Question

Account for the fact that fairly reactive arenes (e.g., benzene, toluene, and ethylbenzene) are nitrated with excess nitric acid in nitromethane solution at a rate that is independent of the concentration of the arene (i.e., zeroth order). Does this mean that nitration of an equimolal mixture of benzene and toluene would necessarily give an equimolal mixture of nitrobenzene and nitrotoluenes? Why or why not?

Short answer

In the nitration of fairly reactive arenes like benzene, toluene, and ethylbenzene, the reaction follows zeroth-order kinetics, meaning the rate is independent of the concentration of the arenes involved. However, this doesn't guarantee that nitration of an equimolar mixture of benzene and toluene would yield an equimolar mixture of nitrobenzene and nitrotoluenes, as the rate constant k could be different for each arene. The reaction mechanism, involving electrophilic aromatic substitution with a nitronium ion, can be influenced by various factors such as electron density, electron-donating or electron-withdrawing groups, and steric factors, leading to a deviation from the expected product distribution.

Step-by-step solution

Understanding the zeroth-order reaction kinetics

A zeroth-order reaction is one in which the rate of the reaction is independent of the concentration of the reactants. In this case, the rate of nitration of arenes (benzene, toluene, and ethylbenzene) is given to be independent of their concentration, hence exhibiting zeroth-order kinetics. Mathematically, for a zeroth-order reaction, the rate law equation is expressed as: Rate = k Here, k is the rate constant.

Determining if the equimolar mixture of benzene and toluene would yield equimolar mixture of nitrobenzene and nitrotoluenes

When nitration of an equimolar mixture of benzene and toluene is carried out, it doesn't necessarily imply that an equimolar mixture of nitrobenzene and nitrotoluenes would be obtained. This is because the kinetics of the nitration process, i.e., the reaction rate, doesn't solely depend on the concentration of the arenes involved. The rate constant k may vary for different arenes, which means that nitration may proceed at different rates for benzene, toluene, and ethylbenzene, even if the reaction is zeroth-order with respect to their concentrations.

Understanding the reaction mechanism

To support the explanation provided in the previous step, we must consider the reaction mechanism for the nitration of arenes. Nitration typically occurs via an electrophilic aromatic substitution mechanism, in which a nitronium ion (NO2+) acts as the electrophile. The rates at which nitronium ions attack different arenes could be influenced by their electron density, the presence of electron-donating or electron-withdrawing groups, steric factors, and other factors, which may lead to a deviation from the expected equimolar mixture of nitrobenzene and nitrotoluenes. In conclusion, even though the nitration of fairly reactive arenes follows zeroth-order kinetics with respect to their concentrations, that doesn't mean that nitration of an equimolar mixture of benzene and toluene would necessarily yield an equimolar mixture of nitrobenzene and nitrotoluenes. This is because the rate of nitration depends on other factors such as the specific reactivity of each arene and its reaction mechanism, which may lead to differences in the reaction rate constant k and result in deviation from the expected product distribution.

Key concepts

Zeroth-order kinetics

Zeroth-order kinetics describe reactions where the reaction rate is constant and doesn't depend on the concentration of the reactants. This can seem counterintuitive because, in many reactions, you'd expect the rate to increase with more reactant present. However, in a zeroth-order reaction, the only factor affecting the rate is the rate constant, denoted as \( k \). The equation for such reactions simplifies to:

• Rate = \( k \)

This means for arenes like benzene, toluene, and ethylbenzene being nitrated with excess nitric acid, their concentration doesn’t influence the speed of the reaction.
This is particularly interesting because it suggests that other factors, beyond concentration, are controlling the reaction. These might include catalysts, surface conditions, or rate-determining steps in the mechanism.

Electrophilic aromatic substitution

Electrophilic aromatic substitution is a fundamental mechanism where an arene, such as benzene, reacts with an electrophile. In the nitration process, the electrophile is typically the nitronium ion \( \text{NO}_2^+ \). This ion seeks out the high electron density in the aromatic ring and substitutes a hydrogen atom.
How this substitution occurs depends largely on the nature of the arene. Factors like electron-donating or withdrawing groups can affect reactivity.

• Arenes with electron-donating groups may react faster because these groups increase electron density, making the arene more attractive to radicals.
• Arenes with electron-withdrawing groups tend to react slower as the electron density is decreased, making it harder for the electrophile to attack.

Therefore, this substitution can lead to different products or rates of reaction for various arenes, explaining why equimolar arenes might not yield equimolar nitrated products.

Reaction mechanism

The reaction mechanism for nitration involves several steps, providing a deeper understanding of how an arene reacts with nitric acid. First, the formation of the nitronium ion \( \text{NO}_2^+ \) occurs, often facilitated by an acid catalyst. This ion acts as the electrophile due to its positive charge.
Subsequently, it approaches the aromatic ring and temporarily forms a sigma complex. Finally, through a rearrangement process known as deprotonation, the sigma complex releases a proton (\( \text{H}^+ \)), restoring the aromaticity of the ring and completing the reaction.

• The presence of different substituents on the aromatic ring influences the stability of this intermediate complex and the overall reaction path.
• The efficiency of nitronium ion formation also dictates how quickly nitration occurs in synthetic or industrial processes.

Understanding these steps highlights why the reaction rate and product formation can vary despite the simpler kinetics usually proposed.

Rate constant

The rate constant \( k \) is crucial in zeroth-order kinetics because it uniquely determines the rate of the reaction. Unlike in first-order or second-order reactions where concentrations play a significant role, here \( k \) remains the primary protagonist.
The value of \( k \) itself can be influenced by several external conditions:

• Temperature: Generally, as temperature increases, \( k \) increases due to the added energy available to overcome activation barriers.
• Presence of catalysts: Catalysts can lower the activation energy needed, effectively increasing \( k \).
• Reaction environment: Variables like solvents or pressure can impact reaction dynamics, subtly shifting \( k \).

Thus, while zeroth-order kinetics might simplify the equation, understanding the role and variability of \( k \) remains essential in predicting real-world reaction outcomes, especially in cases like nitration of arenes.