Chemical Kinetics Chapter 13

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Chemical KineticsChapter 13
An automotive catalytic muffler.
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• Rate of reaction -

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13.1
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Factors Affecting Reaction Rate

• Chemical nature
• Bond strengths
• General reactivity
• Ability to establish contact with one another
• Physical state
• Surface area for liquids, solids, and
  heterogeneous mixtures
• Amount of Mixing
• Particle shape/size

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Factors (Cont.)

• Concentration of reactants
• Molarity for solutions
• Pressure effects for gases
• Volume effects for gases
• Temperature
• Catalysts

                                                                                                                        
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Your Turn!

• Which of the following would speed a reaction?
• stirring it
• dissolving the reactants in water, if ionic
• adding a catalyst
• grinding any solids
• all of these

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Measuring Rates

• instantaneous rate (text uses this unless
  specified)
• average rate
• initial rate

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DBr2 a DAbsorption
13.1
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Fig. 13.5
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instantaneous rate rate for specific instance
in time
13.1
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(No Transcript)
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Fig. 13.6
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rate a Br2
rate k Br2 rate law
rate constant
3.50 x 10-3 s-1
13.1
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Your Turn!

• What is the average rate of B between 10 and 40
  s?
• -0.006 M/s
• 0.006 M/s
• -0.002 M/s
• 0.002 M/s
• cant tell form the information

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Rates And Stoichiometry

• Rates based on each substance are related to one
  another by the stoichiometric coefficients of the
  reaction
• Examine the reaction aA bB ?dD
• the stoichiometric relationship between
  substances A and B is given as a mole A b mole
  B
• RateA(b/a)RateB

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Consider the combustion of propane

• Compared to the rate with respect to propane
• Rate with respect to oxygen is five times faster
• Rate with respect to carbon dioxide is three
  times faster
• Rate with respect to water is four times faster
• Since the rates are all related any may be
  monitored to determine the reaction rate

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Learning Check

• In the reaction 2A 3B ?5D We measured the rate
  of disappearance of substance A to be
  3.510-5M/s. What is the rate of appearance of
  D?
• In the reaction 3A 2B ?C, we measured the rate
  of B. How does the rate of C relate?

8.7510-5 M/s
RC1/2 RB
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• 3A 2B C ? Products
• Rate k A2BC3
• The exponents in the rate law are generally
  unrelated to the chemical equations coefficients
• Never simply assume the exponents and
  coefficients are the same
• The exponents must be determined from the results
  of experiments
• The exponent in a rate law is called the order of
  reaction with respect to the corresponding
  reactant

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Your Turn!

• In the reaction 2CO(g) O2(g) ?2CO2(g), the rate
  of the reaction of CO is measured to be 2.0 M/s.
  What would be the rate of the reaction of O2?
• the same
• twice as great
• half as large
• you cannot tell from the given information

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Learning Check

• The rate law for the reaction 2A B?3C is
• rate 0.045M-1s-1 AB
• if the concentration of A is 0.2M and that of B
  is 0.3M, what will be the reaction rate?

rate0.045 M-1 s-1 0.20.3
rate0.0027 M/s
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• Table 13.2 from Page 529

Determine the rate law
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• The initial rate for the reaction of nitrogen
  monoxide and oxygen was measured at 25 ºC for
  various concentrations shown in the table below.
  Determine the rate equation for the reaction, the
  value of the rate constant with proper units, and
  the initial rate if NOO20.010 M
• Exp NO O2 initial rate mol/L mol/L
  mol/Ls
• 1 0.020 0.010 0.028
• 2 0.020 0.020 0.057
• 3 0.020 0.040 0.114
• 4 0.040 0.020 0.227
• 5 0.010 0.020 0.014

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• Concentration rate data for reaction A B C ?
  Products Initial Conc.mol/L Initial Rate
  mol/Ls A B C Rate 0.10 0.10
  0.10 0.20 0.20 0.10
  0.10 0.40 0.30 0.10 0.30 0.60 0.30 0.2
  0 0.30 2.40 0.30 0.30
  0.60 5.40 Determine the rate law for this
  reactionDetermine the rate constant for the
  reactionDetermine the overall reaction order for
  the reactionDetermine the rate of reaction when
  AB0.50 mol/L

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• A certain reaction follows the equation 2A B ?
  3C D.
• Experimental results yielded the following data.
  Determine the rate law, reaction order for A and
  B, the overall reaction order, the value for the
  rate constant k, and the rate of reaction when
  A B 1.0 mol/L
• Concentration rate data for reaction A B ? C
  D
• Initial Concentration mol/L
• A B Rate
• 0.40 0.30 1.0e-4
• 0.80 0.30 4.0e-4
• 0.80 0.60 1.6e-3

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Your Turn!

• For the following data, determine the order of
  NO2 in the reaction at 25 2 NO2(g) F2(g)?
  2 NO2F(g)

Exp. NO2 F2 Rate NO2 disappearance (M/s)
1 0.001 0.005 2 (10-4)
2 0.002 0.005 4 (10-4)
3 0.006 0.002 4.8 (10-4)

1. 0
2. 1
3. 2
4. 3
5. not enough information given

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Your Turn!

• Chlorine Dioxide, ClO2, is a reddish-yellow gas
  that is soluble in water. In basic solution it
  gives ClO3- and ClO2- ions. 2ClO2(aq)
  2OH-(aq)? 6ClO3- (aq) ClO2- (aq) H2O(l)
• The rate law is RatekClO22OH-, what is the
  value of the rate constant given that when
  ClO20.060M, OH- 0.030, the reaction rate
  is 0.0248 M/s
• 0.02 M-1 /s
• 0.02 M/s
• 0.02 s-
• None of these

2.3(102) M-2 s-1
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Zero-Order Reactions

• Ratek A0 k
• Plot of reactant vs. time will be linear
• The equation of the line will be
  AA0-kt
• A amount remaining after elapsed time, t.
• Aooriginal amount
• Diffusion controlled - usually are fast reactions
  in viscous media
• Rate is independent of concentrations of
  reactants, but the reaction still requires
  reactants

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Learning Check

• The rate law for the reaction of A?B is zero
  order in A and has a rate constant of 0.02 M/s.
  If the reaction starts with 1.50 M A, how much is
  present 15 seconds after the reaction begins?

• AA0-kt
• A1.2M

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Learning Check

• The rate law for the reaction of A?2B is zero
  order in A and has a rate constant of 0.12 M/s.
  If the reaction starts with 1.50 M A, after what
  time will the concentration of A be 0.90M?

• AA0-kt
• t5 s

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Your Turn!

• Which of the following is the correct set of
  units for the rate constant for a zero order
  reaction?
• M/s
• M-1/s
• M-2/s
• Cant tell from the given data

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First Order Reactions

• RatekA1
• Typically these reactions are decomposition type,
  or radioactive decay
• If the rate law is specified as dA/dtkA or
  Integrating the equation gives us

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Learning Check

• The radioactive decay of a new atom occurs so
  that after 21 days, the original amount is
  reduced to 33. What is the rate constant for
  the reaction in s-?

k 6.1110-7 s-1
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• Consider the first order decomposition reaction
• N2O5 ? N2O4 O2
• For which rate kN2O5. At 45?C the rate
  constant is 6.22e-4 s-1.
• If the initial concentration of dinitrogen
  pentoxide is 0.100 M, how long will it take for
  the concentration to drop to 0.0100 M?

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i-Clicker Classroom Participation
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i-Clicker Classroom Participation
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• Consider the first order decomposition reaction
• N2O5 ? N2O4 O2 for which rate kN2O5. At
  45?C the rate constant is 6.22e-4 s-1.
• If at 100?C the concentration falls from 0.800 to
  0.100 M in 45.0 minutes, what is the rate
  constant at 100?C?

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Fig. 13.12
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Derive the equation for half-life
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Learning Check

• The half-life of I-132 is 2.295h. What
  percentage remains after 24 hours?

0.302 h-1 k
A .0711
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Your Turn!

• What is the half-life of a new element,
  Barclium-146, if, after 2.2 h, 1.3 remains?
• 2.0 h
• 0.35 h
• 0.51 h
• None of these

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i-Clicker Classroom Participation
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• Hydrogen peroxide decomposes in dilute sodium
  hydroxide at 20 ºC in a first-order reaction
  where the rate constant is 1.06e-3 min-1
• 2 H2O2 (aq) ? 2 H2O (l ) O2 (g)
• If the initial concentration of H2O2 is 0.202
  mol/L what is the concentration after exactly 100
  minutes?
• What fraction of the original hydrogen peroxide
  is remaining after 100 minutes?
• What is the rate of reaction after 100 minutes?
• What is the half-life of this reaction at 20 ºC

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Second Order Reaction

• Are of several types RatekA2,
  RatekA1B1 and RatekA2B0, etc

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Learning Check

• The rate constant for the second order reaction
  2A?B is 5.310-5 M-1s-1. What is the original
  amount present if, after 2 hours, there is 0.35M
  available?

A00.40 M
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Second Order Half-Life

• Depends on the amount present at the start of the
  time period
• What is the relationship between k and t1/2 for
  this reaction type?

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Learning Check

• The rate constant for a second order reaction is
  4.510-4 M-1s-1. What is the half-life if we
  start with a reactant concentration of 5.0 M?

t1/2 440 s 7.4 min
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i-Clicker Classroom Participation
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• The gas-phase decomposition of hydrogen iodide is
  second order with a rate constant of 30. L/mol
  min at 443 ºC. How much time does it take for
  the concentration to fall from 0.010 mol/L to
  0.0050 mol/L at this temperature?
• What will be the HI concentration after just 12
  minutes?
• HI (g) ? 1/2 H2 (g) 1/2 I2 (g)

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• a) If k0.020 L/mol s for the second order
  reaction NOCl ? NO Cl2 what will the
  concentration be after 30 minutes if the initial
  concentration is 0.0500 M
• b) How long will it take for the concentration of
  NOCl to fall from 0.0500 to 0.001 M at the same
  temperature?

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Your Turn!

• Which order has a half-life that is independent
  of the original amount?
• Zero
• First
• Second
• None depend on the original quantity

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Your Turn!

• A 0.10M solution of moxium, a new antidepressant
  is bottled. The drug decays to fortium, a toxic
  chemical as a second order process. The rate
  constant is 2.310-3 M-1h-1. What quantity of
  moxium is present after 90. days?
• 0.098M
• 5.5(10-5)M
• 0.067M
• None of the above

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• Graphical methods can be used to determine the
  first-order rate constant, note

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• A plot of lnAt versus t gives a straight line
  with a slope of -k

The decomposition of N2O5. (a) A graph of
concentration versus time for the decomposition
at 45oC. (b) A straight line is obtained from a
logarithm versus time plot. The slope is negative
the rate constant.
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Learning Check

• Determine the order of the reactant graphically

0 order plot 1st order plot 2nd order plot
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• Graphical methods can also be applied to
  second-order reactions
• A plot of 1/Bt versus t gives a straight line
  with a slope of k

Second-order kinetics. A plot of 1/HI versus
time (using the data in Table 15.1).
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Collision Theory Of Reactions

• For a reaction to occur, three conditions must be
  met
• Reactant particles must collide
• Collision energy must be enough to break
  bonds/initiate
• Particles must be oriented so that the new bonds
  can form

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Potential Energy Diagrams

• Demonstrate the energy needs and products as a
  reaction proceeds
• Tell us whether a reaction is exothermic or
  endothermic
• Tell us if a reaction occurs in one step or
  several steps
• Show us which step is the slowest

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Potential Energy Diagrams
                                                                                                                                                                                                                                                                                                
What about the reverse reaction?
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i-Clicker Classroom Participation
Where does Ea come from?
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Features of PE Diagrams
Connect to the graph Activation Energies
Activated Complexes
Product Energy
P.E.
Enthalpy of reaction
Reactant Energy
Reaction Coordinate (progress of reaction)
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Exothermic reaction of NO O3
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Your Turn!

• Examine the Potential energy diagram. Which is
  the Slowest (Rate Determining) Step?
• Step 1
• Step 2
• Cant tell from the given information

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Fig. 13.13
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Fig. 13.16
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Temperature Effects

• Changes in temperature affect the rate constant,
  k, according to the Arrhenius equation
• p is the steric factor
• Z is the frequency of collisions.
• Ea is the activation energy
• R is the Ideal Gas Constant (8.314 J/mol K)
• T is the temperature (K)
• A is the frequency factor

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Working With The Arrhenius Equation

• Linear Form To determine the Ea and A value

Ratio form Can be used when A isnt known.
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Learning Check

• Given that k at 25C is 4.6110-1 M/s and that at
  50C it is 4.6410-1 M/s, what is the activation
  energy for the reaction?

208 J/molEa
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Working With The Arrhenius Equation

• Given the following data, predict k at 75C using
  the graphical approach

k (M/s) T C
0.000886 25
0.000894 50
0.000918 150
0.000908 100
graph
ln (k) -0.0278/T-0.1917
k8.2510-1
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• The reaction CH3I HI ? CH4 I2 was observed to
  have rate constants
• k 3.2 L/(mol s) at 350?C and
• k23 L/(mol s) at 400?C.
• What is the value of Eafor this reaction
  expressed in kJ/mol?
• What would the rate constant be at 300?C?

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Your Turn!

• In the reaction 2N2O5(g) ?4 NO2(g) O2(g) the
  following temperature and rate constant
  information is obtained. What is the activation
  energy of the reaction?
• 99.7 kJ
• -99.7 kJ
• 1004 kJ
• -1004 kJ
• none of these

T (K) k (s-1)
338 328 318 4.87(10-3) 1.50(10-3) 4.98(10-4)
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• The first order reaction 2NO2 ? 2 NO O2 has an
  activation energy of 111 kJ/mol. At 400?C, k
  7.8 L/mol s
• 1. What is the value of k at 430?C?
• 2. If the NO2 is 1.5e-2M, what is the rate of
  reaction at 430 ?C?

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i-Clicker Classroom Participation
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Reaction Mechanisms

• The rate determining step is the slowest step of
  the reaction that accounts for most of the
  reaction time
• Elementary steps sum to the overall reaction
• Catalysts interact with the reactant, they will
  appear in the mechanism
• Intermediates are temporary products, formed in
  an early step and consumed in a later step

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Learning Check

• The reaction mechanism that has been proposed for
  the decomposition of H2O2 is
• H2O2 I- ? H2O IO- (slow)
• H2O2 IO- ? H2O O2 I- (fast)
• Which is the rate determining step?
• Are there any intermediates?

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Learning Check

• The reaction mechanism that has been proposed for
  the decomposition of H2O2 is
• H2O2 I- ? H2O IO- (slow)
• H2O2 IO- ? H2O O2 I- (fast)
• What is the expected rate law?

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Learning Check

• The reaction A 3 B ? D F was
  studied and the following mechanism was finally
  determined
• A B ? C (fast)
• C B ? D E (slow)
• E B ? F (very fast)
• What is the expected rate law?

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Catalysts

• Speed a reaction, but are not consumed by the
  reaction
• May appear in the rate law
• Lower the Ea for the reaction.
• May be heterogeneous or homogeneous

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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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Iodine-Catalyzed Isomerization of cis-2-Butene
Figure 15.19
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Catalytic Actions

• May serve to weaken bonds through induction
• May serve to change polarity through
  amphipathic/surfactant effects
• May reduce geometric orientation effects
• Heterogeneous catalyst reactant and product
  exist in different states.
• Homogeneous catalyst reactants and catalyst
  exist in the same physical state

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Heterogeneous catalysts
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i-Clicker Classroom Participation
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i-Clicker Classroom Participation
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• For the reaction
• C2H6(g) 2CH3(g) rate kC2H6
• If k 5.50 E4 s1 and C2H6initial 0.0200 M,
  calculate
• the rate of reaction after 30 min.

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Solutions slides- graphs to accompany previous
slides

• Ch 13 Brady Senese, 5th

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Reactant vs. time
return to problem
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Ln Reactant vs time
return to problem
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Inverse Reactant vs time
return to problem
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return to the problem