Transition State Theory

Question 1

What can you calculate using transition state theory?

Answer 1

Transition state theory allows the calculation of the rate constant using thermodynamic principles, specifically those of the transition state

Question 2

Describe the model for transition state theory

Answer 2

The reaction pathway from reactants to products passes through a transition state at the highest point of the energy profile

Question 3

What assumptions are made?

Answer 3

It assumes that a pre equilibrium is established between the reactants and the transition state ABC which then goes on to form the products

Question 4

What is a general reaction for TST?

Answer 4

A + BC -> AB + C (k)
A + BC(K#) -> ABC# -> AB +C(k#)
K# is the equilibrium constant for the reversible step to form the transition state
k# is the rate constant for the formation of the products

Question 5

What happens to the molecules as they react?

A + BC -> AB + C

Answer 5

The reactants A and BC will collide during a reaction
As atom A approaches atom B, the distance rAB will decrease and as A gets sufficiently close to B distance rBC between B and C will start to increase as A and B interact

Question 6

What happens to the energy of the system?

Answer 6

As the molecules react and interatomic distances change, the energy of the system will increase

Question 7

What is the point of maximum energy?

Answer 7

This is the transition state

Once the colliding atoms reach this point, they can continue on to the products

Question 8

How can the reaction be represented?

Answer 8

It can be represented in the potential energy diagram

Question 9

What does the reaction coordinate represent?

Answer 9

This represents the changing interatomic distances

Question 10

Describe the state of the system at the transition state

Answer 10

At the transition state, the system is at unstable equilibrium
It can only exist transiently

Question 11

Describe how the reaction can be represented in terms of rate constants

Answer 11

A + BC -> AB + C
A + BC(K#) -> ABC# -> AB +C(k#)

Reversible equilibrium forming the transition state (k1, k-1)
The transition state decomposes to the final products (k2)

Question 12

A + BC(K#) -> X# -> AB +C(k#

What is the rate of reaction with respect to AB?

Answer 12

d[AB]/dt= k2[X#]

Question 13

How can you find the concentration of the transition state?

Answer 13

It can be found from the equilibrium constant for its formation
A + BC(K#) -> X#
K#= [X#]/ [A][BC]
Rearrange to: [X#]=K#[A][BC]
Sub into d[AB]/dt= k2[X#]
d[AB]/dt= koverall[A][BC]= k2K#[A][BC]
Therefore koverall = k2[K#]

Question 14

What is the koverall equation for

A+BC-> X -> AB+C

Answer 14

d[AB]/dt= koverall [A][BC]

For k overall do not include the transition state

Question 15

What is koverall in this theory?

Answer 15

koverall= k2[K#]

Question 16

How does free energy relate to equilibrium constant?

Answer 16

^G#= -RT lnK#

You can rearrange this to find what K# equals
K#= e^-^G#/RT

Question 17

How can you find K in terms of entropy and enthalpy?

Answer 17

^G#= -RT lnK#

You can rearrange this to find what K# equals 
K#= e^-^G#/RT
sub in ^G= ^H- T^S
K#= e^-^H# +T^S#)/RT
K#= e^(^S#/R) x e^(-^H#/RT)

Question 18

What is ^H# and ^S#

Answer 18

This is the activation enthalpy and entropy

Question 19

Express the overall rate constant in terms of thermodynamics

Answer 19

koverall= k2[K#]
K#= e^(^S#/R) x e^(-^H#/RT)
Sub in to get
koverall= k2 e^(^S#/R) x e^(-^H#/RT)

This represents the rate constant going from reactants to transition state as well as rate constant going from the transition state to the products

Question 20

What is asymmetric stretch?

Answer 20

This is a contract at one bond and stretch at another

Equivalent to a translation, pushed X# over the transition state

Question 21

Describe the properties of the reaction coordinate leading to and away from transition state

Answer 21

In the vicinity of the transition state, the reaction coordinate has the properties of an asymmetric stretch vibrational mode
As the reaction proceeds away from the transition state and on the products, the reaction coordinate changes to have the properties of a translational degree of freedom

Question 22

What is k2?

Answer 22

k2= KBT/h

Question 23

What is the complete evaluation of koverall?

Answer 23

Sub k2= kBT/h

koverall= (KBT/h) x e^(^S#/R) x e^(-^H#/RT)

Question 24

What is the eyring equation?

Answer 24

koverall= t(KBT/h) x e^(^S#/R) x e^(-^H#/RT)

Question 25

What does t account for?

Answer 25

The t accounts for the fact that a proportion of collisions that reach the transition state, could actually return to reactants

Question 26

Compare the eyring equation with the Arrhenius equation to give A factors and Ea

Answer 26

koverall=  t(KBT/h) x e^(^S#/R) x e^(-^H#/RT)
k= Ae-(-Ea/RT)

Therefore Ea= +^H#
A factor= t(kBT/h) e^(^S#/R)

Question 27

What is A factor and what does it tell us about the transition state?

Answer 27

A factor= t(kBT/h) e^(^S#/R)

The A factor now tells us something about the entropy change going to the transition state

Question 28

What does a positive ^S imply?

Answer 28

This implies an increase in entropy= a loose transition state, weakening of bonds and a more floppy, less well ordered molecule
Afactor will be greater than the universal frequency factor

Question 29

What does a negative value of ^S imply?

Answer 29

This implies a decrease in entropy
Eg forming a single complex from two reactants
If a reaction only occurs with collisions of well defined orientations this implies an even more well ordered system and an even more negative ^S
This means A factor will be less than the universal frequency factor