Glossary

12.2 Complex reactions and rate-determining steps

4 min read•july 30, 2024

Complex reactions involve multiple steps, unlike elementary reactions that occur in a single collision. The , the slowest in the mechanism, controls the overall reaction rate. Understanding this concept is crucial for deriving rate laws and predicting reaction behavior.

The for complex reactions can't be determined directly from the balanced equation. Instead, it depends on the rate-determining step and involves applying the to reactive intermediates. This approach helps predict how changes in conditions affect reaction rates.

Elementary vs Complex Reactions

Reaction Mechanisms

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  • Elementary reactions involve a single step and occur in a single molecular collision
    • The and the balanced chemical equation are the same for an elementary reaction
  • Complex reactions involve two or more and occur through a series of molecular collisions
    • The reaction mechanism for a complex reaction consists of multiple elementary steps
    • The overall balanced equation is the sum of these steps

Rate Laws

  • The rate law for an elementary reaction can be determined directly from the balanced chemical equation
    • The order of the reaction with respect to each reactant equals its stoichiometric coefficient
    • The overall order of an elementary reaction is the sum of the orders with respect to each reactant
  • The rate law for a complex reaction cannot be determined directly from the balanced overall equation
    • It depends on the relative rates of the elementary steps in the reaction mechanism
    • The slowest step often determines the rate (rate-determining step)

Rate-Determining Step Significance

Characteristics of the Rate-Determining Step

  • The rate-determining step (RDS) is the slowest step in a multi-step reaction mechanism
    • It limits the overall rate of the reaction, acting as a bottleneck for the entire process
  • The RDS often has the highest activation energy
    • This corresponds to the largest energy barrier that must be overcome for the reaction to proceed

Impact on Overall Rate Law

  • The overall rate law for a complex reaction is determined by the rate law of the RDS
    • The concentrations of the reactants involved in the RDS appear in the overall rate law
    • The concentrations of reactants not involved in the RDS do not appear in the overall rate law
  • If the RDS changes due to a change in reaction conditions (temperature or reactant concentrations), the overall rate law for the complex reaction may also change

Deriving Rate Laws for Complex Reactions

Steady-State Approximation

  • To derive the rate law for a complex reaction, consider the rate laws for each elementary step in the reaction mechanism
  • Identify the RDS by comparing the relative rates of the elementary steps
    • The step with the slowest rate will be the RDS
  • Apply the steady-state approximation to any reactive intermediates formed in the mechanism
    • This assumes that the concentrations of these intermediates remain constant over time
    • Their rates of formation and consumption are equal

Expressing Concentrations and Substitution

  • Express the concentrations of the reactive intermediates in terms of the concentrations of the reactants and the rate constants of the elementary steps
  • Substitute these expressions into the rate law for the RDS to obtain the overall rate law for the complex reaction
    • The concentrations of the reactants involved in the RDS appear in the overall rate law
    • The concentrations of reactants not involved in the RDS do not appear in the overall rate law

Rate Effects of Concentration and Conditions

Reactant Concentrations

  • Changes in reactant concentrations can affect the rates of individual elementary steps in a complex reaction mechanism, potentially leading to a change in the RDS
  • Increasing the concentration of a reactant involved in the RDS increases the overall reaction rate
    • The RDS is the slowest step and limits the overall rate
  • Increasing the concentration of a reactant not involved in the RDS has no effect on the overall reaction rate

Temperature and Catalysts

  • Changing the temperature of a reaction can affect the rates of individual elementary steps differently, depending on their activation energies
    • If the RDS changes as a result of a temperature change, the overall rate law and the temperature dependence of the reaction rate may also change
  • Catalysts lower the activation energy of one or more elementary steps in a complex reaction mechanism
    • If the catalyzed step becomes faster than the previous RDS, the RDS may change, leading to a change in the overall rate law

Activation Energy and Rate Constant Relationship

Arrhenius Equation

  • The overall for a complex reaction depends on the rate constant of the RDS
    • The RDS is the slowest step and limits the overall rate of the reaction
  • The rate constant for the RDS, and thus the overall rate constant for the complex reaction, can be expressed using the :
    • k=A∗e(−Ea/RT)k = A * e^(-Ea/RT)
    • kk is the rate constant, AA is the pre-exponential factor, EaEa is the activation energy, RR is the gas constant, and TT is the absolute temperature

Temperature Dependence and Pre-Exponential Factor

  • The activation energy (EaEa) of the RDS determines the temperature dependence of the overall rate constant and the reaction rate
    • A higher EaEa results in a stronger temperature dependence
    • The reaction rate increases more rapidly with increasing temperature
  • The pre-exponential factor (AA) of the RDS relates to the frequency of collisions between reactant molecules and their orientation
    • It represents the fraction of collisions with sufficient energy and proper orientation to lead to a successful reaction
  • Changes in the RDS due to changes in reaction conditions can lead to changes in the activation energy and pre-exponential factor
    • This affects the overall rate constant and temperature dependence of the complex reaction

Key Terms to Review (17)

Arrhenius Equation: The Arrhenius equation describes how the rate of a chemical reaction depends on temperature and activation energy. It shows that as the temperature increases, the reaction rate typically increases, highlighting the connection between kinetic energy and molecular collisions. This equation is crucial for understanding reaction kinetics, linking to concepts like ionic conductivity, rate laws, and transition states.
Collision theory: Collision theory is a fundamental concept in physical chemistry that explains how chemical reactions occur and why reaction rates differ. It posits that for a reaction to take place, reactant molecules must collide with sufficient energy and proper orientation. This theory highlights the importance of molecular interactions and is crucial for understanding the behavior of both elementary and complex reactions.
Elementary Steps: Elementary steps are the individual, simple reactions that make up a complex reaction mechanism. Each elementary step represents a distinct chemical change, and together they describe the overall process of how reactants are converted into products. Understanding these steps is crucial for determining the rate of a reaction and identifying the rate-determining step, which is the slowest step in the mechanism that controls the overall reaction rate.
Heterogeneous catalyst: A heterogeneous catalyst is a substance that accelerates a chemical reaction by providing an alternative reaction pathway, while existing in a different phase from the reactants. Typically, this means that the catalyst is solid and the reactants are either liquids or gases. The effectiveness of heterogeneous catalysts can often be attributed to their surface properties and the interactions between the catalyst and the reactants, which are crucial in determining the rate of the reaction.
Integrated Rate Equations: Integrated rate equations are mathematical expressions that relate the concentration of reactants or products in a chemical reaction to time. These equations are essential for understanding how the concentration of a species changes as a reaction progresses, particularly in complex reactions where multiple steps may be involved. They help in determining the order of the reaction and predicting the behavior of the system over time, especially when identifying the rate-determining step.
Intermediate: An intermediate is a transient species that forms during a chemical reaction and exists between the reactants and products. These species play a crucial role in understanding complex reactions as they can influence the overall reaction mechanism and kinetics. Intermediates are often unstable and may not be present in significant amounts in the final reaction mixture, but they are essential for illustrating how a reaction proceeds step by step.
Linus Pauling: Linus Pauling was an influential American chemist and peace activist known for his work in quantum chemistry and molecular biology. He made significant contributions to our understanding of chemical bonding, particularly through the development of concepts like hybridization and resonance, which are crucial in analyzing bond energies and formation enthalpies. His pioneering ideas also laid the groundwork for understanding complex reactions and the role of rate-determining steps in chemical kinetics.
Multi-step reactions: Multi-step reactions are chemical processes that involve two or more elementary reactions to convert reactants into products. Each step in the sequence may have its own rate and mechanism, leading to a more complex overall reaction pathway. The interplay of these steps is crucial in understanding reaction kinetics and the concept of the rate-determining step, which influences the overall speed of the reaction.
Rate Constant: The rate constant is a proportionality factor in a rate law that relates the rate of a chemical reaction to the concentrations of reactants. It indicates how fast a reaction proceeds and is affected by factors like temperature and activation energy. The rate constant plays a crucial role in understanding reaction kinetics, including elementary and complex reactions, as well as the influence of molecular collisions and the transition state.
Rate Law: The rate law is a mathematical equation that relates the rate of a chemical reaction to the concentration of its reactants. It expresses how the speed of a reaction depends on the concentrations of the reactants raised to a power, reflecting their roles in the reaction mechanism. Understanding rate laws helps in determining how different factors influence reaction rates, including molecular interactions and energy barriers.
Rate-determining step: The rate-determining step is the slowest step in a chemical reaction mechanism that limits the overall reaction rate. It plays a crucial role in determining how fast a reaction proceeds, as it effectively dictates the rate at which reactants are converted into products. Understanding this step helps in analyzing complex reactions and connecting to the principles of collision theory, which explains how reactants must collide with sufficient energy and orientation for a reaction to occur.
Reactant concentration: Reactant concentration refers to the amount of a substance present in a given volume of solution, which influences the rate of a chemical reaction. Higher concentrations of reactants typically lead to increased reaction rates because there are more particles available to collide and form products. The relationship between reactant concentration and reaction rate is fundamental in understanding how complex reactions and their rate-determining steps operate.
Reaction mechanism: A reaction mechanism describes the step-by-step sequence of elementary reactions that occur during a chemical transformation, detailing how reactants convert to products at a molecular level. Understanding the reaction mechanism is crucial for predicting reaction rates, identifying intermediates, and determining the influence of various factors such as temperature and concentration on the overall reaction. It helps to break down complex reactions into simpler parts, allowing for better comprehension of their kinetics and energetics.
Reaction Order: Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction, indicating how the rate of reaction is influenced by the concentration of that reactant. It provides insight into the relationship between the reaction's speed and the concentrations of reactants involved, often determining how changes in these concentrations will affect the rate at which products are formed. Understanding reaction order is crucial for analyzing complex reactions and identifying the rate-determining step, which is the slowest step in a reaction mechanism that dictates the overall reaction rate.
Steady-state approximation: The steady-state approximation is a simplification used in chemical kinetics that assumes the concentrations of intermediates in a reaction remain constant over time. This means that the rate of formation of the intermediates is equal to the rate of their consumption, allowing for easier mathematical modeling of complex reactions and identification of rate-determining steps.
Svante Arrhenius: Svante Arrhenius was a Swedish physical chemist best known for his work on the theory of electrolytic dissociation and the development of the Arrhenius equation, which describes how temperature affects the rate of chemical reactions. His contributions laid the groundwork for understanding reaction kinetics, including complex reactions and the concept of activation energy, as well as providing insight into transition state theory.
Transition State Theory: Transition state theory is a framework that explains how chemical reactions occur by describing the transition state, which is a high-energy, unstable arrangement of atoms that exists momentarily during the transformation from reactants to products. This theory helps in understanding the energy barriers that must be overcome for a reaction to proceed and relates closely to reaction rates, molecular interactions, and reaction mechanisms.
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