Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following alkenes: 1\. \(\mathrm{H}_{2} \mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{2} \mathrm{CH}_{3}\right) \mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}\) 2\. \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{3}\right) \mathrm{CH}_{2} \mathrm{CH}_{3}\) 3\. \(\mathrm{CH}_{3} \mathrm{CH}=\mathrm{C}\left(\mathrm{CH}_{3}\right) \mathrm{CH}\left(\mathrm{CH}_{3}\right)_{2}^{5}\) The correct sequence of increasing order of stability of these alkenes is (a) \(3,1,2\) (b) \(1,3,2\) (c) \(1,2,3\) (d) \(2,1,3\)

Step-by-Step Solution

Answer

The increasing order of stability is 1, 2, 3. Correct choice is (c).

Step 1: Understanding Alkene Stability

Alkenes' stability is influenced by the degree of substitution at the double bond. The more substituted the alkene (i.e., the more alkyl groups attached to the carbon atoms of the double bond), the more stable it is. This is due to the hyperconjugation and inductive effects that stabilize the alkene.

Step 2: Analyze Alkene 1

Alkene 1 is \(\text{H}_{2} \text{C} = \text{C}\text{(CH}_{2} \text{CH}_3\text{)} \text{CH(CH}_{3})_{2}\), which has two additional substituents on one side of the double bond. Its structure can be seen as a simple terminal alkene with a substitution on one carbon of the double bond.

Step 3: Analyze Alkene 2

Alkene 2 is \(\left(\text{CH}_3\right)_2 \text{C} = \text{C}\left(\text{CH}_3\right) \text{CH}_2 \text{CH}_3\) and it is tri-substituted. The double bond has three substituents, making it more stable than alkene 1 due to higher substitution.

Step 4: Analyze Alkene 3

Alkene 3 is \(\text{CH}_3 \text{CH} = \text{C}\left(\text{CH}_3\right)\text{CH}\left(\text{CH}_3\right)_2^{5}\), a tetra-substituted alkene. It has four substituents around the double bond, offering the highest stability among the three due to maximum hyperconjugative stabilization.

Step 5: Arranging Alkenes by Stability

Based on the substitution and hence the stability, the correct order is: Most stable is alkene 3 (tetra-substituted), followed by alkene 2 (tri-substituted), and least stable is alkene 1 (di-substituted). Thus, the increasing order of stability is 1, 2, 3.

Key Concepts

Substitution Effect

Alkenes, which contain a carbon-carbon double bond, show a fascinating feature called substitution effect. This effect arises when different groups are attached to the carbons of the double bond. Generally, the more substituted an alkene is, the more stable it becomes. Consider an analogy of how more legs make a table steadier. Similarly,

• A monosubstituted alkene has one substituent group around the double bond.
• A disubstituted alkene has two, and so on.
• Tetra-substituted alkenes, with four such groups, are the most stable.

This stability increase via substitution mostly comes from electronic interactions and steric benefits provided by the substituents. Each additional substituted group can distribute electronic density, which results in a more energetically favorable arrangement of atoms. This means subtle structural changes can lead to significant increases in stability.

Hyperconjugation

Hyperconjugation is a concept that explains the stability of alkenes and other carbocations. It involves the interaction between the electrons in a sigma bond (usually C-H or C-C) and an adjacent empty or partially filled p-orbital, allowing delocalization of electrons. This happens because the sigma electrons of C-H bonds of alkyl groups attached to a double bond can overlap with the vacant p-orbitals of the sp2 carbon atoms in the double bond.
During hyperconjugation:

• Electrons are spread over multiple atoms, effectively lowering electron-electron repulsion.
• The electron delocalization provides additional stability to the molecule.

The strength of hyperconjugation depends on the number of overlapping C-H bonds from the substituents around the double bond. Therefore, alkenes with more alkyl substituents exhibit a higher degree of hyperconjugation, leading to greater stability.

Inductive Effect

The inductive effect is another aspect that affects alkene stability, and it involves the transmission of charge through a chain of atoms in a molecule. This effect is all about the polarization of the sigma bonds within molecules.
Here's how the inductive effect works in alkenes:

• Alkyl groups are electron-releasing groups that push electron density towards the double bond.
• This increases the electron cloud at the site of the double bond, stabilizing it.
• More substituents surrounding the double bond mean more electron donation, hence greater stability.

The inductive effect complements hyperconjugation. Together, they enhance the overall stability of substituted alkenes. It is one of the reasons why tri-substituted and tetra-substituted alkenes exhibit higher stability compared to less substituted counterparts.