12.1 Elementary reactions and molecularity

Elementary reactions and molecularity are key concepts in understanding reaction mechanisms. They help us break down complex reactions into simpler steps, making it easier to analyze and predict reaction rates.

Molecularity tells us how many molecules are involved in a single reaction step. This concept is crucial for determining rate laws and understanding the likelihood of different types of reactions occurring in chemical systems.

Elementary vs Complex Reactions

Defining Elementary and Complex Reactions

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• Elementary reactions occur in a single step and involve the direct conversion of reactants to products without any intermediate species
  • Reactant molecules collide and transform into product molecules in a single event (A + B → C)
  • No reaction intermediates are formed during the process
• Complex reactions involve multiple elementary steps and the formation of one or more reaction intermediates before yielding the final products
  • Reaction proceeds through a series of elementary steps, each with its own transition state
  • Intermediate species are formed and consumed during the reaction (A + B → X, X + C → D)
  • Overall reaction may have a different rate law than individual elementary steps

Relationship Between Elementary Steps and Overall Reaction

• The overall reaction equation for a complex reaction is the sum of all the elementary steps in the reaction mechanism
  • Elementary steps are added together to give the balanced equation for the overall reaction
  • Reaction intermediates cancel out when elementary steps are summed
  • Rate of the overall reaction depends on the rates of individual elementary steps

Molecularity of Elementary Reactions

Defining Molecularity

• Molecularity is defined as the number of reactant molecules that must collide simultaneously for an elementary reaction to occur
  • Represents the number of molecules involved in the rate-determining step
  • Determines the kinetic order of the reaction with respect to each reactant
• The molecularity of an elementary reaction can be determined by counting the number of reactant molecules in the balanced chemical equation for that specific reaction step
  • Reactant molecules are counted on the left side of the equation arrow
  • Coefficients in the balanced equation do not affect molecularity
• Molecularity is always a positive integer (1, 2, or 3) and should not be confused with the stoichiometric coefficients in the balanced equation
  • Stoichiometric coefficients represent the relative amounts of reactants and products
  • Molecularity refers to the number of molecules involved in the rate-determining step

Classifying Elementary Reactions

Unimolecular Reactions

• Unimolecular reactions have a molecularity of one, involving a single reactant molecule undergoing a reaction, such as isomerization or decomposition
  • Reaction involves the rearrangement or fragmentation of a single molecule (A → B)
  • Examples include radioactive decay, thermal decomposition, and cis-trans isomerization
• Rate law for a unimolecular reaction: Rate = k[A]
  • Rate is directly proportional to the concentration of the reactant molecule

Bimolecular Reactions

• Bimolecular reactions have a molecularity of two, involving the collision and reaction of two reactant molecules, which can be the same or different species
  • Two molecules must collide with sufficient energy and proper orientation for the reaction to occur (A + B → C)
  • Examples include Diels-Alder reactions, SN2 reactions, and the formation of hydrogen iodide (H2 + I2 → 2HI)
• Rate law for a bimolecular reaction: Rate = k[A][B] or Rate = k[A]^2 (if A and B are the same species)
  • Rate depends on the concentrations of both reactant molecules

Termolecular Reactions

• Termolecular reactions have a molecularity of three, involving the simultaneous collision and reaction of three reactant molecules
  • Three molecules must collide simultaneously with sufficient energy and proper orientation (A + B + C → D)
  • Examples include the formation of ozone (O + O2 + M → O3 + M) and the recombination of nitric oxide with oxygen (2NO + O2 → 2NO2)
• Rate law for a termolecular reaction: Rate = k[A][B][C]
  • Rate depends on the concentrations of all three reactant molecules

Rate Law and Molecularity

Relationship Between Rate Law and Molecularity

• For an elementary reaction, the rate law can be determined directly from the balanced chemical equation
  • Molecularity of the reaction determines the form of the rate law
  • Order of the reaction with respect to each reactant is equal to its stoichiometric coefficient in the balanced equation
• The rate law for an elementary reaction is proportional to the product of the concentrations of the reactants, with each concentration raised to a power equal to its molecularity
  • Unimolecular reaction: Rate = k[A]
  • Bimolecular reaction: Rate = k[A][B] or Rate = k[A]^2 (if A and B are the same species)
  • Termolecular reaction: Rate = k[A][B][C]
• The overall order of an elementary reaction is equal to its molecularity
  • Sum of the exponents in the rate law equals the molecularity of the reaction
  • Unimolecular reactions are first-order, bimolecular reactions are second-order, and termolecular reactions are third-order

Determining Rate Laws from Elementary Steps

• Rate law for a complex reaction cannot be determined directly from the overall balanced equation
  • Overall rate law depends on the slowest elementary step (rate-determining step)
  • Reaction intermediates do not appear in the overall rate law
• To determine the rate law for a complex reaction, identify the slowest elementary step and use its rate law as the overall rate law
  • Slowest step is the bottleneck of the reaction and determines the overall rate
  • Other elementary steps are assumed to be at equilibrium and do not affect the overall rate

Molecularity: Unimolecular vs Bimolecular vs Termolecular

Prevalence of Different Molecularities

• Unimolecular and bimolecular reactions are the most common types of elementary reactions
  • Majority of elementary reactions involve one or two reactant molecules
  • Unimolecular reactions are common in isomerization, decomposition, and radioactive decay
  • Bimolecular reactions are prevalent in substitution, addition, and elimination reactions
• The probability of three molecules colliding simultaneously with sufficient energy and proper orientation is extremely low, making termolecular reactions rare
  • Collision of three molecules is statistically improbable
  • Termolecular reactions have very low reaction rates and are kinetically unfavorable
• Most apparent termolecular reactions are actually a sequence of bimolecular and/or unimolecular elementary steps
  • Overall reaction may appear to be termolecular but proceeds through a series of lower-molecularity steps
  • Reaction intermediates are formed and consumed in the process

Examples of Rare Termolecular Reactions

• Formation of ozone (O + O2 + M → O3 + M)
  • Involves the collision of an oxygen atom, an oxygen molecule, and a third molecule (M) that absorbs excess energy
  • Third molecule (M) is necessary to stabilize the ozone molecule and prevent its rapid decomposition
• Recombination of nitric oxide with oxygen (2NO + O2 → 2NO2)
  • Involves the simultaneous collision of two nitric oxide molecules and an oxygen molecule
  • Reaction is important in the formation of nitrogen dioxide in the atmosphere
• Termolecular reactions are rare exceptions to the general trend of unimolecular and bimolecular elementary steps
  • Require highly specific conditions and molecular orientations
  • Play a minor role in the overall kinetics of most chemical systems