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PPT – 06523 Kinetics. Lecture 10 Transition state theory Thermodynamic approach Statistical thermodynamics PowerPoint presentation | free to view

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06523 Kinetics. Lecture 10Transition state

theoryThermodynamic approachStatistical

thermodynamicsEyring equation Potential energy

surfacesReactions in solutionSolvent effects

Kinetic and mass transfer controlNote. It is

not necessary to learn complex derivations.These

are provided to assist appreciation of the

theory.

- Dr John J. Birtill

Transition state theory (TST) or activated

complex theory (ACT).

- In a reaction step as the reactant molecules A

and B come together they distort and begin to

share, exchange or discard atoms. - They form a loose structure AB of high potential

energy called the activated complex that is

poised to pass on to products or collapse back to

reactants C D. - The peak energy occurs at the transition state.

The energy difference from the ground state is

the activation energy Ea of the reaction step. - The potential energy falls as the atoms rearrange

in the cluster and finally reaches the value for

the products - Note that the reverse reaction step also has an

activation energy, in this case higher than for

the forward step.

Ea

A B

C D

Transition state theory continued

- The theory attempts to explain the size of the

rate constant kr and its temperature dependence

from the actual progress of the reaction

(reaction coordinate). - The progress along the reaction coordinate can be

considered in terms of the approach and then

reaction of an H atom to an F2 molecule - When far apart the potential energy is the sum of

the values for H and F2 - When close enough their orbitals start to overlap
- A bond starts to form between H and the closer F

atom H ? ? ?F-F - The F-F bond starts to lengthen
- As H becomes closer still the H ? ? ? F bond

becomes shorter and stronger and the F-F bond

becomes longer and weaker - The atoms enter the region of the activated

complex - When the three atoms reach the point of maximum

potential energy (the transition state) a further

infinitesimal compression of the H-F bond and

stretch of the F-F bond takes the complex through

the transition state.

Thermodynamic approach

- Suppose that the activated complex AB is in

equilibrium with the reactants with an

equilibrium constant designated K and

decomposes to products with rate constant k

K

k A B activated

complex AB products where K

- Therefore rate of formation of products k AB

k K AB - Compare this expression to the rate law rate of

formation of products kr AB - Hence the rate constant kr k K
- The Gibbs energy for the process is given by ? G

-RTln(K ) and so K exp(- ? G/RT) - Hence rate constant kr k exp (-(? H - T?

S)/RT). - Hence kr k exp(? S/R) exp(- ? H/RT)
- This expression has the same form as the

Arrhenius expression. - The activation energy Ea relates to ? H
- Pre-exponential factor A k exp(? S/R)
- The steric factor P can be related to the change

in disorder at the transition state

Statistical thermodynamic approach

- The activated complex can form products if it

passes though the transition state AB

- The equilibrium constant K can be derived from

statistical mechanics - q is the partition function for each species
- ?E0 (kJ mol-1)is the difference in internal

energy between A, B and AB at T0

- Suppose that a very loose vibration-like motion

of the activated complex AB with frequency v

along the reaction coordinate tips it through the

transition state. - The reaction rate is depends on the frequency of

that motion. Rate v AB

- It can be shown that the rate constant kr is

given by the Eyring equation - the contribution from the critical vibrational

motion has been resolved out from quantities K

and qAB - v cancels out from the equation
- k Boltzmann constant h Plancks constant

Statistical thermodynamic approach continued

- Can determine partition functions qA and qB from

spectroscopic measurements but transition state

has only a transient existence (picoseconds) and

so cannot be studied by normal techniques (into

the area of femtochemistry) - Need to postulate a structure for the activated

complex and determine a theoretical value for q

. - Complete calculations are only possible for

simple cases, e.g., H H2 ? H2 H - In more complex cases may use mixture of

calculated and experimental parameters - Potential energy surface 3-D plot of the energy

of all possible arrangements of the atoms in an

activated complex. Defines the easiest route

(the col between regions of high energy ) and

hence the exact position of the transition state. - For the simplest case of the reaction of two

structureless particles (e.g., atoms) with no

vibrational energy reacting to form a simple

diatomic cluster the expression for kr derived

from statistical thermodynamics resembles that

derived from collision theory. - Collision theory works.for spherical

molecules with no structure

Example of a potential energy surface

- Hydrogen atom exchange reaction HA HB-HC ?

HA-HB HC - Atoms constrained to be in a straight line

(collinear) HA ?? HB ?? HC - Path C goes up along the valley and over the col

(pass or saddle point) between 2 regions

(mountains) of higher energy and descends down

along the other valley. - Paths A and B go over much more difficult routes

through regions of high energy - Can investigate this type of reaction by

collision of molecular/ atomic beams with defined

energy state. - Determine which energy states (translational and

vibrational) lead to the most rapid reaction.

MolHA-HB

MolHB-HC

Diagramwww.oup.co.uk/powerpoint/bt/atkins

Advantages of transition state theory

- Provides a complete description of the nature of

the reaction including - the changes in structure and the distribution of

energy through the transition state - the origin of the pre-exponential factor A with

units t-1 that derive from frequency or velocity - the meaning of the activation energy Ea
- Rather complex fundamental theory can be

expressed in an easily understood pictorial

diagram of the transition state - plot of energy

vs the reaction coordinate - The pre-exponential factor A can be derived a

priori from statistical mechanics in simple cases - The steric factor P can be understood as related

to the change in order of the system and hence

the entropy change at the transition state - Can be applied to reactions in gases or liquids
- Allows for the influence of other properties of

the system on the transition state (e.g., solvent

effects). - Disadvantage
- Not easy to estimate fundamental properties of

the transition state except for very simple

reactions - theoretical estimates of A and Ea may be in the

right ball-park but still need experimental

values

Reactions in solution

- Kinetic energy of molecules in solution is

approximately similar to gas phase at same

temperature but there are some important

differences compared to reactions in gases. - Free space between solvent molecules is much less

than in gas phase and so the overall collision

frequency for solute may be higher - Reactant molecules must jostle their way

(diffuse) through the solvent a slow process - The encounter frequency is much lower than in the

gas phase - The molecules stay close together longer than in

the gas phase and so collision frequency is high

for the encounter pair --- the cage effect. - Molecules which do not have sufficient energy for

reaction may gain energy during the encounter

period by collisions with the solvent cage.

- The solvent cage may modify the activation energy

of the transition state - Especially so for reactions involving ions

Diffusion control and activation (kinetic) control

- Some very fast reactions may be under diffusion

control. - Consider the irreversible 2nd order reaction A

B ? C D via encounter pair AB

- The reaction scheme can be written as follows
- A B AB formation of encounter

pair k1AB C

D reaction - The rate law can be derived via the steady state

approximation (see box opposite).

- Solvent viscosity decreases with temperature and

so diffusion coefficient D and kd increase.

Effect is often expressed as an activation

energy (15 kJ mol-1 for reactions in water).

Solvent effects on rate

- The rate constant for many reactions under

activation control nevertheless vary greatly with

the nature of the solvent. - Example (C2H5)3N C2H5I ? (C2H5)4NI- Rate

constant kr at 100 ºC

- Solvent effects on reaction rate may be

understood in terms of the solvent effect on the

equilibrium between the reactants and the

transition state and hence on ?G.

- The Eyring relation can be expanded in terms of

?G.

- Solvent may affect ?G by effect on Gibbs energy

of reactants or of transition state - Hence interpret change of rate constants in

different solvents in terms of solvation energies

of reactants and the transition state in each

solvent. - Mechanisms that involve ionic species or any

degree of ionization in transition state are

especially susceptible.

Mixing in multiphase reactions mass transfer

control

- When reactions take place between two separate

phases (bubbles of gas in a liquid or 2

immiscible liquid phases) then two processes must

occur - - contact of the reactants and reaction.
- The term mass transfer is used to describe all

diffusion and mixing processes that lead to

contact of reactants. - Consider reaction between 2 liquid phases A and B

(say water and a long chain organic). A is

insoluble in B but B is weakly soluble in A

(CBA). - For reaction to take place A must diffuse across

the interphase region or film barrier. In this

region there will be a concentration gradient

from pure B (CB 1) to the solution (CBA).

- Three control regimes
- Kinetic control. Slow reaction B remains at

saturation level in A. Rate krCBA , independent

of diffusion. Agitation has no effect. - Mass transfer control. Moderate reaction CB lt

CBA . Rate partly dependent on diffusion and so

increases with agitation due to greater area of

interface up to maximum rate krCBA - Mass transfer control. Film-diffusion limited.

Fast reaction. Reaction takes place entirely

within diffusion film. Rate increases

indefinitely with increased agitation (as far as

practicable).

No lecture in week 12

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