Problem 39 - A Complete Resource Book in Chemistry for JEE Main

Question

In buta- 1,3 -diene, the \(\mathrm{C}_{2}-\mathrm{C}_{3}\) bond length is (a) \(1.20 \AA\) (b) \(1.35 \AA\) (c) \(1.54 \AA\) (d) \(1.46 \AA\)

Step-by-Step Solution

Answer

In buta-1,3-diene, the C2-C3 bond length is 1.46 4A (option d).

Step 1: Understand the Structure

Buta-1,3-diene is a conjugated diene with the structure H2C=CH-CH=CH2. It consists of two double bonds separated by a single bond.

Step 2: Determine the Bond Type

The C2-C3 bond is between the two double bonds in buta-1,3-diene, making it a single bond that is part of a conjugated system. Single bonds in such systems are shorter than typical single bonds due to partial double-bond character.

Step 3: Analyze Typical Bond Lengths

In conjugated systems, the typical bond length for a C-C single bond (typically 1.54 4A) falls in between that of a single and a double bond due to resonance. A standard C=C bond is about 1.34 4A, and a C-C bond in such a system is generally between these values.

Step 4: Compare With Given Options

Compare the C2-C3 bond length between typical values for single and double bonds with the options provided: 1.20, 1.35, 1.54, and 1.46 4A. The value closest to the expected bond length for a single bond in a conjugated system is 1.46 4A.

Key Concepts

Bond Length

In chemistry, bond length is a crucial parameter that defines the distance between two bonded atoms. In the context of buta-1,3-diene, the bond length of the C2-C3 bond is quite interesting.

Bond length is influenced by the type of bond present. In conjugated dienes like buta-1,3-diene, we find that the C2-C3 bond length typically falls between a standard single and a double bond due to resonance effects. This makes accurate measurement crucial for understanding molecular behavior and reactivity.

• Typical C-C single bond length: 1.54 Å
• Typical C=C double bond length: 1.34 Å
• Conjugated diene C-C bond: Generally around 1.46 Å

This intermediate bond length allows for unique electron delocalization and resonance in conjugated systems.

Single Bond

A single bond, often represented in structural formulas by a single line connecting two atoms, results from the sharing of one pair of electrons between two atoms. It is the most basic form of a covalent bond and forms a fundamental part of various chemical structures.

In the structure of buta-1,3-diene, the C2-C3 single bond holds an unusual place because it resides in a conjugated system. While it's typically expected to be around 1.54 Å in length, the influence of resonance in the system actually shortens this bond to approximately 1.46 Å. This partial double-bond character makes the single bond in such systems stronger and shorter than typical single bonds.

• Forms between two atoms sharing electrons
• Allows free rotation in isolated systems
• Strengthened by resonance in conjugated systems

Resonance

Resonance is a key concept that helps explain the behavior of electrons within a molecule. It occurs when electrons can be delocalized across two or more adjacent atoms, enhancing the stability of a molecule.

In conjugated dienes like buta-1,3-diene, resonance arises from overlapping p-orbitals across double bonds and the intervening single bond. This results in a blend of single and double bond characteristics, intensifying the stability and altering the typical bond lengths and strengths.

• Leads to electron delocalization
• Strengthens and shortens bonds
• Results in mixed bond characteristics

Understanding resonance is essential for predicting the physical properties of conjugated molecules.

Double Bond

A double bond is a type of covalent bond in which two pairs of electrons are shared between two atoms. In the structure of buta-1,3-diene, the double bonds play a pivotal role in the behavior and arrangement of the molecule.

Double bonds are generally shorter and stronger than single bonds, characteristically around 1.34 Å in length compared to the 1.54 Å of single bonds. However, in a conjugated system like buta-1,3-diene, these double bonds contribute to overall electron delocalization, allowing for unique properties such as stability and reactivity due to the resonance effect.

• Involves sharing two pairs of electrons
• Restricts rotational freedom
• Shorter and stronger than single bonds
• Critical for resonance in conjugated systems

Double bonds contribute significantly to the special characteristics of conjugated dienes.