The proposed mechanism for a reaction is (1) A(g)+B(g) ⇌X(g) (2) X(g)+C(g) ⟶Y(g)

step 1 Hi guys, let's solve problem 16 .72 for the given reactions. We need to find the overall reactio

The proposed mechanism for a reaction is (1) A(g)+B(g)...

The proposed mechanism for a reaction is $$ \begin{array}{l}{\text { (1) } \mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{X}(g)} \\ {\text { (2) } \mathrm{X}(g)+\mathrm{C}(g) \longrightarrow \mathrm{Y}(g)} \\ {\text { (3) } \mathrm{Y}(g) \longrightarrow \mathrm{D}(g)}\end{array} $$ (a) What is the overall equation? (b) Identify the intermediate(s), if any. (c) What are the molecularity and the rate law for each step? (d) Is the mechanism consistent with the actual rate law: Rate $=k[\mathrm{A}][\mathrm{B}][\mathrm{C}] ?$ (e) Is the following one-step mechanism equally valid: $\mathrm{A}(g)+\mathrm{B}(g)+\mathrm{C}(g) \longrightarrow \mathrm{D}(g) ?$

The proposed mechanism for a reaction is
$$
\begin{array}{l}{\text { (1) } \mathrm{A}(g)+\mathrm{B}(g) \rightleftharpoons \mathrm{X}(g)} \\ {\text { (2) } \mathrm{X}(g)+\mathrm{C}(g) \longrightarrow \mathrm{Y}(g)} \\ {\text { (3) } \mathrm{Y}(g) \longrightarrow \mathrm{D}(g)}\end{array}
$$
(a) What is the overall equation?
(b) Identify the intermediate(s), if any.
(c) What are the molecularity and the rate law for each step?
(d) Is the mechanism consistent with the actual rate law: Rate $=k[\mathrm{A}][\mathrm{B}][\mathrm{C}] ?$
(e) Is the following one-step mechanism equally valid: $\mathrm{A}(g)+\mathrm{B}(g)+\mathrm{C}(g) \longrightarrow \mathrm{D}(g) ?$

Key Concepts

Equilibrium in a Reaction Mechanism

An equilibrium step in a reaction mechanism refers to a fast, reversible reaction where the forward and reverse rates are nearly equal, establishing a rapid equilibrium between the reactants and an intermediate. This equilibrium can be used to express the concentration of the intermediate in terms of the initial reactants, aiding in the derivation of the overall rate law when combined with slower, rate-determining steps.

Termolecular Reactions in a Single-Step Mechanism

Termolecular reactions involve the simultaneous collision of three molecules and are typically rare due to the improbability of three particles colliding with the precise orientation and energy required. Proposing a single-step mechanism with a termolecular reaction is generally less favored compared to multi-step mechanisms, which can better account for observed kinetics while avoiding the statistical improbability inherent in a direct three-body collision.

Rate Laws for Elementary Steps

In elementary reactions, the rate law can be written directly from the molecularity of the step. For example, a unimolecular step leads to a first-order rate law, a bimolecular step to a second-order rate law, and a termolecular step to a third-order rate law. Understanding this connection is key to predicting and rationalizing the kinetics of each step in a complex mechanism, often allowing for the derivation of the overall rate law when combined with additional factors, such as equilibrium conditions.

Reaction Intermediates

Reaction intermediates are species that are produced in one step of a reaction mechanism and then consumed in a subsequent step. Although they play a crucial role in the pathway from reactants to products, they do not appear in the overall balanced equation. Their fleeting existence means that they are often difficult to detect experimentally, but they are central to understanding the detailed mechanism of complex reactions.

Overall Reaction in Mechanisms

This concept involves combining all the elementary steps of a reaction mechanism to produce the net chemical change from reactants to products. It is obtained by algebraically adding the individual steps and canceling any species that appear as intermediates. The overall reaction provides a macroscopic view of the chemical transformation without detailing the step?by?step pathway or the transient intermediates that may form during the process.

Molecularity of Elementary Reactions

Molecularity refers to the number of reactant molecules that collide and react in an elementary step. It can be unimolecular, bimolecular, or termolecular, each corresponding to one, two, or three reactant molecules involved in the rate-determining collision event. This concept is critical because it helps in determining the form of the rate law for that step and reveals the nature of the collision process required for the chemical transformation.

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