Postulates The theory for ideal gases makes the following assumptions: .... have 7 degrees of freedom, but the lighter gases act as if they have only 5. .... Introduction to the kinetic molecular theory of gases, from The Upper Canada ...

Transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes.

TST is used primarily to understand qualitatively how chemical reactions take place. TST has been less successful in its original goal of calculating absolute reaction rate constants because the calculation of absolute reaction rates requires precise knowledge of potential energy surfaces, but it has been successful in calculating the standard enthalpy of activation (Δ^‡H^⦵), the standard entropy of activation (Δ^‡S^⦵), and the standard Gibbs energy of activation (Δ^‡G^⦵) for a particular reaction if its rate constant has been experimentally determined. (The ^‡ notation refers to the value of interest at the transition state.)

This theory was developed simultaneously in 1935 by Henry Eyring, then at Princeton University, and by Meredith Gwynne Evans and Michael Polanyi of the University of Manchester. TST is also referred to as “activated-complex theory,� “absolute-rate theory,� and “theory of absolute reaction rates.�

Before the development of TST, the Arrhenius rate law was widely used to determine energies for the reaction barrier. The Arrhenius equation derives from empirical observations and ignores any mechanistic considerations, such as whether one or more reactive intermediates are involved in the conversion of a reactant to a product. Therefore, further development was necessary to understand the two parameters associated with this law, the pre-exponential factor (A) and the activation energy (E_a). TST, which led to the Eyring equation, successfully addresses these two issues; however, 46 years elapsed between the publication of the Arrhenius rate law, in 1889, and the Eyring equation derived from TST, in 1935. During that period, many scientists and researchers contributed significantly to the development of the theory.

Theory

Basic ideas behind the transition state theory are as follows:

1. Rates of the reactions are studied by studying activated complexes which lie at the col (saddle point) of a potential energy surface. The details of how the complexes are formed are not important.

2. The activated complexes are in a special equilibrium (quasi-equilibrium) with the reactant molecules.

3. The activated complexes can convert into products which allows kinetic theory to calculate the rate of this conversion.

Development

In the development of TST, three approaches were taken as summarized below

Thermodynamic Treatment

In 1884, Jacobus van't Hoff proposed the Van't Hoff equation describing the temperature dependence of the equilibrium constant for a reversible reaction:

A B

\frac{d\ln K}{dT} = \frac{\Delta U}{RT^{2}}

where ΔU is the change in internal energy, K is the equilibrium constant of the reaction, R is the universal gas constant, and T is thermodynamic temperature. Based on experimental work, in 1889, Svante Arrhenius proposed a similar expression for the rate constant of a reaction, given as follows:

\frac{d\ln k}{dT} = \frac{\Delta E}{RT^{2}}

Integration of this expression leads to the Arrhenius equation

k = Ae^{\frac{-E}{RT}}

A was referred to as the frequency factor (now called the pre-exponential coefficient), and E is regarded as the activation energy. By the early 20th century many had accepted the Arrhenius equation, but the physical interpretation of A and E remained vague. This led many researchers in chemical kinetics to offer different theories of how chemical reactions occurred in an attempt to relate A and E to the molecular dynamics directly responsible for chemical reactions.

In 1910, Rene Marcelin introduced the concept of standard Gibbs energy of activation. His equation can be written as

k\propto\exp\left(\frac{-\Delta^\ddagger G^\ominus}{RT}\right)

At about the same time as Marcelin was working on his formulation, Dutch chemists Philip Abraham Kohnstamm, Frans Eppo Cornelis Scheffer, and Wiedold Frans Brandsma introduced for the first time standard entropy of activation and the standard enthalpy of activation. They proposed the following rate constant equation

k\propto\exp\left(\frac{\Delta^\ddagger S^\ominus}{R}\right)\exp\left(\frac{-\Delta^\ddagger H^\ominus}{RT}\right)

However, the nature of the constant was still unclear.

Kinetic-Theory Treatment

In early 1900, Max Trautz and William Lewis studied the rate of the reaction using collision theory, based on the kinetic theory of gases. Collision theory treats reacting molecules as hard spheres colliding with one another; this theory neglects entropy changes.

Lewis applied his treatment to the following reaction and obtained good agreement with experimental result.

2HI → H₂ + I₂

However, later when the same treatment was applied to other reactions, there were large discrepancies between theoretical and experimental results.

Statistical-Mechanical Treatment

Statistical mechanics played a significant role in the development of TST. However, the application of statistical mechanics to TST was developed very slowly given the fact that in mid-19th century, James Clerk Maxwell, Ludwig Boltzmann, and Leopol