Christiansen proposed the concept almost simultaneously in 1921,[4][1] and Cyril Hinshelwood developed it to take into account the energy distributed among vibrational degrees of freedom for some reaction steps.
[5][6] It breaks down an apparently unimolecular reaction into two elementary steps, with a rate constant for each elementary step.
The Lindemann mechanism is used to model gas phase decomposition or isomerization reactions.
Although the net formula for 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 activation step so that the kinetics may actually be second-order in certain cases.
[7] 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 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 The rate equation for the rate of formation of product P may be obtained by using the steady-state approximation, in which the concentration of intermediate A* is assumed constant because its rates of production and consumption are (almost) equal.
[8] 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 The rate of production of the intermediate A* in the first elementary step is simply: A* is consumed both in the reverse first step and in the forward second step.
, it is found that The overall reaction rate is Now, by substituting the calculated value for [A*], the overall reaction rate can be expressed in terms of the original reactants A and M:[9][8] The steady-state rate equation is of mixed order and predicts that a unimolecular reaction can be of either first or second order, depending on which of the two terms in the denominator is larger.
which is first order, and the rate-determining step is the second step, i.e. the unimolecular reaction of the activated molecule.
The theory can be tested by defining an effective rate constant (or coefficient)
which would be constant if the reaction were first order at all pressures:
The Lindemann mechanism predicts that k decreases with pressure, and that its reciprocal
does decrease at low pressure, but the graph of
To account accurately for the pressure-dependence of rate constants for unimolecular reactions, more elaborate theories are required such as the RRKM theory.
[9][8] In the Lindemann mechanism for a true unimolecular reaction, the activation step is followed by a single step corresponding to the formation of products.
Whether this is actually true for any given reaction must be established from the evidence.
Much early experimental investigation of the Lindemann mechanism involved study of the gas-phase decomposition of dinitrogen pentoxide[10] 2 N2O5 → 2 N2O4 + O2.
This reaction was studied by Farrington Daniels and coworkers, and initially assumed to be a true unimolecular reaction.
However it is now known to be a multistep reaction whose mechanism was established by Ogg[10] as: An analysis using the steady-state approximation shows that this mechanism can also explain the observed first-order kinetics and the fall-off of the rate constant at very low pressures.
[10] The Lindemann-Hinshelwood mechanism explains unimolecular reactions that take place in the gas phase.
Usually, this mechanism is used in gas phase decomposition and also in isomerization reactions.
[11] Although it seems like a simple reaction, it is actually a multistep reaction: This isomerization can be explained by the Lindemann mechanism, because once the cyclopropane, the reactant, is excited by collision it becomes an energized cyclopropane.
And then, this molecule can be deactivated back to reactants or produce propene, the product.