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) \(1.46 \AA\)

Short answer

The Cbond length in buta-1,3-diene is 1.46 .

Step-by-step solution

Identify the Type of Bonding

Buta-1,3-diene contains alternating single and double carbon-carbon bonds, specifically a conjugated structure. The C\(_2\)-C\(_3\) bond that we are interested in is a single bond, which is part of this alternating structure.

Recall Typical Bond Lengths

Typically, a carbon-carbon single bond (C-C) has a bond length of approximately 1.54 Å, while a carbon-carbon double bond is shorter, around 1.34 Å. However, due to conjugation in buta-1,3-diene, we must consider partial double bond character.

Consider Conjugation Impact

The C\(_2\)-C\(_3\) bond in buta-1,3-diene has a partial double bond character due to conjugation, making it shorter than a standard single bond but longer than a pure double bond.

Evaluate the Options Based on Theory

Given that the C\(_2\)-C\(_3\) bond is a single bond with partial double-bond character, the bond length should be between the typical C-C single bond length (1.54 Å) and C=C double bond length (1.34 Å). Therefore, the bond length should be slightly shorter than 1.54 Å and slightly longer than 1.34 Å.

Choose the Nearest Correct Bond Length

Among the options provided, 1.46 Å is closest to this expected bond length range for a conjugated single bond, influenced by partial double bond character.

Key concepts

Conjugation Effect on Bond Length

In molecules like buta-1,3-diene, conjugation refers to the overlapping of p-orbitals across adjacent single and double bonds. This overlap allows

• Enhancement of electronic delocalization
• Decreased energy levels
• Increased stability of the molecule

What does this mean for bond length? The delocalization due to conjugation allows a blend of characteristics from both single and double bonds.

Because of this influence, a single bond in a conjugated system may not behave entirely like a typical single bond. Instead, its bond length is tweaked—usually shorter than a regular single bond, indicative of some double bond character without being as short as a true double bond.

Single and Double Carbon-Carbon Bonds

Carbon-carbon bonds come in two primary types:

• Single bond (\( \sigma \) bond): Typically measured at \(1.54 \text{ Å} \)
• Double bond (\( \sigma + \pi \) bonds): Typically measured at \(1.34 \text{ Å} \)

The difference in their bond lengths stems from the type and number of bonds they form.
The single bond consists of a \( \sigma \) bond, while the double bond comprises a \( \sigma \) and a \( \pi \) bond.

This presence of a \( \pi \) bond in a double bond brings the atoms closer together, resulting in a shorter bond length.

Partial Double Bond Character

A partial double bond character arises in conjugated systems like buta-1,3-diene due to resonance. This concept reflects a state between a single and a double bond. It signifies:

• Intermediate bond length
• Shared properties of both bond types

Due to resonance, the electrons in \(\pi\) bonds delocalize over multiple atoms.
The C\(_2\)-C\(_3\) bond appears shorter than a single bond but longer than a double bond.

This particular adjustment brings about enhanced structural stability and unique chemical properties.

Typical Bond Lengths

Understanding typical bond lengths is crucial for predicting molecular structure and reactivity. For carbon-carbon bonds, generally observed lengths are:

• Single bond: \(1.54 \text{ Å} \)
• Double bond: \(1.34 \text{ Å} \)
• In conjugated systems, such as buta-1,3-diene, \(1.46 \text{ Å} \) indicates a middle state.

The bond length of \(1.46 \text{ Å} \) reflects a compromise between single and double bonds due to partial double bond character.
This length is specifically significant in understanding conjugated systems because it provides insights into resonance influence and hybridization within the molecule.

Recognizing these variations helps in predicting how different molecular structures will behave in chemical reactions and how they arrange themselves in three-dimensional space.