KINETICS

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Chemical KineticsChapter 15

• KINETICS the study of REACTION RATES and their
  relation to the way the reaction proceeds, i.e.,
  its MECHANISM.

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Reaction Mechanisms

• The sequence of events at the molecular level
  that control the speed and outcome of a reaction.

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Reaction Rates

• change in concentration of a reactant or product
  with time
• initial rate
• average rate
• instantaneous rate

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Concentration/Time Relations

• Need to know what conc. of reactant is as
  function of time. Consider FIRST ORDER REACTIONS
• For 1st order reactions, the rate law is - (D
  A / D time) k A

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Concentration/Time Relations

• Integrating - (D A / D time) k A, we get

A / A0 fraction remaining after time t has
elapsed.
Called the integrated first-order rate law.
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Half-LifeSection 15.4 and Screen 15.8

• HALF-LIFE is the time it takes for 1/2 a sample
  is disappear.
• For 1st order reactions, the concept of HALF-LIFE
  is especially useful.

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Half-Life

• Reaction after 654 min, 1 half-life.
• 1/2 of the reactant remains.

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Half-Life

• Reaction after 1306 min, or 2 half-lives.
• 1/4 of the reactant remains.

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Half-Life

• Reaction after 3 half-lives, or 1962 min.
• 1/8 of the reactant remains.

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Half-LifeSection 15.4 and Screen 15.8
Rate ksugar and k 3.3 x 10-4 sec-1. What
is the half-life of this reaction?

• Solution
• A / A0 1/2 when t t1/2
• Therefore, ln (1/2) - k t1/2
• - 0.693 - k t1/2
• t1/2 0.693 / k
• So, for sugar,
• t1/2 0.693 / k 2100 sec 35 min

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Half-LifeSection 15.4 and Screen 15.8
Rate ksugar and k 3.3 x 10-4 sec-1.
Half-life is 35 min. Start with 5.00 g sugar. How
much is left after 2 hr and 20 min?

• Solution
• 2 hr and 20 min 4 half-lives
• Half-life Time Elapsed Mass Left
• 1st 35 min 5.00 g
• 2nd 70 2.50 g
• 3rd 105 1.25 g
• 4th 140 0.625 g

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Half-LifeSection 15.4 and Screen 15.8
Start with 1.50 mg of tritium, how much is left
after 49.2 years? t1/2 12.3 years

• Solution
• ln A / A0 -kt
• A ? A0 1.50 mg t 49.2 mg
• Need k, so we calc k from k 0.693 /
  t1/2
• Obtain k 0.0564 y-1
• Now ln A / A0 -kt - (0.0564 y-1)
  (49.2 y)
• - 2.77
• Take antilog A / A0 e-2.77 0.0627
• 0.0627 is the fraction remaining!

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Factors Affecting Rates Section 15.2

• Concentrations and physical state of reactants
  and products
• Temperature
• Catalysts

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Collision Theory

• Reactions require
• (a) activation energy and
• (b) correct geometry.
• O3(g) NO(g) ---gt O2(g) NO2(g)

O3 NO reaction occurs in a single ELEMENTARY
step.
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Collision Theory explains effects Of Conc.
Temp on Rates!

• Molecules must collide
• Molecules must collide with enough energy
• Molecules must collide with the right orientation

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Collision Theory

• Reactions require
• (a) activation energy and
• (b) correct geometry.
• O3(g) NO(g) ---gt O2(g) NO2(g)

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Concentrations and Rates

• To postulate a reaction mechanism, we study
• reaction rate and
• its concentration dependence

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Arrhenius Equation

• k A e Ea/Rt

A frequency of collisions with correct geometry.
e Ea/Rt fraction of molecules with mimimum
energy for the reaction
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Arrhenius Equation

• k A e Ea/RT
• ln k ln A - (Ea/RT)
• ln k ln A - Ea/R ( 1/T)

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Arrhenius Equation
As Temperature increases, the fraction of
molecules with sufficient activation energy
increases.
Temp (K) e -Ea/Rt
298 9.7 x 10-8
400 5.9 x 10-6
600 3.3 x 10-4
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MECHANISMSSections 15.5 and 15.6

• How are reactants converted to products at the
  molecular level?
• RATE LAW ----gt MECHANISM
• experiment ----gt theory

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MECHANISMS

• For example
• Rate k trans-2-butene
• Conversion requires twisting around the CC bond.

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MECHANISMS

• Energy involved in conversion of trans to cis
  butene

See Figure 15.15
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MECHANISMS

• TRANSITION STATE
• ACTIVATION ENERGY, Ea energy reqd to form
  activated complex.
• Here Ea 233 kJ/mol

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Activation Energy

• Molecules are moving..but how many of them have
  enough Energy to go to product?
• What does increasing T do?
• A flask full of trans-butene is stable because
  only a tiny fraction of trans molecules have
  enough energy to convert to cis.
• In general, differences in activation energy are
  the reason reactions vary from fast to slow.

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MECHANISMS

• 1. Why is reaction observed to be 1st order?
• As trans doubles, number of molecules with
  enough E also doubles.
• 2. Why is the reaction faster at higher
  temperature?
• Fraction of molecules with sufficient
  activation energy increases with T.

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MECHANISMS

• Reaction of trans --gt cisis UNIMOLECULAR- only
  one reactant is involved.
• BIMOLECULAR two different molecules must
  collide --gt products

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MECHANISMS

• BIMOLECULAR two different molecules must
  collide --gt products

A bimolecular reaction
Exo- or endothermic?
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MECHANISMS

• Most reactions involve a sequence of elementary
  steps.
• Adding elementary steps gives NET reaction.

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Relationship to Reaction order

• Molecularity of an Elementary Step and its order
  are the same.
• Not necessarily true for overall reaction, just
  for elementary steps!

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Rate Equations again
A ? unimolecular Rate k A
A B ? Bimolecular Rate k AB
A A ? Bimolecular Rate k A2
2 A B ? Termolecular Rate k A2B
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MECHANISMS

• 2 I- H2O2 2 H ---gt I2 2 H2O
• Rate k I- H2O2
• Step 1 HOOH I- --gt HOI OH-
• Step 2 HOI I- --gt I2 OH-
• Step 3 2 OH- 2 H --gt 2 H2O

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MECHANISMS
2 I- H2O2 2 H ---gt I2 2 H2O Rate
k I- H2O2 Step 1 slow HOOH I- --gt
HOI OH-Step 2 fast HOI I- --gt I2
OH- Step 3 fast 2 OH- 2 H --gt 2 H2O

• Step 1 is bimolecular and involves I- and HOOH.
  Therefore, this predicts the rate law should be
• Rate ? I- H2O2 as observed!!
• The species HOI and OH- are reaction
  intermediates.

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Exercise 15.12

• 2 NO ? N2O2
• N2O2 H2 ?N2O H2O
• N2O H2 ? N2 H2O
• Molecularity? Rate Eqns? Sum of Steps?

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Rate of the reaction controlled by slow step
RATE DETERMINING STEP Rate can be no faster than
RDS!
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CATALYSIS

• Catalysts speed up reactions by altering the
  mechanism to lower the activation energy barrier.

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Catalysts in Industry

• Petroleum refining
• Industrial production of chemicals,
  pharmaceuticals
• Environmental controls
• Heterogeneous vs. Homogeneous

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CATALYSIS

• In auto exhaust systems Pt, NiO
• 2 CO O2 ---gt 2 CO2
• 2 NO ---gt N2 O2

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CATALYSIS

• 2. Polymers H2CCH2 ---gt polyethylene
• 3. Acetic acid
• CH3OH CO --gt CH3CO2H
• 4. Enzymes biological catalysts

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CATALYSIS

• Catalysis and activation energy

MnO2 catalyzes decomposition of H2O2 2 H2O2 ---gt
2 H2O O2
Uncatalyzed reaction
Catalyzed reaction
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MnO2 catalyzes decomposition of H2O2

• Figure 15.18

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Iodine-Catalyzed Isomerization of cis-2-Butene
Figure 15.19
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Cis-2-butene ? trans-2-butene

• 1) I2 ? 2 I
• 2) I cis-2-butene ? I-cis-2-butene
• 3) I-cis-2-butene ? I-trans-2-butene
• 4) I-trans-2-butene ? I trans-2-butene
• 5) I I ? I2
• Rate k cis-2-buteneI21/2
• One I2 gets broken, one I used, but
  regenerated. In the end, the two I can
  recombine. No net consumption of I2!