Question

The heat of hydrogenation of 1-hexene is \(126 \mathrm{kJmol}\). When a second double bond is introduced in 1 -hexene, the heat of hydrogenation of the resulting compound is found to be \(230 \mathrm{~kJ} \mathrm{~mol}^{-1}\). The resulting compound (diene) is (A) 1,5 -hexadiene (B) 1,4 -hexadiene (C) 1,3 -hexadiene (D) 2,4-hexadiene

Short answer

The correct diene is (D) 2,4-hexadiene, as it has a less stable conjugation and its heat of hydrogenation (230 kJ/mol) is closer to the combined heat of hydrogenation of two isolated double bonds (252 kJ/mol).

Step-by-step solution

Recall the concept of heat of hydrogenation

Heat of hydrogenation is the amount of energy released when one mole of a compound reacts with hydrogen to form a single-bonded compound. It is an exothermic process, so the heat of hydrogenation is always negative. Stabilized compounds generally have lower heat of hydrogenation, while less stabilized compounds have higher heat of hydrogenation.

Compare the heat of hydrogenation of 1-hexene and the diene

We are given that the heat of hydrogenation of 1-hexene is 126 kJ/mol and the diene is 230 kJ/mol. Since the heat of hydrogenation of the diene is higher than that of 1-hexene, it means the diene is less stable than 1-hexene.

Compare the stability of each diene

Now, we can analyze the stability of each diene compound and their respective heats of hydrogenation. a) 1,5-hexadiene: This compound consists of two isolated double bonds where there is no conjugation between them. Therefore, it has two separate heats of hydrogenation like 1-hexene. b) 1,4-hexadiene: This compound also has two isolated double bonds, so both the double bonds have separate heats of hydrogenation. c) 1,3-hexadiene: This compound has a conjugated diene system, meaning that the two double bonds share electron density, resulting in increased stability and lower heat of hydrogenation. d) 2,4-hexadiene: This compound also has a conjugated diene system with increased stability and lower heat of hydrogenation than isolated dienes.

Determine the diene with the closest heat of hydrogenation

Considering the stability of each diene, we can estimate the heat of hydrogenation of each diene by adding up the heat of hydrogenation values for each double bond and comparing them to the given heat of hydrogenation of the diene. From our analysis in Step 3, it is clear that 1,3-hexadiene and 2,4-hexadiene have a lower heat of hydrogenation than 1,5-hexadiene and 1,4-hexadiene because they are conjugated dienes. The combined heat of hydrogenation of two isolated double bonds is approximately 126 * 2 = 252 kJ/mol. Since the diene with the heat of hydrogenation of 230 kJ/mol is higher than that for 1-hexene but lower than that for two isolated double bonds, we can conclude that it is either 1,3-hexadiene or 2,4-hexadiene.

Identify the correct diene

However, since the heat of hydrogenation of the diene is 230 kJ/mol, which is closer to the combined heat of hydrogenation of two isolated double bonds (252 kJ/mol), we can determine that the correct diene is the one with a less stable conjugation. Between 1,3-hexadiene and 2,4-hexadiene, 2,4-hexadiene is less stable due to its double bond closer to the end of the carbon chain. Therefore, the correct diene is (D) 2,4-hexadiene.

Key concepts

Stability of Dienes

The stability of dienes is an important concept when evaluating their chemical properties. Dienes are compounds with two double bonds, and their stability can significantly vary depending on their structure.

• **Isolated Dienes**: These have double bonds separated by at least one sp3 hybridized carbon. The double bonds do not affect each other directly, leading to a higher heat of hydrogenation, indicating less stability.
• **Conjugated Dienes**: Here, double bonds alternate with single bonds, sharing electron density, which results in increased stability. The lower heat of hydrogenation compared to isolated dienes is a characteristic of their stability.
• **Cumulative Dienes**: Also known as "allenes", these have adjacent double bonds and can be quite reactive, often less stable than isolated or conjugated dienes.

The increased stability of conjugated dienes is due to electron delocalization - a phenomenon where electrons are not confined to a single bond or atom, thus providing stability to the molecule. In terms of heat of hydrogenation, this means conjugated dienes release less energy when hydrogenated compared to isolated dienes.

Conjugated Diene System

The conjugated diene system is characterized by alternating double and single bonds along a carbon chain. This specific arrangement allows the formation of pi systems, leading to unique mechanical and chemical properties.

• **Electron Delocalization**: The overlapping p orbitals in conjugated systems allow for the delocalization of electrons, thereby enhancing molecular stability.
• **Stability and Reactivity**: Generally, conjugated dienes are more stable than isolated dienes and exhibit unique characteristics such as the Diels-Alder reaction, a useful synthetic pathway in organic chemistry.
• **Resonance Structures**: Conjugated dienes can also be represented by multiple resonance structures, showing the possibility of electron distribution throughout the system.

A simple example, such as 1,3-butadiene, demonstrates this: two conjugated double bonds facilitate the stabilization through resonance, reducing their heat of hydrogenation compared to non-conjugated or isolated systems.

Organic Chemistry Problem Solving

Effective problem solving in organic chemistry requires understanding fundamental principles and applying logical reasoning. For exercises involving heat of hydrogenation, systematic analysis is key.

• **Step-by-Step Comparison**: Begin by assessing the heat of hydrogenation data provided. Analyze differences between the single and multiple double bonded forms of the compounds.
• **Identifying Conjugation**: Recognize if a diene is conjugated or isolated, as this impacts stability and energy release during hydrogenation.
• **Evaluating Stability**: Use knowledge of molecular structures to assess the stability of the compounds. More stable dienes will generally have lower heats of hydrogenation due to electron delocalization.

Applying these strategies allows one to deduce correct outcomes efficiently, similar to identifying that 2,4-hexadiene displays the heat of hydrogenation closely aligning with that of conjugated dienes, making it less stable compared to 1,3-hexadiene but more stabilized than completely isolated dienes.