Question

The heat of hydrogenation for allene (Problem 7.52 ) to yield propane is \(-295 \mathrm{~kJ} / \mathrm{mol}\), and the heat of hydrogenation for a typical monosubstituted alkene such as propene is \(-126 \mathrm{~kJ} / \mathrm{mol}\). Is allene more stable or less stable than you might expect for a diene? Explain.

Short answer

Allene is less stable than expected for a diene due to its larger heat of hydrogenation.

Step-by-step solution

Understand the Concept of Heat of Hydrogenation

The heat of hydrogenation is the enthalpy change when an alkene (or diene) is converted to an alkane through the addition of hydrogen. It serves as an indicator of an alkene's stability; the more negative the heat of hydrogenation, the less stable the compound prior to hydrogenation.

Compare the Heats of Hydrogenation

Given are: - Heat of hydrogenation of allene = \(-295 \text{ kJ/mol}\)- Heat of hydrogenation of propene = \(-126 \text{ kJ/mol}\).Since allene is more negative, it implies allene is less stable than a typical monosubstituted alkene.

Expectations for Diene Stability

In general, conjugated dienes are usually more stable than isolated double bonds due to resonance stabilization. However, the larger negative value for allene's hydrogenation suggests that allene is less stable than expected for a diene.

Conclude Allene's Stability

The heat of hydrogenation for allene being significantly more negative than that for typical alkenes indicates that allene is less stable than expected. This can be due to the lack of resonance stabilization that is often present in more stable dienes.

Key concepts

Alkene Stability

Alkenes are organic compounds featuring carbon-carbon double bonds. Their stability can be assessed by measuring the heat of hydrogenation. This is the energy change when hydrogen is added to convert them into saturated alkanes. A more negative heat of hydrogenation value means the alkene was less stable. Conversely, a less negative or more positive value indicates greater stability.

Several factors affect alkene stability:

• **Substitution pattern**: Alkenes with more substituents on the double bond are generally more stable due to hyperconjugation and the inductive effect of the substituents.
• **Conjugation**: Alkenes that can resonate with neighboring π-systems can distribute electron density better, making them more stable.
• **Sterics**: Less crowded double bonds can stabilize into a lower energy state.

Determining alkene stability is key in predicting their reactions and behaviors in chemical processes. Analyzing their energy profiles is a common practice in understanding organic reaction dynamics.

Diene Stability

Dienes possess two double bonds, which can be either conjugated or isolated. Conjugated dienes, which have alternating single and double bonds, are usually more stable because their π-electron cloud is extensively delocalized over all participating atoms.

Compared to isolated dienes, where double bonds do not overlap, conjugated dienes benefit from resonance stabilization. This increased stability influences both their chemical reactivity and their physical properties.

Energy calculations often reveal that conjugated dienes have lower heats of hydrogenation than expected. This lower energy state results from the effective overlapping of p-orbitals across all carbon atoms involved in the conjugation. Therefore, when assessing a given diene, its position and connections determine how stable it will be.
The surprising instability of allene, as noted from its heat of hydrogenation, lies in its structure, which does not allow for such conjugation benefits.

Resonance Stabilization

Resonance stabilization refers to the delocalization of electrons across adjacent atoms leading to a lower energy state. This phenomenon prominently occurs in conjugated systems like conjugated dienes. The resonance effect allows such molecules to dissipate and stabilize charge over an extended molecular framework.

Consider aromatic compounds like benzene, which owe much of their remarkable stability to resonance. In these systems, the continuous overlap of p-orbitals across multiple bonds allows the electrons to "flow" and stabilize the entire structure.

Resonance impacts chemical behavior significantly:

• **Enhanced Stability**: Through electron delocalization, compounds achieve a more stable configuration than if electrons were localized.
• **Reactivity Influence**: Molecules can behave differently under reactions due to their ability to stabilize intermediates in transition states.
• **Bond Character**: Resonance imparts partial single, double or triple bond characters to affected bonds, altering their lengths and strengths.

Resonance is a crucial concept in organic chemistry, helping explain the unexpected stability and reactivity profiles of numerous compounds that otherwise look simple.