Question

The rate of the Diels-Alder addition between cycloocta tetraene and tetracyanoethylene is proportional to the tetracyanoethylene concentration \(\left[\mathrm{C}_{2}(\mathrm{CN})_{4}\right]\) at low concentrations of the addends but becomes independent of \(\left[\mathrm{C}_{2}(\mathrm{CN})_{4}\right]\) at high concentrations. Write a mechanism which accounts for this behavior.

Short answer

In the Diels-Alder reaction between cyclooctatetraene and tetracyanoethylene, the rate dependence on concentration can be explained by a saturation effect. At low concentrations, the reaction rate is proportional to the tetracyanoethylene concentration, as the cyclooctatetraene is in excess. However, at high concentrations, the reactive sites on the diene are saturated with tetracyanoethylene, making the reaction rate independent of the tetracyanoethylene concentration and only dependent on the diene.

Step-by-step solution

Identify the Diels-Alder reaction mechanism

The Diels-Alder reaction is a [4+2] cycloaddition reaction, where a diene (4 π-electron system) reacts with a dienophile (2 π-electron system) to form a six-membered ring. In this case, cyclooctatetraene is the diene and tetracyanoethylene is the dienophile. The mechanism is a single, concerted step in which the diene and dienophile react to form a six-membered ring with the new single bonds being formed simultaneously.

Determine the rate-determining step

As the Diels-Alder reaction is a concerted process, the rate-determining step is the single step that forms the six-membered ring. This means that the rate of the reaction depends on both the concentration of the diene and the dienophile, which can be expressed as: \[rate = k[\text{diene}][\text{dienophile}]\]

Explain the behavior at low concentrations

At low concentrations, the rate of the reaction is directly proportional to the concentration of tetracyanoethylene. This implies that the concentration of cyclooctatetraene is in excess and does not significantly affect the rate of the reaction. This proportional relationship between the rate and the tetracyanoethylene concentration is consistent with the rate law derived in Step 2.

Explain the behavior at high concentrations

At high concentrations, the reaction rate becomes independent of the tetracyanoethylene concentration. This can be explained by a saturation effect, where the concentration of tetracyanoethylene is so high that the reactive sites on the diene (cyclooctatetraene) are saturated, meaning that further increases in tetracyanoethylene concentration do not result in a significant increase in the reaction rate. This saturation means that the reaction essentially becomes first-order with respect to the diene only, as the reaction rate is limited by the diene concentration. In conclusion, the observed behavior in the rate of the Diels-Alder addition between cyclooctatetraene and tetracyanoethylene could be explained by a saturation effect, where at high concentrations of tetracyanoethylene, the reactive sites of the diene are fully occupied, making the reaction rate independent of the tetracyanoethylene concentration.

Key concepts

Cycloaddition Reaction

In chemistry, a cycloaddition reaction allows molecules to form rings by bringing together smaller units. This is seen in the Diels-Alder reaction, a [4+2] cycloaddition. Here, a diene interacts with a dienophile. Imagine a diene as a 4 π-electron system and a dienophile as a 2 π-electron system. Together, they create a six-membered ring, all in one concerted step. This means the bonds form simultaneously as opposed to sequentially. This is a crucial aspect because it dictates the speed and conditions under which the reaction occurs.

• Diene: In the exercise, it's cyclooctatetraene.
• Dienophile: In this case, tetracyanoethylene.

Understanding this concept is key because it highlights the nature of Diels-Alder reactions. Despite happening in a single step, the reaction has complexities that relate to molecular interactions and the formation of intricate structures.

Rate-Determining Step

When studying reaction rates, the rate-determining step is vital. In a Diels-Alder reaction, this is the phase where the actual six-membered ring forms. Because it is a concerted reaction, everything happens in one go, meaning the rate will be dependent on both the diene and dienophile concentrations.

You can express this relationship using the equation:\[ rate = k[ ext{diene}][ ext{dienophile}] \]Here, \( k \) stands for the rate constant, a fixed number describing the reaction rate under certain conditions.

Initially, the rate is influenced equally by both reactants, but this can change depending on concentration variations. Understanding this rate equation helps explain why changes in reactant concentration affect how quickly the reaction proceeds.

Saturation Effect

The saturation effect is crucial to comprehend why the rate of a Diels-Alder reaction varies with reactant concentration. At lower concentrations of tetracyanoethylene, the rate is proportional to its concentration because cyclooctatetraene is in excess.

Yet, as the tetracyanoethylene concentration rises, a point of saturation is reached. Saturation means all available reactive sites on the diene (cyclooctatetraene) are fully utilized.

• This is the tipping point: further increasing tetracyanoethylene concentration won't make the reaction go faster.
• The rate of reaction then becomes dependent only on the concentration of the diene.

This principle applies to many reactions where one reactant is in excess. Once saturation is reached, the reaction rate levels off. This is a key understanding of how chemical reactions can shift from being second-order to first-order by changing the dominant limiting factor.