11.1 Rate laws and reaction mechanisms

Chemical kinetics dives into how fast reactions happen and why. Rate laws and reaction mechanisms are key to understanding this. They show us how reactant concentrations affect reaction speed and reveal the step-by-step process of chemical changes.

This part of the chapter breaks down rate laws, reaction orders, and mechanisms. We'll see how these concepts help predict reaction behavior and uncover the hidden steps between reactants and products. It's all about decoding the speed and path of chemical reactions.

Reaction Kinetics Fundamentals

Rate Law and Reaction Order

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• Rate law expresses the relationship between the reaction rate and the concentrations of reactants
• Determined experimentally by measuring the reaction rate at different initial concentrations of reactants
• General form of a rate law: $Rate = k[A]^m[B]^n$, where $k$ is the rate constant, $[A]$ and $[B]$ are the concentrations of reactants, and $m$ and $n$ are the reaction orders with respect to $A$ and $B$
• Reaction order is the sum of the exponents in the rate law ($m + n$) and represents the overall dependence of the reaction rate on the concentrations of reactants
• Zero-order reactions have a constant rate independent of reactant concentrations (decomposition of N2O)
• First-order reactions have a rate directly proportional to the concentration of one reactant (radioactive decay)
• Second-order reactions have a rate proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants (dimerization of cyclopentadiene)

Rate Constant and Elementary Reactions

• Rate constant ($k$) is the proportionality constant in the rate law and depends on temperature, activation energy, and the frequency factor
• Arrhenius equation relates the rate constant to temperature: $k = Ae^{-E_a/RT}$, where $A$ is the frequency factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the absolute temperature
• Elementary reaction is a single-step reaction that occurs exactly as written in the balanced chemical equation
• Molecularity is the number of reactant molecules that participate in an elementary reaction
  • Unimolecular reactions involve one reactant molecule (isomerization of cyclopropane)
  • Bimolecular reactions involve two reactant molecules (formation of HI from H2 and I2)
  • Termolecular reactions involve three reactant molecules and are rare (formation of ozone from oxygen atoms and O2 molecules)

Reaction Mechanisms

Reaction Mechanisms and Rate-Determining Step

• Reaction mechanism is a series of elementary steps that describe the detailed molecular pathway leading from reactants to products
• Overall reaction is the sum of the elementary steps in the mechanism
• Rate-determining step (RDS) is the slowest step in a reaction mechanism and controls the overall reaction rate
• Overall rate law for a multistep reaction is determined by the rate law of the RDS
• Intermediates are species formed in one step of the mechanism and consumed in a subsequent step, not appearing in the overall balanced equation (formation and consumption of HOBr in the bromination of acetone)

Steady-State Approximation and Catalysis

• Steady-state approximation assumes that the concentrations of reactive intermediates remain constant during the majority of the reaction
• Allows the derivation of rate laws for complex reaction mechanisms by setting the rate of formation and consumption of intermediates equal to each other
• Catalysis is the process of increasing the rate of a reaction by providing an alternative reaction pathway with a lower activation energy
• Catalysts participate in the reaction but are regenerated at the end of the catalytic cycle, remaining unchanged (enzymatic catalysis in biological systems)
• Homogeneous catalysis involves catalysts in the same phase as the reactants (acid-base catalysis in aqueous solutions)
• Heterogeneous catalysis involves catalysts in a different phase from the reactants (surface catalysis on solid catalysts)

Complex Reaction Systems

Consecutive and Parallel Reactions

• Consecutive reactions involve the formation of an intermediate product that undergoes further reaction to form the final product ($A \rightarrow B \rightarrow C$)
• Kinetics of consecutive reactions can be analyzed using the steady-state approximation for the intermediate species
• Parallel reactions involve the simultaneous formation of multiple products from the same reactants ($A \rightarrow B$ and $A \rightarrow C$)
• Relative rates of parallel reactions determine the product distribution and can be influenced by reaction conditions (selectivity in the chlorination of methane)

Chain Reactions

• Chain reactions involve the repetitive cycle of elementary steps, with reactive intermediates (often radicals) propagating the chain
• Initiation step generates the initial reactive intermediates (formation of chlorine atoms in the chlorination of methane)
• Propagation steps involve the reaction of intermediates with reactants to form products and regenerate intermediates (reaction of chlorine atoms with methane to form methyl radicals and HCl)
• Termination steps consume the reactive intermediates, ending the chain (recombination of methyl radicals to form ethane)
• Chain reactions can exhibit rapid and explosive behavior due to the self-propagating nature of the reaction (combustion of hydrocarbons)