Question

Which one of the following compounds would have the highest heat of hydrogenation? (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\) (b) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}\) (c) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\) (d) \(\mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}\)

Short answer

Compound (d) \(\mathrm{H}_{2}\mathrm{C}=\mathrm{CH}_{2}\) has the highest heat of hydrogenation.

Step-by-step solution

Understand the Concept of Hydrogenation

The heat of hydrogenation is the amount of heat released when an alkene is converted to an alkane by adding hydrogen in a hydrogenation reaction. It reflects the stability of the alkene; less stable alkenes have higher heats of hydrogenation.

Analyze Stability of Alkenes

For alkenes, stability can often be analyzed by looking at the number and type of substituents attached to the doubly-bonded carbons. Alkenes with more alkyl substituents are more stable due to hyperconjugation and inductive effects.

Examine Each Compound

(a) \(\left(\mathrm{CH}_{3}\right)_{2}\mathrm{C}=\mathrm{C}\left(\mathrm{CH}_{3}\right)_{2}\) is a tetrasubstituted alkene. (b) \(\mathrm{H}_{3}\mathrm{C}-\mathrm{CH}_{2}-\mathrm{CH}=\mathrm{CH}_{2}\) is a monosubstituted alkene. (c) \(\mathrm{H}_{3}\mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\) is a disubstituted alkene. (d) \(\mathrm{H}_{2}\mathrm{C}=\mathrm{CH}_{2}\) is an unsubstituted alkene.

Determine Most Unstable Alkene

\(\mathrm{H}_{2}\mathrm{C}=\mathrm{CH}_{2}\) is the least substituted and therefore the least stable. Unsubstituted alkenes have the highest heat of hydrogenation because they are less stable.

Choose the Compound with Highest Heat of Hydrogenation

Given that \(\mathrm{H}_{2}\mathrm{C}=\mathrm{CH}_{2}\) is the least stable, it will have the highest heat of hydrogenation.

Key concepts

Alkene Stability

Alkenes are hydrocarbons containing a carbon-carbon double bond. The stability of alkenes is a crucial trait influencing their reactivity and chemical behavior. Many factors contribute to alkene stability, including:

• Number of alkyl groups attached to the doubly-bonded carbons.
• Electronic effects such as hyperconjugation and inductive effects.

In essence, the more alkyl substituents on the double bond, the more stable the alkene. This is because the additional substituents can donate electron density. Hyperconjugation involves the delocalization of electrons, which stabilizes the system. Inductive effects also encourage stability as electronegative substituents can pull electron density away from electron-rich regions, balancing the molecule's stability.
Comparing different alkenes involves examining these substituent factors to determine their respective stabilities.

Tetrasubstituted Alkene

Tetrasubstituted alkenes have four alkyl groups attached to the carbon atoms of the double bond. This configuration provides extensive hyperconjugation and inductive effects, making them highly stable.
For example, consider the compound \( (\mathrm{CH}_3)_2\mathrm{C}=\mathrm{C}(\mathrm{CH}_3)_2 \). Here, each carbon in the double bond is linked to two methyl groups. This results in significant electron donation through hyperconjugationa stabilizing factor. The additional electron density provided by these alkyl groups reduces the electron-rich nature of the double bond, enhancing stability through inductive effects.
The high stability of tetrasubstituted alkenes correlates with their lower heats of hydrogenation. They release less energy when hydrogenated compared to less substituted alkenes.

Monosubstituted Alkene

Monosubstituted alkenes have a single alkyl group attached to one of the double-bonded carbons, as seen in the compound \( \mathrm{H}_3\mathrm{C}-\mathrm{CH}_2-\mathrm{CH}=\mathrm{CH}_2 \). In this structure, only one methyl group contributes to stability.
Although less stable than more substituted alkenes, monosubstituted alkenes still benefit from some hyperconjugative stabilization due to their single alkyl group. However, with only one alkyl substituent, they have fewer opportunities for hyperconjugation and weaker inductive effects.

• Monosubstituted alkenes tend to have moderate heats of hydrogenation.
• The presence of the lone alkyl group provides minimal electron-donating capability.

These factors contribute to moderate stability in monosubstituted alkenes.

Disubstituted Alkene

Disubstituted alkenes, containing two alkyl groups on their double bond, present a middle ground in terms of stability. They offer improved stability compared to monosubstituted alkenes but less than tetrasubstituted alkenes.
Taking \( \mathrm{H}_3\mathrm{C}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_3 \) as an example, each carbon in the double bond is linked to one methyl group. These methyl groups participate in hyperconjugation and contribute to the inductive effect. As such:

• Disubstituted alkenes exhibit a moderate level of electron delocalization.
• Their electron-withdrawing and -donating interactions produce a balanced stability.

The stability of disubstituted alkenes reflects in their moderate heat of hydrogenation, lying between those of monosubstituted and tetrasubstituted alkenes.

Unsubstituted Alkene

Unsubstituted alkenes, or terminal alkenes, lack any alkyl group attached to their carbon-carbon double bond, such as \( \mathrm{H}_2\mathrm{C}=\mathrm{CH}_2 \). This absence of substituents makes them the least stable type of alkenes.
Due to their lack of electron-donating groups, unsubstituted alkenes exhibit the highest electron density at the double bond. This results in a heightened reactivity and instability. Consequently, they release the highest amount of energy during hydrogenation.

• Unsubstituted alkenes have the highest heats of hydrogenation, reflecting their poor stability.
• The lack of any stabilizing interactions renders them less electronically favorable.

Their inherent instability makes them key operators in reactions where a high release of energy is typical.