Question

Allene, ${\mathbf{CH}}_{\mathbf{2}}\mathbf{=}\mathbf{C}\mathbf{=}{\mathbf{CH}}_{\mathbf{2}}$has a heat of hydrogenation of $\mathbf{-}\mathbf{298}\mathbf{}\mathbf{kJ}\mathbf{/}\mathbf{mol}$

$\mathbf{(}\mathbf{-}\mathbf{71}\mathbf{.}\mathbf{3}\mathbf{}\mathbf{kcal}\mathbf{/}\mathbf{mol}\mathbf{)}$. Rank a conjugated diene, a nonconjugated diene, and an

allene in order of stability.

Short answer

The stability order of a given alkene is as follows:

$$\begin{gathered} \mathrm{Allene}<\mathrm{Non}-\mathrm{conjugated}\mathrm{diene}<\mathrm{conjugated}\mathrm{diene} \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\overrightarrow{\mathit{}\mathit{}\mathit{}\mathrm{stability}\mathit{}\mathit{}\mathit{}} \end{gathered}$$

Step-by-step solution

Alkene stability

The stability of alkene is increased by making it more substituted by the alkyl group due to the hyperconjugation effect; e.g., a disubstituted alkene is more stable than a monosubstituted alkene.

The stability of alkene can be connected to the heat of hydrogenation; a more stable alkene produces less heat (having less energy) while the less stable (having more energy) alkene produces more heat.

Order of stability of the given alkene compound

The more the heat of hydrogenation $\left(\Delta {\text{H}}_{\text{hydrog}}\right)$, the less is the stability of alkene.

Allene having two double bonds, the excepted heat of hydrogenation data-custom-editor="chemistry" $\left(\Delta {\text{H}}_{\text{hydrog}}\right)$is given as:

$$\begin{gathered} \left(\Delta {\text{H}}_{\text{hydrog}}\right)\text{=}\text{- 126 + ( - 126)} \\ \text{=}\text{- 252}\text{kJ/mol} \end{gathered}$$

Expected role="math" localid="1663240392459" $\Delta {\text{H}}_{\text{hydro}}$for allene is $-252\mathrm{kJ}/\mathrm{mol}$when the heat of hydrogenation for each bond is the same as that of the isolated double bond.

The measure$\Delta {\text{H}}_{\text{hydro}}$for allene is $-298\mathrm{kJ}/\mathrm{mol}$, more than that of the expected value $(252\mathrm{kJ}/\mathrm{mol})$.

Thus, the allene has higher energy than a nonconjugated diene, which is higher than a conjugated diene.

The stability order for the given alkene is as follows:

role="math" localid="1663240895312" $$\begin{gathered} \mathrm{Allene}<\mathrm{Non}-\mathrm{conjugated}\mathrm{diene}<\mathrm{conjugated}\mathrm{diene} \\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\overrightarrow{\mathit{}\mathit{}\mathit{}stability\mathit{}\mathit{}\mathit{}} \end{gathered}$$