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# Elementary Reactions

An elementary reaction is a single step reaction having a single transition state and no intermediates

### Introduction

Elementary reactions add up to complex reactions. In other words, non-elementary reactions can be explained in multiple elementary reaction steps. A set of elementary reactions comprises a reaction mechanism, which predicts the elementary steps involved in a  complex reaction. Below are two reaction coordinates of two reactions. One describes an elementary reaction while the other describes a non-elementary reaction.

 Elementary Reaction Complex Reaction $\text{Reactants} \rightarrow \text{Products}$ This is a sample reaction coordinate of an elementary reaction. Note that there is one transition state and no intermediates. Again, elementary steps cannot be explained in simpler reactions. $\text{Reactants} \rightarrow \text{Intermediates} \rightarrow \text{Products}$ This is a sample reaction coordinate of a complex reaction. Note that it involves an intermediate and multiple transition states. Again, a complex reaction can be explained in terms of elementary reactions.

### Types of Elementary Reactions

The molecularity of a reaction refers to the number of reactant particles involved in the reaction. As there can only be discrete number of particles, the molecularity must be an integer. Molecularity can be described as either unimolecular, bimolecular, or termolecular. There are no known elementary reactions involving four or more molecules.1The following table summarizes the three known types of elementary reactions:

Molecularity Elementary Step Rate Law Example
Unimolecular $$A \rightarrow Products$$ $$rate = k[A]$$ $$N_2O_{4(g)} \rightarrow 2NO_{2(g)}$$
Bimolecular $$A + A \rightarrow Products$$ $$rate = k[A]^2$$ $$2NOCl \rightarrow 2NO_{(g)} + CO_{2(g)}$$
$$A + B \rightarrow Products$$ $$rate = k[A][B]$$ $$CO_{(g)} + NO_{3(g)} \rightarrow NO_{2(g)} + CO_{2(g)}$$
Termolecular $$A + A +A \rightarrow Products$$ $$rate = k[A]^3$$
$$A + A + B \rightarrow Products$$ $$rate = k[A]^2[B]$$ $$2NO_{(g)} + O_{2(g)} \rightarrow 2NO_{2(g)}$$ 2
$$A + B + C \rightarrow Products$$ $$rate = k[A][B][C]$$ $$H + O_{2(g)} + M \rightarrow HO_{2(g)} + M$$ 3

#### Unimolecular Reaction

unimolecular reaction occurs when a molecule rearranges itself to produce one or more products.  An example of this is radioactive decay, in which particles are emitted from an atom. Other examples include "cis-trans isomerization, thermal decomposition, ring opening, and racemization."1  The rate at which a substance decomposes is dependent on its concentration. Unimolecular reactions are often first-order reactions as explained by Frederick Alexander Lindemann in 1922.3 To read further about Lindemann and why unimolecular reactions are not second-order, read here or here.

#### Bimolecular Reaction

bimolecular reaction involves the collision of two particles. Bimolecular reactions are common in organic chemical reactions such as nucleophilic subsitution.  The rate of reaction depends on the product of both species involved, which makes bimolecular reactions second-order reactions.

#### Termolecular Reaction

termolecular reaction requires the collision of three particles at the same place and time.  This type of reaction is very uncommon as all three reactants must simultaneously collide with each other, with sufficient energy and correct orientation, in order to produce a reaction.  There are three ways termolecular reactions can react, and all are third order.

### Practice Problems

1. How are non-elementary steps and elementary steps related?
2. Choose the correct statements.
a. An elementary step has 0 intermediates.
b. An elementary step has 1 intermediate.
c. An elementary step has 2 intermediates.
d. An elementary step has 0 transition states.
e. An elementary step has 1 transition state.
f. An elementary step has 2 transition states.
3. Which of the following is a termolecular reaction?
a. $$A + 2B + C \rightarrow D$$
b. $$A + B + B \rightarrow C$$
c. all of the above
d. $$2A + 2B + 2C \rightarrow 2D$$
e. b and d
f. none of the above
4. Which rate law corresponds to a bimolecular reaction?
a. $$rate = k[A][A]^2$$
b. $$rate = k[A][B]$$
c. all of the above
d. $$rate = k[A]^2$$
e. b and d
f. none of the above
5. Give an example of a reaction with a molecularity of 1/2.
6. True or False: Given species A and B inside a container, instruments detect that three (3) collisions occured before product was formed. That is, we know a reaction occured after detecting three collisions in a box. We can conclude that the reaction is a termolecular reaction (as the reaction could have been produced from A+A+B or A+B+B).

#### Solutions

1. Non-elementary steps, or complex reactions, are sets of elementary reactions. That is to say, the addition of elementary steps produces complex, non-elementary reactions.
2. The correct statements are "a" and "e". By definition of elementary reactions they have 0 intermediates because they cannot be broken down. Again by definition of an elementary reaction, a single-step reaction will have 1 transition state. There is no reaction with 0 transition states. Having 2 transition states implies having 1 intermediate, making the reaction non-elementary.
"a" is not a termolecular reaction as it involves A + B + B + C, or 4 molecules
"b" is a termolecular reaction as it involves 3 particles: A + B + B
"c" is incorrect because "a" is incorrect
"d" is a termolecular reaction as the coefficients cancel out to give the reaction: $$A + B + C \rightarrow D$$, which involves 3 particles (A + B + C)
"e" is the correct answer as "b" and "d" are correct
"a" is incorrect because the rate law describes a third-order reaction, which is true for termolecular reactions
"b" is a possible rate law for the bimolecular reaction: \(A + B \rightarrow Products") }}
"c" is incorrect because "a" is incorrect
"d" is a possible rate law for the bimolecular reaction: \(A + A \rightarrow Products") }}
"e" is the correct answer as "b" and "d" are correct
5. Impossible. The molecularity of a reaction MUST be an integer as there cannot be "a half of a particle" producing a reaction.
6. False, we cannot conclude anything. While a termolecular reaction requires the collision of three particles, the reverse logic is not necessarily true. That is, having three collisions is not sufficient for a termolecular reaction.
1. For example, particles A + A + B collide with each other at the same place and time. However, particle B was in the wrong orientation, so no reaction occurred. Instead, the two A particles were in the correct orientation and produced a reaction, which is a bimolecular reaction.
2. Consider a second example: two collisions between particles A + A + B occured, but there was not enough energy to produce a reaction. Instead, a third collision between A and B had the sufficient energy and correct orientation to produce a reaction. Such a reaction is, again, only bimolecular.
3. A last example: particle A collides twice with a wall, and then once with B to produce a reaction. Such a reaction involving three collisions at different places and different time is only a bimolecular reaction.

### References

1. Chang, Raymond. "Chemical Kinetics." Physical Chemistry for the Biosciences. Sansalito, CA: University Science, 2005. 325-328. Print.
2. Olbregts, J. (1985), Termolecular reaction of nitrogen monoxide and oxygen: A still unsolved problem. International Journal of Chemical Kinetics, 17: 835–848. doi: 10.1002/kin.550170805.
3. Kerr, James Alistair. "Notes on the Tables." CRC Handbook of bimolecular and termolelucar gas reactions . Boca Raton, Florida: CRC Press, 1987. 2. Print.
4. Baer, Tomas, and William L. Hase. "Introduction." Unimolecular reaction dynamics: theory and experiments. New York: Oxford University Press, 1996. 4-5. Print.

### Contributors

• Tho Nguyen (UCD), Minh Ngo (UCD)

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reaction coordinate of a complex reaction and how elementary reactions relate
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