In chemical kinetics, the Lindemann mechanism (also called the Lindemann–Christiansen mechanism or the Lindemann–Hinshelwood mechanism) is a schematic reaction mechanism for unimolecular reactions. Frederick Lindemann and J. A. Christiansen proposed the concept almost simultaneously in 1921, and Cyril Hinshelwood 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 steps, with a rate constant for each elementary step. The rate law and rate equation 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 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.
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 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
A + M ↽ − − ⇀ A ∗ + M A ∗ ⟶ P {\displaystyle {\begin{aligned}{\ce {{A}+M}}\ &{\ce {<=>{A^{\ast }}+M}}\\{\ce {A^{\ast }}}\ &{\ce {->P}}\end{aligned}}}
Rate equation in steady-state approximation 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. This assumption simplifies the calculation of the rate equation. For the schematic mechanism of two elementary steps above, rate constants are defined as k 1 {\displaystyle k_{1}} for the forward reaction rate of the first step, k − 1 {\displaystyle k_{-1}} for the reverse reaction rate of the first step, and k 2 {\displaystyle k_{2}} 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:
d [ A ∗ ] d t = k 1 [ A ] [ M ] {\displaystyle {\frac {\mathrm {d} [{\ce {A}}^{*}]}{\mathrm {d} t}}=k_{1}[{\ce {A}}][{\ce {M}}]} (forward first step) A* is consumed both in the reverse first step and in the forward second step. The respective rates of consumption of A* are:
− d [ A ∗ ] d t = k − 1 [ A ∗ ] [ M ] {\displaystyle -{\frac {\mathrm {d} [{\ce {A}}^{*}]}{\mathrm {d} t}}=k_{-1}[{\ce {A}}^{*}][{\ce {M}}]} (reverse first step)
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