Question

Number of carbocation from the following that are not stabilized by hyperconjugation is _________ .

Answer 1

Correct Answer: 5

In the given structures, only certain carbocations can be stabilized by hyperconjugation. The carbocations which are not stabilized by hyperconjugation are:

Therefore, the number of carbocations that are not stabilized by hyperconjugation is 5.

Answer 2

The problem asks to identify and count the number of carbocations from a given list that are not stabilized by the hyperconjugation effect.

Concept Used:

Hyperconjugation is a stabilizing interaction that involves the delocalization of sigma (\(\sigma\)) electrons of a C-H bond of an alkyl group directly attached to an atom with an unshared p-orbital (like a carbocation). This is also known as no-bond resonance.

The necessary condition for a carbocation to exhibit hyperconjugation is the presence of at least one hydrogen atom on the \(\alpha\)-carbon (the carbon atom adjacent to the positively charged carbon). This hydrogen is called an \(\alpha\)-hydrogen. Carbocations with zero \(\alpha\)-hydrogens are not stabilized by hyperconjugation.

\[ \text{No. of Hyperconjugating Structures} = \text{No. of } \alpha\text{-hydrogens} \]

Step-by-Step Solution:

We will analyze each carbocation to count its number of \(\alpha\)-hydrogens.

1. 3-Methylpentan-2-yl cation:

The carbocation is \( (CH_3)_2CH-\overset{+}{C}H-CH_2CH_3 \). The positively charged carbon is attached to a \(CH\) group and a \(CH_2\) group.

• Number of \(\alpha\)-hydrogens = 1 (from \(CH\)) + 2 (from \(CH_2\)) = 3.

Since it has \(\alpha\)-hydrogens, it is stabilized by hyperconjugation.

 

2. Di-tert-butylmethyl cation:

The carbocation is \( ((CH_3)_3C)_2\overset{+}{C}H \). The positively charged carbon is attached to two quaternary carbons of the tert-butyl groups. These \(\alpha\)-carbons have no hydrogen atoms attached.

• Number of \(\alpha\)-hydrogens = 0.

This carbocation is not stabilized by hyperconjugation.

 

3. Methyl cation:

The carbocation is \( \overset{+}{C}H_3 \). There are no \(\alpha\)-carbon atoms adjacent to the positively charged carbon.

• Number of \(\alpha\)-hydrogens = 0.

This carbocation is not stabilized by hyperconjugation.

 

4. Cyclopentadienyl cation:

In this cyclic carbocation, the positively charged carbon is \(sp^2\)-hybridized and is adjacent to two other \(sp^2\)-hybridized carbons of the double bonds. Hyperconjugation requires \(\alpha\)-hydrogens on an \(sp^3\)-hybridized carbon for effective orbital overlap. This condition is not met.

• Number of \(\alpha\)-hydrogens on \(sp^3\) carbons = 0.

This carbocation is not stabilized by hyperconjugation. (It is also destabilized by being anti-aromatic with 4\(\pi\) electrons).

 

5. Methoxymethyl cation:

The carbocation is \( \overset{+}{C}H_2-OCH_3 \). The positively charged carbon is bonded to an oxygen atom, not a carbon atom. Therefore, there is no \(\alpha\)-carbon.

• Number of \(\alpha\)-hydrogens = 0.

This carbocation is not stabilized by hyperconjugation. (It is stabilized by resonance with the lone pair on oxygen).

 

6. tert-Butyl cation:

The carbocation is \( (CH_3)_3\overset{+}{C} \). The central positively charged carbon is attached to three methyl (\(-CH_3\)) groups.

• Number of \(\alpha\)-hydrogens = 3 + 3 + 3 = 9.

It is highly stabilized by hyperconjugation.

 

7. (Dimethylamino)methyl cation:

The carbocation is \( (CH_3)_2N-\overset{+}{C}H_2 \). The positively charged carbon is bonded to a nitrogen atom, not a carbon atom. There is no \(\alpha\)-carbon.

• Number of \(\alpha\)-hydrogens = 0.

This carbocation is not stabilized by hyperconjugation. (It is strongly stabilized by resonance with the lone pair on nitrogen).

 

Final Computation & Result:

The carbocations from the list that are not stabilized by hyperconjugation (i.e., have zero \(\alpha\)-hydrogens) are:

1. Di-tert-butylmethyl cation
2. Methyl cation
3. Cyclopentadienyl cation
4. Methoxymethyl cation
5. (Dimethylamino)methyl cation

The total number of such carbocations is 5.