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PPT – Chemical Kinetics : rate of a chemical reaction PowerPoint presentation | free to download - id: 53e1a7-YmM1Y

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- Chemical Kinetics rate of a chemical reaction

Before a chemical reaction can take place the

molecules involved must be raised to a state of

higher potential energy. They are then said to be

activated or to form an activated complex.

- In 1889 Arrhenius said

- vant Hoff eq. for temperature coefficient of

equilibrium - constant is

2) mass-action law relates equilibrium

constant to the ratio of rate constants

Hence a reasonable eq. for the variation of rate

constant with temperature is

Where Ea is the activation energy of the reaction

- If Ea does not depend on temperature, we can

integrate this last eq. to obtain

where ln A is the constant of integration. Hence

This is the famous Arrhenius eq. for the rate

constant. According to Arrhenius, molecules must

acquire a certain critical energy Ea before they

can react. The Boltzmann factor

is the fraction of molecules that manages to

obtain the necessary energy. This interpretation

is still held to be essentially correct.

- Henry Eyring (1901-1981)

The rate of any chemical reaction can be

formulated in terms of its activated complex.

The rate of reaction is the number of activated

complexes passing per second over the top of the

potential energy barrier. This rate is equal to

the concentration of activated complexes times

the average velocity with which a complex moves

across to the product side.

Calculation of conc. of activated complexes is

greatly simplified if we assume that they are in

equil. with the reactants. This equil. can then

be treated by means of thermodynamics or

statistical mechanics.

- Transition State Theory

Consider this equilibrium

equil. constant for the formation of the complex

is

the conc. of complexes is thus

according to transition state theory, the rate of

reaction is

The rate of passage over the barrier is equal to

the frequency with which the complex flies apart

into the products.

- The complex flies apart when one of its

vibrations becomes a translation, and what was

formerly one of the bonds holding the complex

together becomes simply the line of centers

between separating fragments.

The frequency is equal to where

is the average energy of the vibration leading

to decomposition. Since by hypothesis this is a

thoroughly excited vibration at temperature T, it

has its classical energy and hence

frequency

The reaction rate is therefore

with rate constant

- This is the general expression given by

transition state theory for the rate constant of

any elementary reaction. To be precise, the

expression for k2 should be multiplied by a

factor called the transmission coefficient,

which is the probability that the complex will

not recross the transition state and dissociate

back into products. In basic TST,

The activated complex is similar to a normal

stable molecule in every respect save one. The

sole difference is that one of its vibrational

degrees of freedom is missing, having been

transformed into the translation along the

reaction coordinate. Instead of 3N-6 vibrational

modes, it has 3N-7 modes (non-linear case).

- We can formulate k2 in thermodynamic terms by

introducing the standard free energy change

This is the difference between the free energy of

the activated complex and that of the reactants,

when all are in their standard states.

The quantities

are called the free energy of activation, the

heat of activation, and the entropy of

activation. The heat of activation is almost

equivalent to the experimental energy of

activation Ea, except for a PV term which is

negligible for solid or liquid systems.

- Chemical

Before

can correct for a wrong choice of transition

state this way as well

- challenges for computational modeling

- where/what is the transition state?
- what is the reaction coordinate?

Schematic representation of the free energy

landscape with two stable, attractive wells

separated by a transition state ridge, which

connects the highest free energy points of all

possible paths connecting the reactant and

product states. The dotted line represents a new

trajectory that was branched of at point p from

an old trajectory (bold line) and surpasses the

TS ridge at a lower point.

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- Example of a complicated reaction coordinate

aqueous proton transfer reaction

what is the reaction coordinate?

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- Transition path sampling

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