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) \(1.20 \mathrm{~A}\) (b) \(1.35 \mathrm{~A}\) (c) \(1.54 \mathrm{~A}\) (d) \(1.46 \mathrm{~A}\)

Step-by-Step Solution

Answer

The \(C_2-C_3\) bond length in buta-1,3-diene is approximately \(1.46 \mathrm{~A}\), so the answer is (d).

Step 1: Understand the structure of buta-1,3-diene

Buta-1,3-diene is an organic compound with the formula \(CH_2=CH-CH=CH_2\). It consists of four carbon atoms, with alternating single and double bonds that extend across the molecule.

Step 2: Identify the bond type for \(C_2-C_3\)

In the structure \(CH_2=CH-CH=CH_2\), the \(C_2-C_3\) bond is between a double bond \(C=C)\) and a single bond \(C-C)\), making it a bond within a conjugated system.

Step 3: Recall typical bond lengths

Within conjugated systems like buta-1,3-diene, \(C=C\) typically has a bond length of about \(1.34 \mathrm{~A}\) and \(C-C\) about \(1.54 \mathrm{~A}\). The \(C_2-C_3\) bond has partial double-bond character due to resonance, resulting in an average length.

Step 4: Calculate the approximate bond length

The \(C_2-C_3\) bond length is influenced by resonance and lies between a typical single and double bond. The typical length for such a bond in conjugated diene is approximately \(1.46 \mathrm{~A}\).

Step 5: Select the closest option

Comparing the calculated and options given, option (d) \(1.46 \mathrm{~A}\) is the closest match.

Key Concepts

Conjugated Systems

A conjugated system is a fascinating structural feature found in certain molecules. It consists of a sequence of alternating single and double bonds. The magic of conjugated systems, like that in buta-1,3-diene, arises from the delocalization of electrons. In these systems, electrons are not confined to a single bond or atom. Instead, they are spread across several adjacent atoms.

• This delocalization increases the stability of the molecule.
• Conjugated systems can absorb various forms of energy, affecting the molecule's color and reactivity.

Buta-1,3-diene, with its alternating single and double bonds, is a classic example of a conjugated system. This arrangement allows the electrons to move freely between the C=C and C-C bonds, giving the molecule unique chemical properties. Understanding this concept is key to predicting the behavior of molecules with similar patterns.

Bond Length

Bond length is the average distance between two bonded atoms' nuclei. In conjugated systems, bond lengths differ from those in typical single and double bonds due to electron delocalization. In buta-1,3-diene, the bond lengths result from the interaction of its conjugated system.

• Single bonds (C-C) in isolation often measure around 1.54 Å.
• Double bonds (C=C), on the other hand, are shorter, averaging about 1.34 Å.

However, in conjugated systems, the bond length is somewhat unique. As noted in the exercise, the ${C}_2-{C}_3$ bond is part of this conjugated system and combines properties of both double and single bonds. This explains why its bond length is approximately 1.46 Å, a value between that of a typical single and double bond. Such blending of lengths is due to the beneficial overlap of p-orbitals, allowing for shared electron states.

Resonance in Chemistry

Resonance is a crucial concept to grasp as it explains the stability and characteristics of conjugated systems. Resonance occurs when electrons in a molecule can occupy different positions across multiple configurations, or 'resonance structures.' These structures aren't actually separate; rather, they exist simultaneously, creating a hybrid that reflects average properties.

• This collective sharing of electrons enhances stability.
• Resonance helps account for intermediate bond lengths in molecules like buta-1,3-diene.

In buta-1,3-diene, resonance allows for partial double-bond character in what appears to be single bonds. This results in a bond length for the $C_2-C_3$ bond that is longer than a double bond but shorter than a single bond. Without understanding resonance, the prediction of such bond lengths in conjugated systems would be much more challenging. The concept highlights how electrons can be distributed in complex molecular structures and underscores the importance of electronic configuration in determining molecular properties.