Question

(a) Predict the heat of hydrogenation of allene, \(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2}\). (b) The actual value is \(-71 \mathrm{kcal}\). What can you say about the stability of a cumulated diene?

Short answer

(a) To predict the heat of hydrogenation of allene (\(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2}\)), we can calculate it as the heat of hydrogenation per π bond (typical range of 28-30 kcal/mol) multiplied by the number of π bonds (Allene has 2 π bonds). This gives us a predicted heat of hydrogenation between 56-60 kcal/mol. (b) The actual heat of hydrogenation is -71 kcal/mol, which is more exothermic than the predicted value. Thus, the cumulated diene (allene) is less stable compared to a typical alkene with the same number of π bonds. This lesser stability is due to steric repulsion between the two adjacent π bonds and strain in the linear structure.

Step-by-step solution

Identify the molecule and its π bonds

Allene, \(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{CH}_{2}\), has two double bonds, which gives us a total of two π bonds in the molecule.

Determine typical heat of hydrogenation per π bond for alkenes

The heat of hydrogenation of a typical alkene is in the range of 28-30 kcal/mol per π bond.

Calculate the predicted heat of hydrogenation of allene

Since allene has two π bonds, we would predict that the heat of hydrogenation for allene could be around: Predicted heat of hydrogenation = Heat of hydrogenation per π bond × Number of π bonds Predicted heat of hydrogenation = 28-30 kcal/mol × 2 Predicted heat of hydrogenation = 56-60 kcal/mol (b)

Compare the predicted and actual heat of hydrogenation

The predicted heat of hydrogenation for allene was calculated to be between 56-60 kcal/mol, while the actual value given is -71 kcal/mol.

Analyze the stability of the cumulated diene and draw conclusions

The actual heat of hydrogenation for allene is -71 kcal/mol, which is higher (more exothermic) than the predicted value for a typical alkene with two π bonds, which is between 56-60 kcal/mol. This indicates that the cumulated diene (allene) is less stable compared to a typical alkene with the same number of π bonds. The higher actual heat of hydrogenation suggests that when the cumulated diene undergoes hydrogenation , it releases more heat, which means the difference in energy between the reactants (allene) and the products (alkanes) is more than what is typically observed for alkenesto form alkanes. Lesser stability in cumulated diene is due to steric repulsion between the two adjacent π bonds and strain in linear structure.

Key concepts

Allene

An allene is a type of organic molecule known for its distinctive arrangement of bonds. In the structure of allene, represented by the chemical formula \( \mathrm{CH}_2=\mathrm{C}=\mathrm{CH}_2 \), there are two double bonds that directly connect three carbon atoms in a row. This unique lineup, called a cumulated system, sets allenes apart from typical alkene compounds, which usually have their double bonds separated by at least one single bond.

Allenes are noteworthy not just for this peculiar structure but also for their interesting reaction behaviors, especially when it comes to hydrogenation. In the process of hydrogenation, the double bonds in allenes can accept hydrogen atoms to become single bonds, a transformation that's accompanied by the release of heat energy.

Cumulated Diene Stability

When considering the stability of a molecule like allene, we must explore what's meant by a 'cumulated diene.' This term refers to a compound that features two or more double bonds that are directly adjacent, or 'cumulated,' to one another. These cumulated systems are not particularly common and possess unique properties due to the electronic and steric interaction between the double bonds.

A cumulated diene like allene is thought to be less stable because of the inherent strain caused by the proximity of these unsaturated bonds. This instability is often unmasked by how much heat is given off during hydrogenation, known as the heat of hydrogenation. A higher-than-expected heat of hydrogenation suggests more energy is released when the molecule is converted to a more stable form, which implies the initial form was less stable. In allene's case, the high heat signifies it has more strain than a typical alkene.

\( \pi \) Bonds

The \( \pi \) bonds are what give alkenes their characteristic double bonds. Each \( \pi \) bond represents a region of electron density that exists above and below the plane of the atoms bonded together, facilitating these unique electron interactions that are critical to the molecule's chemical properties.

In hydrogenation reactions, \( \pi \) bonds are broken and replaced with single bonds as hydrogen atoms are added to the carbon atoms. The number of \( \pi \) bonds in a molecule can predict how much energy will be released in a hydrogenation reaction; typically, each \( \pi \) bond in an alkene will yield about 28-30 kcal/mol. However, in allenes and other cumulated dienes, this prediction can be skewed due to the additional instability brought about by the accumulation of \( \pi \) bonds.

Exothermic Reactions

Exothermic reactions are chemical processes in which energy is released to the surroundings, usually in the form of heat. These reactions are characterized by a negative value for the change in enthalpy (\( \Delta H \) < 0). The heat of hydrogenation is an excellent example of an exothermic reaction because it releases heat when \( \pi \) bonds in unsaturated hydrocarbons react with hydrogen to form single bonds.

The amount of heat released during these reactions is not just a matter of breaking bonds but also of forming more stable products. In the case of allene, the unexpectedly high heat of hydrogenation relative to a typical alkene indicates that the products (the alkanes formed after hydrogenation) are significantly more stable than the reactants (the allene). This stability difference measures just how much energy is stored in the \( \pi \) bonds of the reactants and thus can be indicative of the molecule's overall stability.