Question

Draw line structures representing the most stable cation with the given molecular formula: a) \(\mathrm{C}_{3} \mathrm{H}_{7}^{+}\) b) \(\mathrm{C}_{4} \mathrm{H}_{9}{ }^{+}\) c) \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{~N}^{+}\) d) \(\mathrm{C}_{4} \mathrm{H}_{7}^{+}\)

Short answer

Based on the drawn molecular structures, describe the stabilization factors that apply to each of the following cations: a) The most stable C3H7+ cation has a tertiary carbocation, which is stabilized through hyperconjugation and inductive effects. b) The most stable C4H9+ cation has a tertiary carbocation and is stabilized by hyperconjugation. c) The C3H8N+ cation has a quaternary nitrogen center with a positive charge, which does not contain any specific stabilization factors like resonance or hyperconjugation, but it satisfies the molecular formula and maintains a complete octet on the nitrogen atom. d) The most stable C4H7+ cation has an allylic carbocation with resonance stabilization, which is a stronger stabilizing effect than hyperconjugation.

Step-by-step solution

a) C3H7+ Cation

For a C3H7+ cation, we can consider a 3-carbon chain with the positive charge on one of the carbons. This can result in three possible structures: primary, secondary, and tertiary carbocations. A tertiary carbocation is more stable than secondary and primary due to hyperconjugation and inductive effects. Thus, the most stable cation for C3H7+ has a tertiary carbocation: ``` H H H | | | H-C-C-C+ | H ```

b) C4H9+ Cation

For a C4H9+ cation, we work with a 4-carbon chain. A quaternary carbocation is not possible in this case. We can create two tertiary carbocations or a secondary carbocation. Among these possibilities, the one with the tertiary carbocation is more stable due to hyperconjugation. The most stable cation for C4H9+ has a tertiary carbocation: ``` H H H | | | H-C-C-C-C+ | | H H ```

c) C3H8N+ Cation

For a C3H8N+ cation, there is a nitrogen atom with a positive charge. The positively charged nitrogen has four bonds with the three carbons in the chain, thus forming a quaternary nitrogen center: ``` H H H | | | H-C-C-C-N+ | | | H H H ```

d) C4H7+ Cation

For a C4H7+ cation, there are fewer hydrogens than the C4H9+ cation. A double bond or a ring formation is necessary to satisfy the molecular formula. The most stable structure can be achieved through a double bond, which forms an allylic carbocation. The allylic carbocation exhibits resonance, and resonance stabilization is a stronger stabilizing effect than hyperconjugation. Consequently, the most stable structure for C4H7+ has an allylic carbocation with a double bond adjacent to the positively charged carbon: ``` H H H | | | H-C-C=C-C+ | H ```

Key concepts

Hyperconjugation

Hyperconjugation is an important concept when discussing the stability of carbocations. It involves the interaction between the filled orbitals of a C-H bond and an adjacent empty p-orbital of a positively charged carbon. This interaction allows for electron density to be delocalized, which in turn increases the stability of the carbocation.

For example, consider a tertiary carbocation compared to a secondary or primary one. A tertiary carbocation will have more hydrogen atoms bonded to adjacent carbon atoms. This translates to more C-H bonds available for hyperconjugation, spreading the positive charge across a larger area. Hyperconjugation helps stabilize the carbocation by:

• Decreasing the overall positive charge on the carbocation.
• Providing a partial overlap between filled orbitals and the empty p-orbital.
• Creating several contributing resonance structures where positive charge is more delocalized.

This delocalization results in a lower energy and more stable carbocation. This concept is particularly helpful in predicting the stability of carbocations like in the case of C3H7+ and C4H9+ cations.

Inductive Effects

Inductive effects play a key role in the stability of carbocations by influencing the distribution of electron density through a sigma bond. They arise from the polarization of sigma bonds due to differences in electronegativity between atoms or groups attached to the carbocation.

Groups that can donate electron density through the sigma bond, known as electron-donating groups, help stabilize a positive charge. Such groups include alkyl chains, which push electron density towards the carbocation and result in a lower overall energy state.

Inductive effects stabilize carbocations by:

• Reducing the positive charge on the carbon atom.
• Creating a more balanced distribution of charge across the molecule.

For instance, in the C4H9+ carbocation, the four carbon atoms create an inductive effect that stabilizes the positive charge on the tertiary carbon. These effects are additive, meaning that more alkyl groups contribute to an increased stabilization of the carbocation.

Resonance Stabilization

Resonance stabilization is a powerful stabilizing factor for carbocations, particularly those with structures allowing the delocalization of charge between atoms. This occurs when a carbocation has a structure that permits different resonance forms to exist.

Resonance allows electrons or positive charge to be "spread out" or delocalized over multiple atoms, which helps to stabilize the carbocation. For example, in the case of an allylic carbocation like C4H7+, resonance occurs because the positive charge can shift between the carbons adjacent to the double bond.

Key aspects of resonance stabilization include:

• The process creates multiple valid resonance structures, enhancing stability.
• Delocalization of the positive charge reduces the energy of the structure.
• Increased possibility of overlapping p-orbitals in a π-system.

Overall, resonance stabilization is often stronger than hyperconjugation or inductive effects, particularly in structures like allylic carbocations. This is why carbocations such as C4H7+ are considered especially stable—they benefit from the significant charge distribution of resonance.
Therefore, understanding resonance is crucial for predicting and comprehending the stability and reactivity of various carbocations in organic chemistry.