Problem 30 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The hyperconjugative stabilities of tert-butyl cation and2-butene, respectively, are due to (a) \(\sigma \rightarrow \mathrm{p}\) (empty) and \(\sigma \rightarrow \pi^{*}\) electron delocalisations (b) \(\sigma \rightarrow \sigma^{*}\) and \(\sigma \rightarrow \pi\) electron delocalisations (c) \(\sigma \rightarrow \mathrm{p}\) (filled) and \(\sigma \rightarrow \pi\) electron delocalisations (d) \(\mathrm{p}\) (filled) \(\rightarrow \sigma^{*}\) and \(\sigma \rightarrow \pi^{*}\) electron delocalisations

Step-by-Step Solution

Answer

The correct answer is (a) \(\sigma \rightarrow \text{p}\) (empty) and \(\sigma \rightarrow \pi^{*}\) electron delocalisations.

Step 1: Identify Hyperconjugation in Tert-butyl Cation

Tert-butyl cation is a carbocation with a positively charged carbon atom, which is sp2 hybridized. The stability of this carbocation is enhanced by hyperconjugation, where an adjacent \sigma-bond (typically C-H bond) can interact with the empty p-orbital of the cation, allowing electron delocalization from the \sigma-bond to the empty p-orbital. This interaction is described as \(\sigma \rightarrow \text{p}\) (empty) electron delocalization.

Step 2: Identify Hyperconjugation in 2-butene

2-butene is an alkene with a \pi-bond between carbon atoms. In this molecule, hyperconjugation involves the interaction of a C-H \sigma-bond with the \pi^{*} antibonding orbital of the double bond, allowing for stabilization. This is described as \(\sigma \rightarrow \pi^{*}\) electron delocalization.

Step 3: Choose the Correct Option

Comparing the identified hyperconjugative interactions in both molecules with the given options, the correct choice must describe \(\sigma \rightarrow \text{p}\) (empty) for the tert-butyl cation and \(\sigma \rightarrow \pi^{*}\) for 2-butene. The option that matches this description is (a) \(\sigma \rightarrow \text{p}\) (empty) and \(\sigma \rightarrow \pi^{*}\) electron delocalisations.

Key Concepts

Tert-butyl cation stability

The tert-butyl cation is a frequently encountered species in organic chemistry, known for its surprising stability compared to other carbocations. A carbocation, by definition, harbors a positively charged carbon atom that is starved of electrons. This makes it highly reactive under normal circumstances. However, the tert-butyl cation showcases exceptional stability for a couple of reasons, one of which is hyperconjugation.
During hyperconjugation, σ-bonds (particularly C-H bonds) from neighboring atoms overlap with the empty p-orbital of the positively charged carbon. This overlap allows for electron density to partly shift into the empty p-orbital, effectively distributing the positive charge across a larger area and thus stabilizing the cation.
Some key points about this concept include:

• The more C-H bonds available for hyperconjugation, the more stabilized the cation becomes.
• The phenomenon is essentially a delocalization of charge, helping to reduce its energetic instability.

This interaction is often denoted by the notation \( \sigma \rightarrow \text{p} \) (empty) electron delocalization.

2-butene stabilization

The stability of 2-butene, a simple alkene, also benefits from the concept of hyperconjugation. Alkenes contain a π-bond between two carbon atoms, which can engage in a fascinating interaction known as \( \sigma \rightarrow \pi^{*} \) delocalization.
In 2-butene, the C-H bonds position adjacent to the carbon-carbon double bond. These σ-bonds can partially transfer electron density into the π* (pi-antibonding) orbital of the alkene. This molecular interaction provides additional stabilization by delocalizing electron density from the C-H σ-bonds to the π* orbitals.

• This electron delocalization in 2-butene helps lower the alkene's energy, making it more stable than might initially be expected.
• This process enhances the overall electron-cloud distribution, reinforcing the double bond itself.

Such stabilization is crucial in understanding the reactivity and properties of alkenes like 2-butene, assisting chemists in predicting and explaining chemical behavior.

Electron delocalization

In chemical species, electron delocalization is a critical concept that contributes prominently to stability and reactivity. It refers to the spread of electron density over several atoms rather than being confined between two.
Electron delocalization is central to the stability observed in molecules like the tert-butyl cation and 2-butene. Through hyperconjugation, electrons in nearby σ-bonds are partly redistributed into empty or antibonding orbitals, distributing the electron cloud more evenly across the structure. This distribution minimizes areas of high energy concentration.

• Delocalization aids in reducing repulsion between electrons by allowing them to occupy a larger space, increasing stability.
• It is a critical concept for understanding resonance structures, aromaticity, and many other phenomena in organic chemistry.

Whether through hyperconjugation in carbocations or double bonds, electron delocalization is a pervasive mechanism that accounts for much of the stability seen in organic molecules.

Sigma bond interactions

Sigma bonds (\( \sigma \)-bonds) are the strong single bonds between atoms, commonly represented in chemistry as the bonding between two nuclei's orbitals that allows for free rotation around the bond axis.
In the context of hyperconjugation and stabilization, sigma bond interactions play a pivotal role. The process involves \( \sigma \)-bonds interacting with either empty p-orbitals or available π* orbitals, facilitating electron delocalization that contributes to molecular stability.

• Sigma bonds possess electron density that can "spill over" into adjacent areas, like empty p-orbitals in carbocations.
• This interaction is typically weak but significant enough to impact the overall energy and configuration of a molecule.

Understanding sigma bond interactions sheds light on the fundamental operations of hyperconjugation, providing insight into how electron clouds shift to stabilize and maintain the integrity of various chemical structures.