Transition State Theory

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According to this theory, the reactant molecules must come together to form an arrangement of atoms/molecules that facilitates the formation of products. This arrangement of the reacting species is called the transition state. A simple way of visualizing the concept of the transition state is to think of a reaction proceeding along a reaction coordinate. For e.g., in a reaction where two reactants A and B react to form (A + B Products), as A and B come close, the energy of the system goes up and reaches a maxima. The arrangement of the atoms or molecules corresponding to this energy maxima is the transition state. Therefore, the energy level of the transition state is higher than that of the reactants. The energy of the system goes down as soon as the transition state breaks and transforms into products. The transition state is considered to be a stable molecule except for the motion of the atoms along the reaction coordinate. Transition state is supposed to be in equilibrium with the reactants. It also has a very short life. That is why, when it was proposed in the 1930s, it was not possible to study the transition state with the techniques available then. With the help of laser pulses of femtosecond to picoseconds lengths, transition state has been shown to exist. It was characterized spectroscopically in a gas-phase reaction by Zewail and Bernstein in 1988. It has only been a decade and a half, that existence of the transition state has been proven. Transition state theory attempts to relate the kinetic rates with thermodynamic properties of the transition state and reactants. Any elementary reaction.

can be written as

The transition state, is in equilibrium with the reactants. Therefore, the equilibrium constant can be given as,

Now, the formation of the product P is given by,

Once the transition state is formed, then the products are formed with a frequency equal to k_B T/h. That is,

k_B is the Boltzmann's constant and h is the Planck's constant. On substitution of this expression in equation the expression for k becomes

Now, from thermodynamics, it is known that the equilibrium constant K is related to the free energy of the reaction. Hence,

DG for the formation of the transition state is, which the free energy of activation is given by,

Then the equation for k transforms to

The same derivation should hold for the reverse reaction. This implies that the free energy of the reaction is

The change in free energy of the system along the reaction coordinate is shown in the below figure.

fig 6.14 - Progress of a reaction according to transition state theory

At constant temperature, DG is related to the enthalpy of activation DH and to the enthalpy of activation DS as follows:

Enthalpy of activation and entropy of activation are incorporated into the rate constant equation as follows:

The equation shows that the rate constant of a reaction is affected by entropy and enthalpy. Transition state theory predicts slightly different temperature dependence from that of Arrhenius. However, both predict exponential temperature dependence for the rate constant k.

Entropy of activation DS is related to the change in the configuration of the reactant species along the reaction path. With the formation of transition state, there is a loss in the randomness, and therefore the entropy of activation is usually negative.