Lindemann mechanism
Encyclopedia
In chemical kinetics
, the Lindemann mechanism, sometimes called the Lindemann-Hinshelwood mechanism, is a schematic reaction mechanism
. Frederick Lindemann discovered the concept in 1921 and Cyril Hinshelwood developed it.
It breaks down a stepwise reaction
into two or more elementary steps, then it gives a rate constant for each elementary step. The rate law and rate equation
for the entire reaction can be derived from this information.
Lindemann mechanisms have been used to model gas phase decomposition
reactions. Although the net formula for a decomposition may appear to be first-order (unimolecular) in the reactant, a Lindemann mechanism may show that the reaction is actually second-order (bimolecular).
, labeled A* (where A can be any element or compound). The activated intermediate is produced from the reactants only after a sufficient activation energy
is applied. It then either deactivates from A* back to A, or reacts with another (dis)similar reagent to produce yet another reaction intermediate or the final product.
because it is the only step that affects the rate. In layman's terms, a rate-determining step could be compared to traveling through a traffic jam: the time it takes to complete a journey is most severely affected by the time spent waiting in the traffic jam, which is the slow step of the journey.
In the steady-state approximation, it is assumed that each of the elementary steps influences the rate, so there is no "fast" or "slow" step. Therefore, all of the steps must be accounted for in calculating the rate equation. It is also assumed that the concentration of intermediate A* remains constant over time because the concentration of A* builds up very quickly but decays very slowly over the course of a reaction, and the concentration of A* never becomes large. This assumption simplifies the calculation of the rate equation.
Assuming that the concentration
of intermediate A* is held constant according to the quasi steady-state approximation, what is the rate of formation of product P?
First, find the rates of production and consumption of intermediate A*. The rate of production of A* in the first elementary step is simply:
A* is consumed both in the reverse first step and in the forward second step. The respective rates of consumption of A* are:
According to the steady-state approximation, the rate of production of A* equals the rate of consumption. Therefore:
Solving for [A*], 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 as follows:
to nitrogen dioxide
and nitrogen trioxide
is postulated to take place via two elementary steps, which are similar in form to the schematic example given above:
Using the quasi steady-state approximation, the rate equation is calculated to be
Experiment has shown that the rate is observed as first-order in the original concentration of N2O5 sometimes, and second order at other times.
If k2 >> k-1 (>> means "much larger than"), then the rate equation may be simplified by assuming that k-1 ~= 0. Then the rate equation is
which is second order. In contrast, if k2 << k-1 (<< means "much less than"), then the rate equation may be simplified by assuming k2 ~= 0. Then the rate equation is
which is first order.
Chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...
, the Lindemann mechanism, sometimes called the Lindemann-Hinshelwood mechanism, is a schematic reaction mechanism
Reaction mechanism
In chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical change occurs.Although only the net chemical change is directly observable for most chemical reactions, experiments can often be designed that suggest the possible sequence of steps in...
. Frederick Lindemann discovered the concept in 1921 and Cyril Hinshelwood developed it.
It breaks down a stepwise reaction
Stepwise reaction
A stepwise reaction is a chemical reaction with one or more reaction intermediates and involving at least two consecutive elementary reactions....
into two or more elementary steps, then it gives a rate constant for each elementary step. The rate law and rate equation
Rate equation
The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with concentrations or pressures of reactants and constant parameters . To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system...
for the entire reaction can be derived from this information.
Lindemann mechanisms have been used to model gas phase decomposition
Chemical decomposition
Chemical decomposition, analysis or breakdown is the separation of a chemical compound into elements or simpler compounds. It is sometimes defined as the exact opposite of a chemical synthesis. Chemical decomposition is often an undesired chemical reaction...
reactions. Although the net formula for a decomposition may appear to be first-order (unimolecular) in the reactant, a Lindemann mechanism may show that the reaction is actually second-order (bimolecular).
Activated reaction intermediates
A Lindemann mechanism typically includes an activated reaction intermediateReaction intermediate
A reaction intermediate or an intermediate is a molecular entity that is formed from the reactants and reacts further to give the directly observed products of a chemical reaction. Most chemical reactions are stepwise, that is they take more than one elementary step to complete...
, labeled A* (where A can be any element or compound). The activated intermediate is produced from the reactants only after a sufficient activation energy
Activation energy
In chemistry, activation energy is a term introduced in 1889 by the Swedish scientist Svante Arrhenius that is defined as the energy that must be overcome in order for a chemical reaction to occur. Activation energy may also be defined as the minimum energy required to start a chemical reaction...
is applied. It then either deactivates from A* back to A, or reacts with another (dis)similar reagent to produce yet another reaction intermediate or the final product.
The steady-state approximation
In some cases, one of the elementary steps is much slower than the other steps. This slow step is called the rate-determining stepRate-determining step
The rate-determining step is a chemistry term for the slowest step in a chemical reaction. The rate-determining step is often compared to the neck of a funnel; the rate at which water flows through the funnel is determined by the width of the neck, not by the speed at which water is poured in. In...
because it is the only step that affects the rate. In layman's terms, a rate-determining step could be compared to traveling through a traffic jam: the time it takes to complete a journey is most severely affected by the time spent waiting in the traffic jam, which is the slow step of the journey.
In the steady-state approximation, it is assumed that each of the elementary steps influences the rate, so there is no "fast" or "slow" step. Therefore, all of the steps must be accounted for in calculating the rate equation. It is also assumed that the concentration of intermediate A* remains constant over time because the concentration of A* builds up very quickly but decays very slowly over the course of a reaction, and the concentration of A* never becomes large. This assumption simplifies the calculation of the rate equation.
General schematic example
The schematic reaction A + M → P is assumed to consist of two elementary steps:- A + M → A* + M (forward reaction rate = k1; reverse reaction rate = k-1)
- A* → P (forward reaction rate = k2)
Assuming that the concentration
Concentration
In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration...
of intermediate A* is held constant according to the quasi steady-state approximation, what is the rate of formation of product P?
First, find the rates of production and consumption of intermediate A*. The rate of production of A* in the first elementary step is simply:
- d[A*]/dt = k1 [A] [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*]/dt = k-1 [A*] [M] (reverse first step)
- -d[A*]/dt = k2 [A*] (forward second step)
According to the steady-state approximation, the rate of production of A* equals the rate of consumption. Therefore:
- k1 [A] [M] = k-1 [A*] [M] + k2 [A*]
Solving for [A*], it is found that
- [A*] = (k1 [A] [M]) / (k-1 [M] + k2)
The overall reaction rate is
- d[P]/dt = k2 [A*]
Now, by substituting the calculated value for [A*], the overall reaction rate can be expressed in terms of the original reactants A and M as follows:
- d[P]/dt = (k1k2 [A] [M]) / (k-1 [M] + k2)
Specific practical example
The decomposition of dinitrogen pentoxideDinitrogen pentoxide
Dinitrogen pentoxide is the chemical compound with the formula N2O5. Also known as nitrogen pentoxide, N2O5 is one of the binary nitrogen oxides, a family of compounds that only contain nitrogen and oxygen...
to nitrogen dioxide
Nitrogen dioxide
Nitrogen dioxide is the chemical compound with the formula it is one of several nitrogen oxides. is an intermediate in the industrial synthesis of nitric acid, millions of tons of which are produced each year. This reddish-brown toxic gas has a characteristic sharp, biting odor and is a prominent...
and nitrogen trioxide
- N2O5 → NO2 + NO3
is postulated to take place via two elementary steps, which are similar in form to the schematic example given above:
- N2O5 + N2O5 → N2O5* + N2O5
- N2O5* → NO2 + NO3
Using the quasi steady-state approximation, the rate equation is calculated to be
- Rate = k2 [N2O5]* = k1k2 [N2O5]2 / (k-1[N2O5] + k2)
Experiment has shown that the rate is observed as first-order in the original concentration of N2O5 sometimes, and second order at other times.
If k2 >> k-1 (>> means "much larger than"), then the rate equation may be simplified by assuming that k-1 ~= 0. Then the rate equation is
- Rate = k1[N2O5]2
which is second order. In contrast, if k2 << k-1 (<< means "much less than"), then the rate equation may be simplified by assuming k2 ~= 0. Then the rate equation is
- Rate = k1k2[N2O5] / k-1
which is first order.