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TEMPERATURE
DEPENDENT TERM
IntroductionArrhenius LawCollision TheoryTransition State Theory
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Temperature Dependent Term
Temperature dependent terms thathave been developed:
Arrhenius Law
Collision Theory
Transition State
Theory
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Temperature Dependent Term
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
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Temperature Dependent Term
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
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Temperature Dependent Term
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
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Temperature Dependent Term
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Temperature Dependent Term
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.
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Temperature Dependent Term
(Levenspiel)
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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)
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Temperature Dependent Term
Collision is assumed when A touchesB, with a collision radius (AB =Aand
B)within a collision area S=(Aand
B)2.
A
B
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Temperature Dependent Term
Distance traveled by molecule A =URt
At time t,A sweeps a volume V,
equal to:
AAUR
AB
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Temperature Dependent Term
While A sweeps out this volume, it will undergocollisions with B within this volume.
Number of collisions is:
B
B
B
AAUR
AB
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Temperature Dependent Term
From kinetic theory of gases:
Where:
Therefore, the frequency of collision of
all molecules A is:
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Temperature Dependent Term
Rate of reaction (with respect to number ofmolecules reacting) = (frequency of collision) x
(fraction of collisions that have energy to react)
Using Avogadros number:
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Transition State Theory Reactants combine to form unstable
intermediates called activated
complexes, which decompose toproducts spontaneously, or revert back to
reactants.
Schematic representation:
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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
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Temperature Dependent Term
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
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KINETIC MODELS
Introduction
IntermediatesReaction SchemesTesting of Mechanisms and ModelsExamples of Reaction Mechanisms
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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.
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Kinetic Models
The * represents unobservedintermediates.
Reactionmechanism/
kinetic model
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INTERMEDIATES AND
REACTION SCHEMES
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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
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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
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Kinetic Models
Initiation
Propagation*
Termination
*the propagation is an essential feature Intermediate is not consumed but acts
as a catalyst
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EXAMPLES OF
REACTION
MECHANISMS
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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
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Kinetic Models
Free Radical, Chain Reaction
Mechanism:
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Kinetic Models
Molecular Intermediate, Non-chainReaction
Mechanism
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Kinetic Models
Transition Complex, Non-chainReaction
Mechanism:
H2+ I2
H H
IIH H
II
2HI
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TESTING OF POSTULATED
REACTION MECHANISM
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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.
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Kinetic Models
How?Answer:
Obtain the theoretical rate laws from
the proposed reaction mechanism and
apply the steady-state approximation.
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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.
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Kinetic Models
Consider:
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Kinetic Models
Use Rules-of-thumb:
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Kinetic Models
Proposal:
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