Transition State Theory Flashcards
What can you calculate using transition state theory?
Transition state theory allows the calculation of the rate constant using thermodynamic principles, specifically those of the transition state
Describe the model for transition state theory
The reaction pathway from reactants to products passes through a transition state at the highest point of the energy profile
What assumptions are made?
It assumes that a pre equilibrium is established between the reactants and the transition state ABC which then goes on to form the products
What is a general reaction for TST?
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
What happens to the molecules as they react?
A + BC -> AB + C
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
What happens to the energy of the system?
As the molecules react and interatomic distances change, the energy of the system will increase
What is the point of maximum energy?
This is the transition state
Once the colliding atoms reach this point, they can continue on to the products
How can the reaction be represented?
It can be represented in the potential energy diagram
What does the reaction coordinate represent?
This represents the changing interatomic distances
Describe the state of the system at the transition state
At the transition state, the system is at unstable equilibrium
It can only exist transiently
Describe how the reaction can be represented in terms of rate constants
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)
A + BC(K#) -> X# -> AB +C(k#
What is the rate of reaction with respect to AB?
d[AB]/dt= k2[X#]
How can you find the concentration of the transition state?
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#]
What is the koverall equation for
A+BC-> X -> AB+C
d[AB]/dt= koverall [A][BC]
For k overall do not include the transition state
What is koverall in this theory?
koverall= k2[K#]
How does free energy relate to equilibrium constant?
^G#= -RT lnK#
You can rearrange this to find what K# equals
K#= e^-^G#/RT
How can you find K in terms of entropy and enthalpy?
^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)
What is ^H# and ^S#
This is the activation enthalpy and entropy
Express the overall rate constant in terms of thermodynamics
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
What is asymmetric stretch?
This is a contract at one bond and stretch at another
Equivalent to a translation, pushed X# over the transition state
Describe the properties of the reaction coordinate leading to and away from transition state
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
What is k2?
k2= KBT/h
What is the complete evaluation of koverall?
Sub k2= kBT/h
koverall= (KBT/h) x e^(^S#/R) x e^(-^H#/RT)
What is the eyring equation?
koverall= t(KBT/h) x e^(^S#/R) x e^(-^H#/RT)
What does t account for?
The t accounts for the fact that a proportion of collisions that reach the transition state, could actually return to reactants
Compare the eyring equation with the Arrhenius equation to give A factors and Ea
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)
What is A factor and what does it tell us about the transition state?
A factor= t(kBT/h) e^(^S#/R)
The A factor now tells us something about the entropy change going to the transition state
What does a positive ^S imply?
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
What does a negative value of ^S imply?
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
