Organic Mechanisms. Xiaoping Sun

FIGURE 1.1 Reaction profiles for a concerted S_N2 reaction (a) and a stepwise S_N1 reaction (b).

      Whether a chemical reaction is concerted or stepwise is determined by geometry and electronic structure of reactant and product molecules and reaction conditions. In many cases, the mechanism is predictable. In the individual chapters of this book, we will study the various types of concerted and stepwise reactions and the specific conditions which make them happen.

1.3 MOLECULARITY

      The number of molecules contained in the transition state of a concerted reaction is called molecularity of the reaction. Clearly, the molecularity is determined by the number of reactant molecules that are involved in the mechanism (microscopic step) of a concerted reaction.

      1.3.1 Unimolecular Reactions

The microscopic steps of many concerted chemical reactions only involve a single reactant molecule. Such a concerted reaction whose mechanism only involves one reactant molecule is defined as a unimolecular reaction. It is generalized as follows (Eq. 1.1):

(1.1)

A, A*, and P represent a reactant molecule, an activated reactant molecule (transition state), and a product molecule, respectively. In a unimolecular reaction, a reactant molecule can possibly gain energy and then is activated by several means, including collision of the reactant molecule with a solvent molecule or with the wall of the reactor, thermally induced vibration of the reactant molecule, and photochemical excitation of the reactant molecule. After the molecule is activated, some simultaneous bond‐breaking and bond‐formation processes will take place in A* intramolecularly. As a result, the reactant molecule A will be transformed into one or more product molecules. Common examples of unimolecular reactions are thermal or photochemical dissociation of a halogen molecule (Reaction 1.2) and intramolecular ring‐opening and ring‐closure reactions (Reaction 1.3).

(1.2)

(1.3)

      1.3.2 Bimolecular Reactions

For most of concerted chemical reactions, their microscopic steps (mechanisms) involve effective collisions between two reactant molecules. Such a concerted reaction that is effected by collision of two reactant molecules to directly lead to the formation of products is defined as a bimolecular reaction. A bimolecular reaction can be effected by collision of two molecules of a same compound (Eq. 1.4) or two molecules of different compounds (Eq. 1.5).

(1.4)

(1.5)

As a result, simultaneous bond‐breaking and bond‐formation take place within the activated complex (transition state) A₂* or [AB]*. This leads to spontaneous collapse of the activated complex (transition state) giving product molecules. Common examples of bimolecular reactions are thermal decomposition of hydrogen iodide (HI) to elemental iodine (I₂) and hydrogen (H₂) (Reaction 1.6), the S_N2 reaction of hydroxide with bromomethane (Reaction 1.7), and Diels–Alder reaction of 1,3‐butadiene and ethylene (Reaction 1.8).

(1.6)

(1.7)

(1.8)

      Almost all the concerted processes in organic reactions are either unimolecular or bimolecular steps.

1.4 KINETICS

      1.4.1 Rate‐Laws for Elementary (Concerted) Reactions

      For elementary reactions, the reaction orders are consistent with the molecularity. A unimolecular reaction is the first‐order in the reactant and a bimolecular reaction has a second‐order rate law.

       Unimolecular reactions

A unimolecular reaction (Eq. 1.1: A ➔ P) follows the first‐order rate law as shown in Equation 1.9

(1.9)

      where k is the rate constant (with the typical unit of s⁻¹) for the reaction, and it is independent of the concentration of the reactant. The rate constant is the quantitative measure of how fast the reaction proceeds at a certain temperature.

      Rearranging Equation 1.9 leads to

(1.10)

Integrating Equation 1.10 on both sides and applying the boundary condition t = 0, [A] = [A]₀ (initial concentration), we have