Question

Choose the correct option(s). (A) As the more hyperconjugating structures form in alkene, bond length of double bond decrease. (B) Isotopic effect is observed in hyperconjugation. (C) \(\mathrm{H}_{3} \mathrm{C}^{\oplus} \mathrm{CH}_{3}\) has 9 hyperconjugation structures involving only \(\mathrm{C}-\mathrm{H}\) bond. (D) Unidirectional hyperconjugation increases stability of isobutene compared to trans-but-2-ene.

Short answer

The correct options are (B), (C), and (D). Option (B) is correct as the isotopic effect can be observed in hyperconjugation. Option (C) is correct as \(\mathrm{H}_{3} \mathrm{C}^{\oplus} \mathrm{CH}_{3}\) has 9 hyperconjugation structures involving only C-H bonds. Option (D) is correct as unidirectional hyperconjugation increases the stability of isobutene compared to trans-but-2-ene.

Step-by-step solution

Understanding hyperconjugation

Hyperconjugation is the stabilizing interaction that results from the interaction of the electrons in a sigma bond (usually C-H or C-C) with an adjacent empty or partially filled p-orbital to distribute the charge. This effect is commonly found in alkenes, carbocations, and radicals.

Option (A): Bond lengths in alkenes and hyperconjugation

As more hyperconjugating structures form in an alkene, the double bond character decreases and the single bond character increases. This change results in an increase in the bond length of the double bond. Therefore, this option is incorrect as it states that bond length decreases with more hyperconjugating structures.

Option (B): Isotopic effect and hyperconjugation

The isotopic effect is observed in hyperconjugation as the rate of reaction and stability depend on the composition of the isotopes involved. Heavier isotopes, such as deuterium, can have a stronger hyperconjugative effect due to their lower vibrational frequency, leading to better overlap with orbitals involved in hyperconjugation. Therefore, option (B) is correct.

Option (C): Hyperconjugation structures in \(\mathrm{H}_{3} \mathrm{C}^{\oplus} \mathrm{CH}_{3}\)

\(\mathrm{H}_{3} \mathrm{C}^{\oplus} \mathrm{CH}_{3}\), or tert-butyl carbocation, has a total of 9 alpha hydrogens attached to adjacent carbon atoms. Each of these 9 hydrogens can participate in hyperconjugation, forming 9 hyperconjugating structures involving only C-H bonds. Therefore, option (C) is correct.

Option (D): Stability of isobutene and trans-but-2-ene

Isobutene (2-methylpropene) has 6 alpha hydrogens that can participate in hyperconjugation, leading to an increase in stability. Trans-but-2-ene, on the other hand, has only 4 alpha hydrogens. Hyperconjugation in trans-but-2-ene doesn't add significant stability, unlike isobutene. Therefore, isobutene is more stable as a result of the unidirectional hyperconjugation involving 6 alpha hydrogens. Option (D) is correct. In conclusion, the correct options are (B), (C), and (D).

Key concepts

Alkene Bond Length

Understanding the intricacies of alkene bond length is crucial when diving into the world of organic chemistry. At a glance, an alkene consists of a double bond between two carbon atoms. This double bond is made up of one sigma bond and one pi bond.

Now, you might be wondering about hyperconjugation in this context. This phenomenon involves electrons in sigma bonds, such as C-H bonds, that can interact with adjacent pi systems. Interestingly, hyperconjugative structures can cause an increase in the single bond character of the double bond. This means the bond length of the alkene can actually increase. This may seem counterintuitive since more 'structures' could suggest a stronger, shorter bond, but in organic chemistry, the story is a different one.

The key takeaway here is that with increased hyperconjugation, we should expect to see a lengthier, less double-bond-character iconic alkene bond. That's why it's crucial to note that any considerable number of hyperconjugating structures won't compact the bond but stretch it to a more single-bond-like state.

Isotopic Effect in Hyperconjugation

Hyperconjugation's charm doesn't end with sigma and pi orbital interactions. Another fascinating aspect of hyperconjugation involves isotopic effects.

Let's talk isotopes. These are atoms of the same element bearing different mass due to a variance in neutron numbers. For example, the hydrogen atom has a heavier sibling called deuterium. In the world of hyperconjugation, an isotopic shift can influence the whole game. Heavier isotopes like deuterium don't vibrate as quickly as their lighter equivalents. Because of this, when they're involved in hyperconjugation, they form more stable bonds due to a better overlap of their orbitals with the pi system.

So, imagine a molecular substitution - replacing a hydrogen with deuterium - and watch hyperconjugation shift gears. It's this intricate dance of nature that permits unique differences within isotopic families to play distinct roles in chemical reactions and stability.

Tert-Butyl Carbocation Stability

Imagine the tert-butyl carbocation - a positively charged carbon at the center of three other carbons, much like a tripod. This carbocation's stability is an intriguing subject. How can such a charged species be stable, you ask? The answer lies within hyperconjugation.

With its nine alpha hydrogens each eager to share their electrons via sigma bonds with the empty p-orbital of the carbocation, the tert-butyl carbocation becomes a celebrated figure in stability. Each hydrogen atom brings its electron to the party, sharing it with the carbocation, thereby delocalizing the charge across multiple structures.

Through these hyperconjugating interactions, there's a spread of positive charge over a larger area, reducing the electron deficiency of the central carbon. This molecular generosity, where hydrogen atoms lend a helping electron, miraculously shores up the tert-butyl carbocation, making it one of the more stable carbocations in organic chemistry.

Stabilization of Alkenes

Alkenes, with their double bonds, are fundamental to organic chemistry and serve as a linchpin for many reactions. But what adds to their stability? Once again, hyperconjugation is a star player.

As discussed earlier, hyperconjugation allows the electrons in sigma bonds to interact with nearby pi orbitals. This capability to share electron density over a broader area lends stability to the molecule. For instance, let's take isobutene and compare it with trans-but-2-ene.

Isobutene, with its additional methyl group, has more alpha hydrogens that can engage in hyperconjugation, thus spreading out the electron density and bolstering stability. Trans-but-2-ene, lacking this additional group and having fewer alpha hydrogens, stands as less stable because it has fewer such interactions to contribute to its electron stability. It all boils down to hyperconjugation's magic touch - weaving sigma and pi bonds together to foster molecular serenity.