D36.1 Bimolecular Elementary Reactions

The collision and reaction of two molecules or atoms in an elementary reaction is a bimolecular elementary reaction. There are two general types of bimolecular elementary reactions. In one type, the two reactants are different:

A + B ⟶ products

The rate law for such a reaction is first-order in [A] and first-order in [B]:

rate = k[A][B]

In the other type of bimolecular elementary reaction, the two reactants are the same:

A + A ⟶ products          or          2 A ⟶ products

The rate law for such a reaction is second-order with respect to [A]:

rate = k[A]2

If a reaction is known to be a bimolecular elementary reaction, then its rate law can be derived by considering how concentration of each reactant affects the number of collisions. This is shown in the figure below for the case of “A + B ⟶ products”. Assuming that the fraction of collisions that results in reaction is the same in all three cases, the rate of reaction doubles when the number (and concentration) of either reactant doubles. The rate law derived from number of collisions agrees with the rate law derived from the reaction equation. A bimolecular reaction is overall second-order.

Figure: Effect of concentration on the frequency of collisions for a bimolecular reaction. (a) A single black molecule moving among 50 white molecules traces the path shown and collides with 5 white molecules in 1 s. Each white molecule that has been struck by a moving black molecule is shown in color. (b) If the number of white molecules is doubled, the frequency of collisions rises to 10 per second. (c) Two black molecules moving among 50 white ones produce 10 collisions per second. The number of collisions can thus be seen to be proportional to both the concentration of white molecules and the concentration of black molecules.

Some chemical reactions have mechanisms that consist of a single bimolecular elementary reaction. An example is the gas-phase reaction of 1,3-butadiene with ethene to form cyclohexene:

C4H6(g) + C2H4(g) ⟶ C6H10(g)          rate = k[C4H6][C2H4]
Figure: mechanism for the reaction of 1,3-butadiene with ethene to produce cyclohexene. In the transition state, bonds that are breaking (three π bonds) are shown in orange and bonds that are forming (one π bond and two σ bonds) are shown in blue.

Another example of a bimolecular elementary reaction is step 2 in the ozone decomposition mechanism given earlier:

O(g) + O3(g) ⟶ 2O2(g)          rate = k[O][O3]

 

Exercise: Bimolecular Reactions

Exercise: Steric Factor

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Chemistry 109 Fall 2021 by John Moore, Jia Zhou, and Etienne Garand is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.