14.2 Reaction mechanisms and elementary steps

Chemical reactions often involve complex processes. Reaction mechanisms break these down into simpler steps, showing how molecules transform. Understanding these steps helps us predict reaction rates and outcomes, crucial for designing efficient chemical processes.

Elementary steps are the building blocks of reaction mechanisms. They represent the simplest possible molecular events, like collisions or bond breaks. By studying these steps, we can uncover the rate-determining step and derive overall reaction rates.

Reaction Mechanisms and Overall Reactions

Reaction Mechanisms: Detailed, Step-by-Step Descriptions

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• A reaction mechanism provides a detailed, step-by-step description of how reactants are converted into products at the molecular level
  • Includes all intermediate species and transition states involved in the reaction
  • Describes the individual molecular events that occur during the reaction, such as the breaking and forming of bonds and the rearrangement of atoms
• The overall reaction is the sum of all the elementary steps in the reaction mechanism
  • Intermediate species cancel out in the overall reaction equation
  • The stoichiometry of the overall reaction is determined by the stoichiometry of the elementary steps

Rate-Determining Step and Overall Reaction Rate

• The slowest step in a reaction mechanism is called the rate-determining step
  • Controls the rate of the overall reaction because it has the highest activation energy among all the elementary steps
  • Represents the bottleneck in the reaction pathway
• The rate law for the overall reaction can be derived from the rate-determining step in the reaction mechanism
  • The rate law for the rate-determining step is identical to the rate law for the overall reaction
  • If the concentration of an intermediate species appears in the rate law for the rate-determining step, the steady-state approximation can be applied to express its concentration in terms of the reactants

Elementary Steps and Rate Laws

Characteristics of Elementary Steps

• Elementary steps are the individual molecular events that occur during a reaction
  • Involve the collision and rearrangement of molecules or ions
  • Cannot be broken down into simpler substeps
  • Occur in a single collision event
• Examples of elementary steps include:
  • Unimolecular dissociation: $AB \rightarrow A + B$
  • Bimolecular collision: $A + B \rightarrow AB$

Rate Laws for Elementary Steps

• The rate law for an elementary step is determined by the molecularity of the reaction
  • Molecularity is the number of molecules or ions that participate in the step as reactants
• For an elementary step, the reaction order for each reactant is equal to its stoichiometric coefficient in the balanced chemical equation for that step
  • Example: For the elementary step $2A + B \rightarrow C$, the rate law is $Rate = k[A]^2[B]$, where $k$ is the rate constant
• The overall reaction order for an elementary step is the sum of the stoichiometric coefficients of the reactants in the balanced chemical equation for that step

Rate-Determining Step in Mechanisms

Identifying the Rate-Determining Step

• The rate-determining step is the slowest step in a multi-step reaction mechanism
  • Controls the overall rate of the reaction because it has the highest activation energy among all the elementary steps
  • Represents the bottleneck in the reaction pathway
• To identify the rate-determining step, compare the rate constants or activation energies of the individual elementary steps
  • The step with the smallest rate constant or the highest activation energy is typically the rate-determining step

Steady-State Approximation for Intermediates

• If the concentration of an intermediate species appears in the rate law for the rate-determining step, the steady-state approximation can be applied
  • Assumes that the concentration of the intermediate remains constant during the reaction because its rate of formation is equal to its rate of consumption
  • Allows the concentration of the intermediate to be expressed in terms of the concentrations of the reactants
• Example: Consider the reaction mechanism:
  • Step 1: $A + B \rightleftharpoons C$ (fast equilibrium)
  • Step 2: $C + D \rightarrow E$ (slow, rate-determining)
  • Applying the steady-state approximation to intermediate $C$, its concentration can be expressed as: $[C] = \frac{k_1[A][B]}{k_{-1} + k_2[D]}$

Molecularity vs Reaction Order

Molecularity of Elementary Steps

• The molecularity of an elementary step is the number of molecules or ions that participate in the step as reactants
  • Determines the reaction order for that step
• Unimolecular elementary steps have a molecularity of one
  • Involve a single reactant molecule or ion
  • Example: $A \rightarrow B + C$
• Bimolecular elementary steps have a molecularity of two
  • Involve the collision of two reactant molecules or ions
  • Example: $A + B \rightarrow C$
• Termolecular elementary steps have a molecularity of three
  • Involve the simultaneous collision of three reactant molecules or ions
  • Example: $A + B + C \rightarrow D$
  • Termolecular steps are rare because the probability of three particles colliding simultaneously is low

Reaction Order and Rate Laws

• The reaction order for an elementary step is determined by the molecularity of the step
  • Unimolecular steps have a first-order rate law: $Rate = k[A]$
  • Bimolecular steps have a second-order rate law: $Rate = k[A][B]$ or $Rate = k[A]^2$ (if both reactants are the same species)
  • Termolecular steps have a third-order rate law: $Rate = k[A][B][C]$, $Rate = k[A]^2[B]$, or $Rate = k[A]^3$ (depending on the reactant species)
• The overall reaction order is the sum of the reaction orders for each reactant in the rate-determining step
  • Example: For the rate-determining step $2A + B \rightarrow C$, the overall reaction order is 3 (2nd order in A, 1st order in B)