D28.3 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 for such a reaction is directly proportional to concentration of A as well as directly proportional to concentration of 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 for such a reaction is proportional to the square of concentration of A:

rate = k[A]2

Consider the first case above, A + B ⟶ products. How does the concentration of each reactant affect the number of collisions, and hence the rate of the reaction? In the figure below, reactant A is shown in black and reactant B in white. We see that the number of collisions doubles when the number (and concentration) of either reactant doubles. Assuming that the fraction of collisions that results in reaction is the same in all three scenarios, this means that the rate of reaction doubles when the concentration of either reactant doubles.

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 to 100, 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.

An example of a bimolecular elementary reaction 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.

Exercise: Bimolecular Reactions

Exercise: Steric Factor

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