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 is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the absolute temperature
Temperature Dependence and Pre-Exponential Factor
The activation energy (Ea) of the RDS determines the temperature dependence of the overall rate constant and the reaction rate
A higher Ea results in a stronger temperature dependence
The reaction rate increases more rapidly with increasing temperature
The pre-exponential factor (A) 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