger area, which stabilizes the carbocation.
- The more sigma bonds that can overlap with the empty p-orbital, the greater the stabilization effect.
Relating Carbocation Structure to Stability
The stability of a carbocation depends on the number of alkyl groups attached to the positively charged carbon atom. Alkyl groups have C-H bonds on the carbon atom directly attached to the positively charged carbon. These are called alpha-hydrogens.
- Tertiary Carbocation ($R_3C^+$): Has three alkyl groups attached to the $C^+$. This typically provides the maximum number of alpha-hydrogens (up to 9, e.g., in $(CH_3)_3C^+$).
- Secondary Carbocation ($R_2CH^+$): Has two alkyl groups attached to the $C^+$. This provides fewer alpha-hydrogens (up to 6, e.g., in $(CH_3)_2CH^+$).
- Primary Carbocation ($RCH_2^+$): Has one alkyl group attached to the $C^+$. This provides even fewer alpha-hydrogens (up to 3, e.g., in $CH_3CH_2^+$).
- Methyl Carbocation ($CH_3^+$): Has no alkyl groups attached to the $C^+$. It has zero alpha-hydrogens.
Stability Trend Determination via Hyperconjugation
Hyperconjugation theory predicts that carbocation stability increases with the number of alpha-hydrogens available for overlap with the empty p-orbital of the $C^+$. Therefore:
- Tertiary carbocations are the most stable because they have the most alpha-hydrogens (up to 9), leading to extensive delocalization.
- Secondary carbocations are less stable than tertiary but more stable than primary, as they have fewer alpha-hydrogens (up to 6).
- Primary carbocations are less stable still, with only a few alpha-hydrogens (up to 3).
- The methyl carbocation ($CH_3^+$) is the least stable because it lacks any alpha-hydrogens and cannot benefit from hyperconjugation.
We can visualize this comparison:
| Carbocation Type | Number of $\alpha$-Hydrogens | Stability based on Hyperconjugation |
| Tertiary ($R_3C^+$) | Maximum (e.g., 9) | Most Stable |
| Secondary ($R_2CH^+$) | Intermediate (e.g., 6) | Intermediate Stability |
| Primary ($RCH_2^+$) | Minimum (e.g., 3) | Less Stable |
| Methyl ($CH_3^+$) | Zero | Least Stable |
Final Stability Order
Based on the extent of hyperconjugation, the stability order of carbocations is directly determined by the number of available alpha-hydrogens. The trend supported by hyperconjugation theory is:
$Tertiary > Secondary > Primary > CH_3^+$
This means a tertiary carbocation is more stable than a secondary carbocation, which is more stable than a primary carbocation, which is the most stable among these related to $CH_3^+$.
Important Questions from Chemistry
Select the option that is true regarding the following two statements labelled Assertion (A) and Reason (R).
Assertion (A): Copper wire in iron sulphate solution shows no visible reaction.
Reason (R): Copper is less reactive than iron.- Which of the following are compressed gases commonly used in daily life? (i) LPG for cooking (ii) Oxygen in hospitals (iii) CNG in vehicles (iv) Water in bottles
- Given below are two statements. Select the correct answer from the options given for these statements.
Statement I: Metals low in the activity series can be obtained from their oxides without using any reducing agent.
Statement II: Heating alone is enough to reduce the oxides of these metals to pure metal. - Which of the following statements about Thomson's model are correct?
i. Atoms consist of a positively charged sphere.
ii. Electrons are randomly moving outside the sphere.
iii. The number of positive and negative charges is equal.
iv. The atom is overall neutral. - Fluorine has 7 electrons in its outermost shell. Its valency is:
