In
chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with chemical thermodynamics, which deals with the direction in wh ...
, the Lindemann mechanism (also called the Lindemann–Christiansen mechanism
or the Lindemann–Hinshelwood mechanism) is a schematic
reaction mechanism for
unimolecular reactions.
Frederick Lindemann
Frederick Alexander Lindemann, 1st Viscount Cherwell, ( ; 5 April 18863 July 1957) was a British physicist who was prime scientific adviser to Winston Churchill in World War II.
Lindemann was a brilliant intellectual, who cut through bureauc ...
and J.A. Christiansen proposed the concept almost simultaneously in 1921,
[ and ]Cyril Hinshelwood
Sir Cyril Norman Hinshelwood (19 June 1897 – 9 October 1967) was a British physical chemist and expert in chemical kinetics. His work in reaction mechanisms earned the 1956 Nobel Prize in chemistry.
Education
Born in London, his parents we ...
developed it to take into account the energy distributed among vibrational degrees of freedom for some reaction steps.
It breaks down an apparently unimolecular reaction into two elementary step A reaction step of a chemical reaction is defined as: ''"An elementary reaction, constituting one of the stages of a stepwise reaction in which a reaction intermediate (or, for the first step, the reactants) is converted into the next reaction inter ...
s, with a rate constant In chemical kinetics a reaction rate constant or reaction rate coefficient, ''k'', quantifies the rate and direction of a chemical reaction.
For a reaction between reactants A and B to form product C
the reaction rate is often found to have the ...
for each elementary step. The rate law
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial react ...
and rate equation
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reacti ...
for the entire reaction can be derived from the rate equations and rate constants for the two steps.
The Lindemann mechanism is used to model gas phase
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetiza ...
decomposition
Decomposition or rot is the process by which dead organic substances are broken down into simpler organic or inorganic matter such as carbon dioxide, water, simple sugars and mineral salts. The process is a part of the nutrient cycle and is e ...
or isomerization
In chemistry, isomerization or isomerisation is the process in which a molecule, polyatomic ion or molecular fragment is transformed into an isomer with a different chemical structure. Enolization is an example of isomerization, as is tautomeriz ...
reactions. Although the net formula for a decomposition or isomerization appears to be unimolecular and suggests first-order kinetics in the reactant, the Lindemann mechanism shows that the unimolecular reaction step is preceded by a bimolecular
In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reactionAtkins, P.; de Paula, J. Physical Chemistry. Oxford University Press, 2014 and is equal to the sum of stoichiometric coeffici ...
activation step so that the kinetics may actually be second-order in certain cases.
Activated reaction intermediates
The overall equation for a unimolecular reaction may be written A → P, where A is the initial reactant molecule and P is one or more products (one for isomerization, more for decomposition).
A Lindemann mechanism typically includes an activated reaction intermediate, labeled A*. The activated intermediate is produced from the reactant only after a sufficient activation energy
In chemistry and physics, activation energy is the minimum amount of energy that must be provided for compounds to result in a chemical reaction. The activation energy (''E''a) of a reaction is measured in joules per mole (J/mol), kilojoules p ...
is acquired by collision with a second molecule M, which may or may not be similar to A. It then either deactivates from A* back to A by another collision, or reacts in a unimolecular step to produce the product(s) P.
The two-step mechanism is then
:
Rate equation in steady-state approximation
The rate equation
In chemistry, the rate law or rate equation for a reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reacti ...
for the rate of formation of product P may be obtained by using the steady-state approximation
In chemistry, a steady state is a situation in which all state variables are constant in spite of ongoing processes that strive to change them. For an entire system to be at steady state, i.e. for all state variables of a system to be constant, ...
, in which the concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: '' mass concentration'', ''molar concentration'', ''number concentration'', an ...
of intermediate A* is assumed constant because its rates of production and consumption are (almost) equal.[ Atkins P. and de Paula J., ''Physical Chemistry'' (8th ed., W.H. Freeman 2006) p.820-1 ] This assumption simplifies the calculation of the rate equation.
For the schematic mechanism of two elementary steps above, rate constants are defined as for the forward reaction rate of the first step, for the reverse reaction rate of the first step, and for the forward reaction rate of the second step. For each elementary step, the order of reaction is equal to the molecularity
In chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reactionAtkins, P.; de Paula, J. Physical Chemistry. Oxford University Press, 2014 and is equal to the sum of stoichiometric coeffic ...
The rate of production of the intermediate A* in the first elementary step is simply:
: