# Lindemann mechanism

The fall-off curve in the Lindemann mechanism. The marked areas are for illustration purposes only, they are not actually existing borders.

In kinetics , the Lindemann mechanism , sometimes also referred to as the Lindemann-Hinshelwood mechanism , is a schematic reaction mechanism for reactions in the gas phase. The concept was proposed by Frederick Lindemann in 1922 and developed by Cyril Norman Hinshelwood . An apparently unimolecular reaction is broken down into two elementary steps. The Lindemann mechanism is used to depict gas phase decomposition or isomerization reactions. The reaction equations of decomposition or isomerization reactions often suggest a unimolecular reaction:

{\ displaystyle {\ begin {aligned} {\ ce {A}} \ & {\ ce {-> P}} \ end {aligned}}}

But the Lindemann mechanism shows that the unimolecular reaction step is preceded by a bimolecular activation step. For certain cases there is therefore a reaction of the second order and not, as would be expected, the first order:

{\ displaystyle {\ begin {aligned} {\ ce {{A} + M}} \ & {\ ce {<=> {A ^ {\ ast}} + M}} \\ {\ ce {A ^ { \ ast}}} \ & {\ ce {-> P}} \ end {aligned}}}

## Speed ​​law

The corresponding law of speed can be derived from the speed equations and constants: The speed with which the product P is formed results from Bodenstein's principle of quasi-stationaryity . We assume here that the concentration of the activated starting material (the intermediate A *) is formed at the same rate as it is consumed. This assumption simplifies the calculation of the rate equation.

We denote the rate constant of the forward reaction of the first step with k 1 , the reverse reaction with k −1 . We denote the rate constant of the forward reaction of the second step by k 2 .

The speed with which A * is formed results from the following differential speed law:

${\ displaystyle {\ frac {d [{\ ce {A}} ^ {*}]} {dt}} = k_ {1} [{\ ce {A}}] [{\ ce {M}}]}$ (Forward reaction in the first step)

A * is consumed both in the reverse reaction and in the product formation in the second step. The following differential speed laws result:

${\ displaystyle {\ frac {-d [{\ ce {A}} ^ {*}]} {dt}} = k _ {- 1} [{\ ce {A}} ^ {*}] [M]}$ (Reverse reaction in the first step)
${\ displaystyle {\ frac {-d [{\ ce {A}} ^ {*}]} {dt}} = k_ {2} [{\ ce {A}} ^ {*}]}$ (Forward reaction in the second step)

According to the quasi-stationary principle, the formation of A * is equal to the consumption of A *. Hence:

${\ displaystyle k_ {1} [{\ ce {A}}] [{\ ce {M}}] = k _ {- 1} [{\ ce {A}} ^ {*}] [{\ ce {M }}] + k_ {2} [{\ ce {A}} ^ {*}]}$

Resolved according to : ${\ displaystyle [{\ ce {A}} ^ {*}]}$

${\ displaystyle [{\ ce {A}} ^ {*}] = {\ frac {k_ {1} [{\ ce {A}}] [{\ ce {M}}]} {k _ {- 1} [{\ ce {M}}] + k_ {2}}}}$

The differential rate law gives for the overall reaction:

${\ displaystyle {\ frac {d [{\ ce {P}}]} {dt}} = k_ {2} [{\ ce {A}} ^ {*}]}$
${\ displaystyle {\ frac {d [{\ ce {P}}]} {dt}} = {\ frac {k_ {1} k_ {2} [{\ ce {A}}] [{\ ce {M }}]} {k _ {- 1} [{\ ce {M}}] + k_ {2}}}}$

## Reaction order

The reaction order of a reaction that approximately follows the Lindemann mechanism is pressure-dependent. At high pressure (high pressure limit value for ) it is a first order reaction and at low pressure (low pressure limit value for ) it is a second order reaction. ${\ displaystyle k _ {\ infty}}$${\ displaystyle [M] \ rightarrow \ infty}$${\ displaystyle k_ {0}}$${\ displaystyle [M] \ rightarrow 0}$