Question

Following is an equation for hydroperoxidation of cumene. Propose a radical chain mechanism for this reaction. Assume that initiation is by an unspecified radical, R'.

Short answer

Question: Briefly describe the three main stages of the proposed radical chain mechanism for the hydroperoxidation of cumene. Answer: The three main stages of the proposed radical chain mechanism for the hydroperoxidation of cumene are initiation, propagation, and termination. Initiation involves the formation of a radical species by reacting an unspecified radical (R') with cumene. Propagation consists of two steps: the cumene radical reacts with molecular oxygen to form a hydroperoxide radical, followed by the hydroperoxide radical reacting with another cumene molecule to form cumene hydroperoxide and regenerate a cumene radical. Finally, termination occurs when two radical species combine to form stable, non-radical products.

Step-by-step solution

Initiation

The initiation step involves the formation of a radical species. Here, an unspecified radical (R') is given to initiate the reaction. This radical will abstract a hydrogen atom from the cumene molecule, generating the cumene radical and an RH molecule. The overall initiation step can be represented as: R' + C_6H_5CH(CH_3)_2 -> C_6H_5CH(CH_3)_2^• + RH

Propagation - Formation of Hydroperoxide Radical

In the first propagation step, the cumene radical reacts with molecular oxygen, O_2, to form a hydroperoxide radical. The reaction can be represented as follows: C_6H_5CH(CH_3)_2^• + O_2 -> C_6H_5CH(CH_3)_2OO^•

Propagation - Formation of Cumene Hydroperoxide

In the second propagation step, the hydroperoxide radical reacts with another cumene molecule, abstracting a hydrogen atom from it to form cumene hydroperoxide. The reaction can be represented as follows: C_6H_5CH(CH_3)_2OO^• + C_6H_5CH(CH_3)_2 -> C_6H_5CH(CH_3)_2OOH + C_6H_5CH(CH_3)_2^• This step regenerates a cumene radical that can continue to propagate the chain reaction.

Termination

The termination step involves the combination of two radical species to form a stable, non-radical product. Some possible termination reactions are: C_6H_5CH(CH_3)_2^• + C_6H_5CH(CH_3)_2^• -> C_6H_5CH(CH_3)_2 + C_6H_5CH(CH_3)_2 C_6H_5CH(CH_3)_2^• + C_6H_5CH(CH_3)_2OO^• -> C_6H_5CH(CH_3)_2OOH C_6H_5CH(CH_3)_2OO^• + C_6H_5CH(CH_3)_2OO^• -> C_6H_5CH(CH_3)_2OO + C_6H_5CH(CH_3)_2OOH Termination steps are usually slower than propagation steps, which allows the chain reaction to continue for multiple cycles before being terminated. In summary, the proposed radical chain mechanism for the hydroperoxidation of cumene involves an initiation step with an unspecified radical, followed by two propagation steps, and a termination step where two radical species combine to form stable products.

Key concepts

Radical Chain Reaction

A radical chain reaction is a sequence of chemical reactions where free radicals — unstable atoms or molecules with an unpaired electron — are key players. In the context of the hydroperoxidation of cumene, such a reaction is facilitated by an initiating radical that starts a cascading series of transformations.

During the initiation phase, a radical known as R' takes a hydrogen atom from a cumene molecule, which in turn becomes a cumene radical. These cumene radicals are central to the propagation stage, where they react continuously, generating new radicals and thus, creating a chain reaction. It's this self-sustaining nature of propagation steps that highlights the hallmark of a radical chain reaction: once initiated, it has the potential to keep going through numerous cycles of reaction until a termination step occurs.

This is critical to grasp because the species involved in a radical chain reaction must maintain a delicate balance — they need to be reactive enough to perpetuate the chain but stable enough not to terminate it prematurely. A good understanding of this balance can help students to predict the reactivity and stability of other radicals in various chemical processes.

Cumene Radical Formation

The formation of the cumene radical is the event that ignites the radical chain reaction in the hydroperoxidation of cumene. It is essential to understand that the cumene radical is formed when the initiating radical R' extracts a hydrogen atom from a stable cumene molecule.

The cumene radical (C_6H_5CH(CH_3)_2^•) is characterized by having an unpaired electron on the carbon atom that was bound to the hydrogen atom removed by R'. Having an unpaired electron makes it highly reactive, and subsequently, this radical will interact with oxygen in the air to form a hydroperoxide radical.
Formation of the cumene radical is a precursor to further chemical transformations in the reaction sequence. This step demonstrates the responsiveness of organic molecules to radicals and provides a basis for exploring other reactions in organic chemistry involving radical species. Students should appreciate the specificity of radical reactions, as the position at which the hydrogen is abstracted can greatly influence the subsequent reactivity of the radical formed.

Cumene Hydroperoxide Synthesis

Following the formation of the cumene radical, the synthesis of cumene hydroperoxide is the aim of the radical chain reaction. This compound has applications in various industries, making the reaction not only chemically interesting but also industrially relevant.

Cumene hydroperoxide is synthesized when the hydroperoxide radical (C_6H_5CH(CH_3)_2OO^•) formed by the reaction of the cumene radical with oxygen, extracts a hydrogen atom from another cumene molecule. The result of this step is the formation of cumene hydroperoxide (C_6H_5CH(CH_3)_2OOH) and the regeneration of a cumene radical, perpetuating the radical chain reaction.
Understanding this synthesis is critical for students as it provides a practical example of how radical reactions can be harnessed to create valuable compounds. Moreover, the concept of regeneration of the radical highlights an essential aspect of chain reactions —the ability to sustain itself through internal feedback.