Chemical Kinetics Rates and Mechanisms of Chemical Reactions

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Chemical KineticsRates and Mechanisms of
Chemical Reactions

• Blackman Chapter 14

KINETICS - the study of REACTION RATES
MECHANISM- the way the reaction proceeds
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Recap

• Integrated rate laws
• Half Lives
• First Order t1/2 ln 2 / k
• Second Order t1/2 1 / (k Ao)
• Reaction Mechanisms
• Rate Determining Step the slowest step in a
  mechanism
• Can be deduced from the rate laws

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COLLISION THEORY

• Molecules/ ions must collide to react
• - Orientation and energy factors slow down
  the reaction.
• - Rates go up faster than collision frequency
  increases as Temperature increases
• Not all collisions consummate a reaction
• - Orientation does not depend on T.
• Not all properly oriented collisions Consummate a
  reaction
• - Energy levels may be inadequate

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Chemical Reaction and Molecular Collisions
Molecular collisions lead to chemical reactions.
Thus, the reaction constant, k is determined by
several factors. k Z f p Z collision
frequencyp, the fraction with proper
orientationf, fraction of collision having
sufficient energy for reactionf is related to
the potential energy barrier called activation
energy, Ea. f ? e Ea / RT or exp ( Ea / R
T) Thus, k A e Ea / RT
z p and A are constants
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Energy in chemical reactions
Potential energy diagram for an endothermic (?H lt
0) reaction.
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Arrhenius Equation

• k A e -Ea/RT
• The activation energy, Ea, of a reaction is the
  minimum amount of energy that the reacting
  molecules must possess if the reaction is to be
  successful
• The Arrhenius equation describes the temperature
  dependence of the rate constant that is
  exponentially related to the activation energy (A
  is the pre-exponential factor, or the A factor
  also called the frequency factor)

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The Arrhenius Equation
The temperature dependence of the rate constant k
is best described by the Arrhenius equation k
A e Ea / R Tor ln k ln A Ea / R T If k1
and k2 are the rate constants at T1 and T2
respectively, then k1 Ea 1 1
ln k2 R T1 T2
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Application of Arrhenius Equation
The reaction 2 NO2(g) ? 2NO(g) O2(g) The
rate constant k 1.0 x 10-10 s-1 at 300 K and
the activation energy Ea 111 kJ mol-1. What
are A, k at 273 K and T when k 1x
10-11? Method Make use of, and rearrange k A
e Ea / R T
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ANSWERS Blanked out of the online
version, these will be completed in the lecture.
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How A works

• Measure of what fraction of the possible
  collision geometries can result in a reaction

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How Ea works
Kinetic energy distributions for a reaction
mixture at two different temperatures
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How Ea works
The greater Ea, the more energy reactants need
to collide together with
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Determining Ea k A e -Ea/RT

• If the rate constant is measured at two or more
  different temperatures, the activation energy may
  then be determined.
• For example
• at T1 Ln k1 Ln A - Ea / RT1
• and at T2 Ln k2 Ln A - Ea / RT2
• subtracting
• Ln k1 - Ln k2 Ln (k1/ k2) - Ea
  (1/T1 - 1/T2)
• R

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Determining Ea k A e -Ea/RT

• Example
• If a reaction has a rate constant of 2.0 x 10-5
  s-1 at 20 ?C and 7.3 x 10-5 s-1 at 30 ?C, what
  is the activation energy ?
• Ln (k1/ k2) - Ea (1/T1
  - 1/T2)
• R
• Ln (2.0 x 10-5)/ (7.3 x 10-5) - (Ea/8.314)
  1/293 - 1/303
• Ea 96 kJ mol-1

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Ideally you want a lot more than two T values
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Question

• The rate constant of a particular reaction
  triples when the temperature is increased from 25
  ?C to 35 ?C. Calculate the activation energy,
  Ea, for this reaction.

• Ln (k1/ k2) - Ea (1/T1 - 1/T2)
• R
• Ln (1/3) - (Ea / 8.314)(1/298 - 1/308)
• -1.099 - Ea(1.310 x 10-5)
• Ea 83 800 J mol-1 or 83.8 kJ mol-1

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Example questions

• TEXT PROBLEMS
• Practice Exercise 14.9, 14.10
• Problems 14.56, 14.80, 14.102
• CONCEPTS
• Collision Theory
• Steady State Approximation
• CALCULATIONS
• Half-life
• Arrhenius Equation