Question

A reaction was believed to occur by the following mechanism. Step \(1 \mathrm{~A}_{2} \longrightarrow \mathrm{A}+\mathrm{A}\) Step \(2 \mathrm{~A}+\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{A}_{2} \mathrm{~B}\) Step \(3 \mathrm{~A}_{2} \mathrm{~B}+\mathrm{C} \longrightarrow \mathrm{A}_{2}+\mathrm{BC}\) (a) Write the overall reaction. (b) Write the rate law for each step and indicate its molecularity. (c) What are the reaction intermediates? (d) A catalyst is a substance that accelerates the rate of a reaction and is regenerated in the process. What is the catalyst in the reaction?

Short answer

The overall reaction is \( \mathrm{B} + \mathrm{C} \longrightarrow \mathrm{BC} \). The rate law for each step is: Step 1, rate = \(k_1[\mathrm{A}_2]\) (unimolecular), Step 2, rate = \(k_2[\mathrm{A}]^2[\mathrm{B}]\) (termolecular), and Step 3, rate = \(k_3[\mathrm{A}_2\mathrm{B}][\mathrm{C}]\) (bimolecular). The reaction intermediates are \(\mathrm{A}\) and \(\mathrm{A}_2\mathrm{B}\). The catalyst is \(\mathrm{A}_2\).

Step-by-step solution

Write the Overall Reaction

To determine the overall reaction, add up the individual steps, ensuring to cancel out all the intermediate species that appear on both the product side and reactant side in the sequence of steps. Intermediates are species that are produced in one step and consumed in another step. They do not appear in the overall reaction.

Write the Rate Law for Each Step

Since the molecularity of a reaction refers to the number of molecules reacting in an elementary step, we can write the rate laws based on the stoichiometry of the reactants in each elementary step. The rate law for each step should be proportional to the concentrations of the reactants involved in that step, raised to the powers of their coefficients.

Identify the Reaction Intermediates

Reaction intermediates are species that are formed in one step of the mechanism and used up in subsequent steps. They are not present in the overall equation for the reaction.

Identify the Catalyst

A catalyst is a substance that is used to initiate or accelerate a chemical reaction and is regenerated by the end of the reaction. It should appear in the mechanism but not in the overall reaction.

Key concepts

Reaction Intermediates

In chemical reactions, reaction intermediates are substances that form in one step of a reaction mechanism and are consumed in a subsequent step. They play a crucial role in the progression from reactants to products but are never seen in the final equation because they are not present in the net reaction. The identification of intermediates helps chemists understand the various stages that occur during a chemical reaction and can be critical in optimizing reaction conditions.

For instance, considering the provided reaction mechanism, certain species are formed and used up during the process, which we classify as reaction intermediates. These intermediates often provide a pathway that lowers the energy required to transform reactants into products, thereby increasing the reaction rate. However, since they are not part of the overall chemical change, intermediates do not appear in the final balanced chemical equation.

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. To determine the rate law for each step, one must examine the molecularity of the step, which refers to the number of molecules involved in a single reaction event. The rate law is invaluable for predicting how changes in concentration affect the reaction rate.

In elementary reactions, the rate law is directly inferred from the stoichiometry of the reactants involved. For a reaction where a molecule A transforms into product P, the rate law could be written as \( \text{Rate} = k[A] \) where \(k\) is the rate constant, and \( [A] \) is the concentration of reactant A. If a reaction involves two A molecules colliding, the rate would be \( \text{Rate} = k[A]^2 \). Understanding the rate laws aids in determining how fast a reaction will proceed under specific conditions.

Molecularity

Molecularity is a term used to describe the number of reactant particles (atoms, ions, or molecules) involved in an elementary reaction step. Molecularity provides insight into the reaction mechanism and is categorized as unimolecular, bimolecular, or trimolecular, corresponding to one, two, or three reacting particles, respectively.

For instance, the first step in the given mechanism is unimolecular, involving the decomposition of a single molecule of \( \mathrm{A}_2 \). On the other hand, the second step is trimolecular because it involves three reactant particles: two A atoms and one B molecule. Recognizing molecularity helps chemists predict the likelihood of a reaction step occurring since, typically, the higher the molecularity, the less likely the step because simultaneous collisions between multiple reactants are rarer.

Catalyst in Chemistry

A catalyst in chemistry is a substance that increases the rate of a reaction without being consumed by the end of the process. It allows for a lower activation energy, leading to a faster reaction. Catalysts work by providing an alternative reaction pathway and are recovered in their original form once the reaction is complete.

In the reaction mechanism provided, if we identify a substance that appears as a reactant in one step and is produced again in a subsequent step, this substance would be considered a catalyst. This characteristic makes catalysts remarkably efficient since a small amount can influence the rate of a large volume of reactants over the reaction's course. Understanding how to identify and use catalysts is significant in both industrial applications and environmental considerations, as they can substantially reduce energy consumption and waste production.