Editing Reaction mechanism (section)

==Chemical kinetics==
Information about the mechanism of a reaction is often provided by analyzing [[chemical kinetics]] to determine the [[reaction order]] in each reactant.<ref>Espenson, James H. ''Chemical Kinetics and Reaction Mechanisms'' (2nd ed., McGraw-Hill, 2002) chap.6, ''Deduction of Reaction Mechanisms'' {{ISBN|0-07-288362-6}}</ref>

Illustrative is the oxidation of carbon monoxide by nitrogen dioxide:
:CO + NO<sub>2</sub> &rarr; CO<sub>2</sub> + NO

The [[rate law]] for this reaction is:
<math>r = k[NO_2]^2</math>
This form shows that the [[rate-determining step]] does not involve CO.  Instead, the slow step involves two molecules of NO<sub>2</sub>. A possible mechanism for the overall reaction that explains the rate law is:
:2 NO<sub>2</sub> &rarr; NO<sub>3</sub> + NO (slow)
:NO<sub>3</sub> + CO &rarr; NO<sub>2</sub> + CO<sub>2</sub> (fast)

Each step is called an elementary step, and each has its own [[rate law]] and [[molecularity]]. The sum of the elementary steps gives the net reaction.

When determining the overall rate law for a reaction, the slowest step is the step that determines the reaction rate. Because the first step (in the above reaction) is the slowest step, it is the [[rate-determining step]]. Because it involves the collision of two NO<sub>2</sub> molecules, it is a bimolecular reaction with a rate <math>r</math> which obeys the rate law <math>r = k[NO_{2}(t)]^2</math>.

Other reactions may have mechanisms of several consecutive steps. In [[organic chemistry]], the reaction mechanism for the [[benzoin condensation]], put forward in 1903 by [[A. J. Lapworth]], was one of the first proposed reaction mechanisms.
[[Image:Benzoin condensation2.svg|center|thumb|700px|[[Benzoin condensation]] '''reaction mechanism'''. [[Cyanide]] ion (CN<sup>−</sup>) acts as a [[catalyst]] here, entering at the first step and leaving in the last step. Proton (H<sup>+</sup>) transfers occur at (i) and (ii).  The [[arrow pushing]] method is used in some of the steps to show where electron pairs go.]]

A [[Chain reaction#Chemical chain reactions|chain reaction]] is an example of a complex mechanism, in which the [[Chain propagation|propagation]] steps form a closed cycle.
In a chain reaction, the intermediate produced in one step generates an intermediate in another step.
Intermediates are called chain carriers. Sometimes, the chain carriers are radicals, they can be ions as well. In nuclear fission they are neutrons.

Chain reactions have several steps, which may include:<ref>{{cite journal |last1=Bäckström |first1=Hans L. J. |title=The chain-reaction theory of negative catalysis |journal=Journal of the American Chemical Society |date=1 June 1927 |volume=49 |issue=6 |pages=1460–1472 |doi=10.1021/ja01405a011 |bibcode=1927JAChS..49.1460B |url=https://pubs.acs.org/doi/abs/10.1021/ja01405a011 |access-date=20 January 2021|url-access=subscription }}</ref>

# Chain initiation: this can be by [[thermolysis]] (heating the molecules) or [[photolysis]] (absorption of light) leading to the breakage of a bond.
# Propagation: a chain carrier makes another carrier.
# Branching: one carrier makes more than one carrier.
# Retardation: a chain carrier may react with a product reducing the rate of formation of the product. It makes another chain carrier, but the product concentration is reduced.
# Chain termination: radicals combine and the chain carriers are lost.
# Inhibition: chain carriers are removed by processes other than termination, such as by forming radicals.

Even though all these steps can appear in one chain reaction, the minimum necessary ones are Initiation, propagation, and termination.

An example of a simple chain reaction is the thermal decomposition of [[acetaldehyde]] (CH<sub>3</sub>CHO) to [[methane]] (CH<sub>4</sub>) and [[carbon monoxide]] (CO). The experimental reaction order is 3/2,<ref>[[Keith J. Laidler|Laidler K.J.]] and Meiser J.H., ''Physical Chemistry'' (Benjamin/Cummings 1982) p.416-417 {{ISBN|0-8053-5682-7}}</ref> which can be explained by a ''Rice-Herzfeld mechanism''.<ref>Atkins and de Paula p.830-1</ref>

This reaction mechanism for acetaldehyde has 4 steps with rate equations for each step :

# Initiation : CH<sub>3</sub>CHO → •CH<sub>3</sub> + •CHO			(Rate=k<sub>1</sub> [CH<sub>3</sub>CHO])
# Propagation: CH<sub>3</sub>CHO + •CH<sub>3</sub> → CH<sub>4</sub> + CH<sub>3</sub>CO•		(Rate=k<sub>2</sub> [CH<sub>3</sub>CHO][•CH<sub>3</sub>])
# Propagation: CH<sub>3</sub>CO• → •CH<sub>3</sub> + CO 			(Rate=k<sub>3</sub> [CH<sub>3</sub>CO•])
# Termination: •CH<sub>3</sub> + •CH<sub>3</sub> → CH<sub>3</sub>CH<sub>3</sub>			(Rate=k<sub>4</sub> [•CH<sub>3</sub>]<sup>2</sup>)

For the overall reaction, the rates of change of the concentration of the intermediates •CH<sub>3</sub> and CH<sub>3</sub>CO• are zero, according to the [[Steady state (chemistry)|steady-state approximation]], which is used to account for the rate laws of chain reactions.<ref>[[Peter Atkins|Atkins P]] and de Paula J, ''Physical Chemistry'' (8th ed., W.H. Freeman 2006) p.812 {{ISBN|0-7167-8759-8}}</ref>

d[•CH<sub>3</sub>]/dt = k<sub>1</sub>[CH<sub>3</sub>CHO] – k<sub>2</sub>[•CH<sub>3</sub>][CH<sub>3</sub>CHO] + k<sub>3</sub>[CH<sub>3</sub>CO•] - 2k<sub>4</sub>[•CH<sub>3</sub>]<sup>2</sup> = 0

and d[CH<sub>3</sub>CO•]/dt = k<sub>2</sub>[•CH<sub>3</sub>][CH<sub>3</sub>CHO] – k<sub>3</sub>[CH<sub>3</sub>CO•] = 0

The sum of these two equations is  k<sub>1</sub>[CH<sub>3</sub>CHO] – 2 k<sub>4</sub>[•CH<sub>3</sub>]<sup>2</sup> = 0. This may be solved to find the steady-state concentration of •CH<sub>3</sub> radicals as [•CH<sub>3</sub>] = (k<sub>1</sub> / 2k<sub>4</sub>)<sup>1/2</sup> [CH<sub>3</sub>CHO]<sup>1/2</sup>.

It follows that the rate of formation of CH<sub>4</sub> is d[CH<sub>4</sub>]/dt = k<sub>2</sub>[•CH<sub>3</sub>][CH<sub>3</sub>CHO] = k<sub>2</sub> (k<sub>1</sub> / 2k<sub>4</sub>)<sup>1/2</sup> [CH<sub>3</sub>CHO]<sup>3/2</sup>

Thus the mechanism explains the observed rate expression, for the principal products CH<sub>4</sub> and CO. The exact rate law may be even more complicated,  there are also minor products such as [[acetone]] (CH<sub>3</sub>COCH<sub>3</sub>) and [[propionaldehyde|propanal]] (CH<sub>3</sub>CH<sub>2</sub>CHO).