handout version (temperature dependent term to kinetic models

7/31/2019 Handout Version (Temperature Dependent Term to Kinetic Models

1/38

TEMPERATURE

DEPENDENT TERM

IntroductionArrhenius LawCollision TheoryTransition State Theory


2/38

Temperature Dependent Term

Temperature dependent terms thathave been developed:

Arrhenius Law

Collision Theory

Transition State

Theory


3/38


Arrhenius, a Swedish Chemist,proposed that the temperaturedependence of the reaction rate

constant, kA, could be correlated by anequation:

ko = frequency factor or pre-exponential

factor E = activation energy (J/mol or cal/mol)

R = gas constant

T = absolute temperature


4/38


Activation Energy Minimum energy that must be possessed

by reacting molecules before the reactionwill occur

Difference between average energy ofthose molecules that do react and theaverage energy of all molecules

Just an empirical parameter relating thereaction rate constant to temperature

= fraction of the collisions betweenmolecules that attain the activation energy


5/38


Experimental Determination of E

The activation energy can be determined

experimentally by carrying out the

reaction at several different temperaturesand determining the rate constants, kA, at

these temperatures.

To determine E, first linearize the

Arrhenius Equation


6/38



7/38


Features of Arrhenuis equation(Levenspiel)

A plot of k vs 1/T gives a straight line, with

a large slope for large E, small slope forsmall E.

Reactions with high activation energies

are very temperature sensitive; reactions

with low activation energies are relatively

temperature-insensitive.


8/38


(Levenspiel)


9/38


Collision Theory

Originally based on the kinetic theory of

gases

reaction occurs when: Molecules collide

Possess enough energy to undergo

transformation

Rate of reaction = (frequency of collision) x(fraction of collisions that have energy to react)


10/38


11/38


Collision is assumed when A touchesB, with a collision radius (AB =Aand

B)within a collision area S=(Aand

B)2.

A

B


12/38


Distance traveled by molecule A =URt

At time t,A sweeps a volume V,

equal to:

AAUR

AB


13/38


While A sweeps out this volume, it will undergocollisions with B within this volume.

Number of collisions is:

B

B

B

AAUR

AB


14/38


From kinetic theory of gases:

Where:

Therefore, the frequency of collision of

all molecules A is:


15/38


Rate of reaction (with respect to number ofmolecules reacting) = (frequency of collision) x

(fraction of collisions that have energy to react)

Using Avogadros number:


16/38



17/38


Transition State Theory Reactants combine to form unstable

intermediates called activated

complexes, which decompose toproducts spontaneously, or revert back to

reactants.

Schematic representation:


18/38


Final form of reaction rate:

K =Boltzman constant

H = Planck constant

QABC,QA,QB = partition functions per unit volume

Eo = energy change going from reactants to

products


19/38


The fraction of collision term is more sensitive than

the Tm term, thus, the variation due to Tm term is

masked.

Arrhenius Law

Collision Theory

Transition State

Theory


20/38

KINETIC MODELS

Introduction

IntermediatesReaction SchemesTesting of Mechanisms and ModelsExamples of Reaction Mechanisms


21/38

Kinetic Models

Kinetics of non-elementary reactionsare explained using the followingassumption:

The overall reaction of a non-elementary reaction can be written asa sequence of elementary reactions(reaction mechanism).

The sequence may postulate theappearance of intermediates, whichcannot be measured or observed as

they are in very minute quantities.


22/38

Kinetic Models

The * represents unobservedintermediates.

Reactionmechanism/

kinetic model


23/38

INTERMEDIATES AND

REACTION SCHEMES


24/38

Kinetic Models

Intermediates

Types of intermediates which may be

postulated in a reaction mechanism:

Free Radicals Contains an unpaired electron

Ion or Polar

Substances

Electrically charged atoms or molecules

Molecules Short life span

Transition

Complexes

Unstable forms of molecules having strained bonds

or unstable associations which either decompose to

give products or return to molecules in the normal

state


25/38

Kinetic Models

Reaction Schemes

Non-chain reactions

Chain Reactions

Generally consists of sequences Initiation

Active intermediate initially formed

Propagation Active intermediate is propagated (increased formation)

with simultaneous product formation Termination

Active intermediate is destroyed by transformation intomore stable products


26/38

Kinetic Models

Initiation

Propagation*

Termination

*the propagation is an essential feature Intermediate is not consumed but acts

as a catalyst


27/38

EXAMPLES OF

REACTION

MECHANISMS


28/38

Kinetic Models

The Kinetic Model/Reactionmechanism can be expressed/ named

from the type of intermediate and

reaction scheme Non-chain reactions

Molecules

Transition Complexes

Chain reactions

Free radicals


29/38

Kinetic Models

Free Radical, Chain Reaction

Mechanism:


30/38

Kinetic Models

Molecular Intermediate, Non-chainReaction

Mechanism


31/38

Kinetic Models

Transition Complex, Non-chainReaction

Mechanism:

H2+ I2

H H

IIH H

II

2HI


32/38

TESTING OF POSTULATED

REACTION MECHANISM


33/38

Kinetic Models

Given a reaction and experimentalrate law which is not elementary, we

can attempt to propose a reaction

mechanism to explain the non-elementary algebraic expression of

the rate law.

To check if the proposed reactionmechanism is correct, the theoretical

rate law must be similar to the

experimental rate law.


34/38

Kinetic Models

How?Answer:

Obtain the theoretical rate laws from

the proposed reaction mechanism and

apply the steady-state approximation.


35/38

Kinetic Models

1. From the reaction mechanism, set-up theelementary rate law of the targetcomponent (reaction product or reactant)rA = will include expressions involving concentrations of

intermediates.

2. Apply the steady state approximation.

3. Substitute CI back to the rate law obtainedin (1), and simplify.

4. Compare the derived/ theoretical rate lawwith the experimental rate law. Ifanalogous, the postulated reactionmechanism is correct.


36/38

Kinetic Models

Consider:


37/38

Kinetic Models

Use Rules-of-thumb:


38/38

Kinetic Models

Proposal:

handout version (temperature dependent term to kinetic models

Documents