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Why is it possible for more than one mechanism to be consistent with the experimentally determined...

Why is it possible for more than one mechanism to be consistent with the experimentally determined rate law for a hemical reaction?

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Expert Solution

Reaction Mechanisms

Table of Contents

The mechanism of a chemical reaction is the sequence of events that take place as reactant molecules are converted into products.

Introduction

The study of kinetics includes very complex and sophisticated reactions that cannot be analyzed without a proposed mechanism, a series of steps that a reaction takes before reaching the final products.

Reaction mechanisms are step-by-step descriptions of what occurs on a molecular level in chemical reactions. Each step of the reaction mechanism is known as an elementary process, a term used to describe a moment in the reaction when one or more molecules changes geometry or is perturbed by the addition or omission of another interacting molecule. Collectively, an overall reaction and a reaction mechanism consist of multiple elementary processes. These elementary steps are the basic building blocks of a complex reaction, and cannot be broken down any further.

A reaction mechanism is only a guess at how a reaction proceeds. Therefore, even if a mechanism agrees with the experimental results of a reaction, it cannot be proven to be correct.

Example

onsider the chlorination reaction of methane, CH4:

\[CH_4 (g) + 2Cl_2(g) \longrightarrow CH_3Cl (g) + HCl (g) + Cl^- (g) \tag{overall reaction}\]

This reaction is proposed to occur via two successive elementary steps. Each step has its own characteristic reactants, product, rate law.

\[CH_4 (g) + Cl_2 (g) \longrightarrow CH_3 (g) + HCl (g) \tag{step 1 (slow)}\]

with an elementary rate law of,

\[k_1 = [CH_4][Cl_2]\]

\[CH_3 (g) + Cl_2 (g) \longrightarrow CH_3 Cl (g) + Cl^- (g) \tag{step 2 (fast)}\]

with an elementary rate law of,

\[k_2 = [CH_4][Cl_2]\]

The steps combine to generate the final reaction equation,

Description of a Reaction Mechanism

Because a reaction mechanism is used to describe what occurs at each step of a reaction, it also describes the transition state, or the state in which the maximum of potential energy is reached. A mechanism must show the order in which the bonds form or break and the rate of each elementary step. Also accounted for are the reaction intermediates, stable molecules that do not appear in the experimentally determined rate law because they are formed in one step and consumed in a subsequent step. Because a reaction cannot proceed faster than the rate of slowest elementary step, the slowest step in a mechanism establishes the rate of the overall reaction. This elementary step is known as the rate-determining step.

A mechanism must satisfy the following two requirements:

  1. The elementary steps must add up to give the overall balanced equation for the reaction.
  2. The rate law for the rate-determining step must agree with the experimentally determined rate law.

Each of these events constitutes an elementary step that can be represented as a coming-together of discrete particles ("collision") or as the breaking-up of a molecule ("dissociation") into simpler units. The molecular entity that emerges from each step may be a final product of the reaction, or it might be an intermediate.

Elementary Processes

Elementary processes are usually either unimolecular or bimolecular. A unimolecular elementary process describes the dissociation of a single molecule. A bimolecular elementary process occurs when two molecules collide. A third process, called termolecular, is rare because it involves three molecules colliding at the same time. In the bimolecular and termolecular processes, the molecules may be different or the same.

Although a rate law for an overall reaction can only be experimentally determined, the rate law for each elementary step can be deduced from the chemical equation through inspection. A unimolecular elementary step has a first order rate law, whereas a bimolecular elementary step has a second order rate law. The table below summarizes the types of elementary steps and the rate laws that they follow. A, B, and C here represent the reactants or reaction intermediates.

Elementary Steps and Rate Laws

Molecularity Elementary Step Rate Law for Elementary step
Unimolecular \[A \longrightarrow products\] \[\text{rate}= k[A]\]
Bimolecular \[A + B \longrightarrow products\] \[\text{rate}= k[A][B]\]
\[A + A \longrightarrow products\] \[\text{rate}= k[A]2\]
Termolecular \[A + A + B \longrightarrow products\] \[\text{rate}= k[A]2[B]\]
\[A + A + A \longrightarrow products\] \[\text{rate} = k[A]3\]
\[A + B + C \longrightarrow products\] \[\text{rate}= k[A][B][C]\]

Elementary processes are also reversible. Some may reach conditions of equilibrium, in which both the forward and reverse reaction rates are equal.

\[CH_4 (g) + 2Cl_2(g) \longrightarrow CH_3Cl (g) + HCl (g) + Cl^- (g) \tag{overall reaction}\]


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