Chemical Kinetics: Rates of Reactions

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Chapter 13

• Chemical Kinetics Rates of Reactions

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Overview

• Reaction Rate
• Effect of Concentration on Reaction Rate
• Rate Law and Order of Reaction
• A Nanoscale View Elementary Reactions
• Temperature and Reaction Rate The Arrhenius
  Equation
• Rate Laws for Elementary Reactions
• Reaction Mechanisms
• Catalysts and Reaction Rate

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Overview

• Chemical Kinetics the study of speeds of
  reactions and the nanoscale pathways or
  rearrangements by which atoms and molecules are
  transformed from reactants to products

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Reaction Rate

• Four Factors affecting the rate of reaction in
  homogenous reactions
• Molecular structure and bonding of the reactants
  and products
• Bond strength
• Orientation of the molecules
• Temperature of the reaction
• Higher temperatures, more collisions
• Presence of a catalyst and its concentration

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• Concentration of the reactants and sometimes
  products

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Reaction Rate

• Factors affecting reaction rate in heterogeneous
  reactions
• Those mentioned previously
• Surface area

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Reaction Rate

• Reaction rate - the change in concentration of a
  reactant or product per unit time

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Concentration of O3 (mol/L)
Time (s)
0.0
3.20x10-5
10.0
2.42x10-5
20.0
1.95x10-5
30.0
1.63x10-5
40.0
1.40x10-5
50.0
1.23x10-5
60.0
1.10x10-5
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Reaction Rate

• Average rate reaction rate calculated from
  change in concentration divided by a change in
  time.
• Rate - ? concentration reactant / ? time

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Problem

• The compound RX3 decomposes according to the
  equation3RX3 ? R R2X3 3X2In an experiment
  the following data were collected for the
  decomposition at 100C. What is the average rate
  of reaction over the entire experiment?

• 0.11 mol L-1 s-1
• 0.019 mol L-1 s-1
• 0.044 mol L-1 s-1
• 0.049 mol L-1 s-1
• 0.069 mol L-1 s-1

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Reaction Rate

• C2H4 O3 ? C2H4O O2
• 11 ratio hence the rate of C2H4O formed rate
  of O3 disappearance
• 2N2O5 ? 4NO2 O2
• Rate -½ N2O5/?t ¼ NO2 /?t O2 /?t

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Effect of Concentration on Reaction Rate

• Rate a O3
• The proportionality can be changed into a
  mathematical expression by adding a
  proportionality constant k
• Rate k x O3
• Rate Law a mathematical equation that
  summarizes the relationship between reactant and
  reaction rate

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Problem

• Consider the following reaction8A(g) 5B(g) ?
  8C(g) 6D(g)If C is increasing at the rate
  of 4.0 mol L-1s-1, at what rate is B changing? 
• A.  -0.40 mol L-1s-1
• B.  -2.5 mol L-1s-1
• C.  -4.0 mol L-1s-1
• D.  -6.4 mol L-1s-1
• E.  none of these choices is correct, since its
  rate of change must be positive

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Effect of Concentration on Reaction Rate

• The relationship between rate and concentration
  (the rate law) must be determined experimentally
• Two methods
• Collect concentration data continuously as a
  function of time
• Initial rates of reactions
• Perform multiple experiments each time varying
  the concentration of one of the reactants and
  collect rate data after no more than 2 of
  limiting reagent has been used

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• 2NO O2 ? 2NO2

Initial Reactant Concentrations (mol/L)
Initial Rate (mol/Ls)
Experiment
O2
NO
1
1.10x10-2
3.21x10-3
1.30x10-2
2
2.20x10-2
1.30x10-2
6.40x10-3
3
1.10x10-2
2.60x10-2
12.8x10-3
4
3.30x10-2
1.30x10-2
9.60x10-3
5
1.10x10-2
3.90x10-2
28.8x10-3
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• Compare 2 experiments in which the concentration
  of one reactant varies and the concentration of
  the other reactant(s) remains constant.

k O22mNO2n
O22m



O21m
k O21mNO1n
6.40x10-3mol/Ls


2 2m
m 1
3.21x10-3mol/Ls

• Do a similar calculation for the other
  reactant(s).

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Problem

• For the reaction3A(g) 2B(g) ? 2C(g)
  2D(g)the following data was collected at
  constant temperature. Determine the correct rate
  law for this reaction.

• kAB
• kAB2
• kA3B2
• kA1.5B
• kA2B

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• 2NOBr(g) ? 2NO(g) Br2(g)
• NOBr(mol L-1) Rate (mol L-1s-1)
• 0.0450 1.62 10-3
• 0.0310 7.69 10-4
• 0.0095 7.22 10-5Based on the initial rate
  data above, what is the value of the rate
  constant? 
• A.  0.0360 L mol-1s-1
• B.  0.800 L mol-1s-1
• C.  1.25 L mol-1s-1
• D.  27.8 L mol-1s-1
• E.  0.0360 s-1

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Rate Law and Order of Reaction

• General Form of Rate Law
• Rate kAmBn.
• Superscripts indicate the order of the reaction
  with respect to each reactant
• Overall Order of Reaction for a reaction sum of
  the superscripts

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SOLUTION
(a) The reaction is 2nd order in NO, 1st order
in O2, and 3rd order overall.
(b) The reaction is 3/2 order in CH3CHO and 3/2
order overall.
(c) The reaction is 1st order in H2O2, 1st order
in I- and zero order in H, while being 2nd order
overall.
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Rate Law and Order of Reaction

• Another approach uses calculus to derive the
  integrated rate law
• Review pg 620 if you wish to see the calculus
  behind integrated rate law

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Rate Law and Order of Reaction

• A ? products

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Problems

• Sulfuryl chloride, SO2Cl2(g), decomposes at high
  temperature to form SO2(g) and Cl2(g). The rate
  constant at a certain temperature is 4.68
  10-5s-1. What is the order of the reaction? 
• A.  zero
• B.  first
• C.  second
• D.  third
• E.  More information is needed to determine the
  order.

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Problems

• When the reaction A ? B C is studied, a plot
  1/At vs. time gives a straight line with a
  positive slope. What is the order of the
  reaction? 
• A.  zero
• B.  first
• C.  second
• D.  third
• E.  More information is needed to determine the
  order.

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Problems

• Ammonium cyanate (NH4CNO) reacts to form urea
  (NH2CONH2). At 65C the rate constant, k, is 3.60
  L mol-1s-1. What is the rate law for this
  reaction? 
• A.  Rate 3.60 L mol-1s-1NH4CNO
• B.  Rate 3.60 L mol-1s-1NH4CNO2
• C.  Rate 0.28 mol L-1 s-1NH4CNO
• D.  Rate 0.28 mol L-1 s-1NH4CNO2
• E.  Rate 3.60 L mol-1s-1NH2CONH2-1

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Problem

• Tetrafluoroethylene, C2F4, can be converted to
  octafluorocyclobutane which can be used as a
  refrigerant or an aerosol propellant. A plot of
  1/C2F4 vs. time gives a straight line with a
  slope of 0.0448 L mol-1s-1. What is the rate law
  for this reaction?
•  
• A.  Rate 0.0448 (L mol-1s-1)C2F4
• B.  Rate 22.3 (mol L-1s)C2F4
• C.  Rate 0.0448 (L mol-1s-1)C2F42
• D.  Rate 22.3 (mol L-1s)C2F42
• E.  Rate 0.0448 s-1 C2F4

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Rate Law and Order of Reaction

• With the integrated rate law, initial
  concentration of reactant, and the rate constant.
  The concentration of a reactant or product at
  any time can be calculated

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(a) If the initial C4H8 concentration is 2.00M,
what is the concentration after 0.010 s?
(b) What fraction of C4H8 has decomposed in this
time?
PLAN
Find the C4H8 at time, t, using the integrated
rate law for a 1st order reaction. Once that
value is found, divide the amount decomposed by
the initial concentration.
SOLUTION
C4H8 0.83mol/L
0.58
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A Nanoscale View Elementary Reactions

• Two types of elementary transformations
• Unimolecular
• Bimolecular

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A Nanoscale View Elementary Reactions
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The Ea(fwd) is 19 kJ, and the DHrxn for the
reaction is -392 kJ. Draw a reaction energy
diagram for this reaction, postulate a transition
state, and calculate Ea(rev).
SOLUTION
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Temperature and Reaction Rate The Arrhenius
Equation

• Increase of temperature increases the rate of
  reaction
• Increased collisions
• Lowering of energy of activation
• A reaction is fast at a higher temperature
  because its rate constant is larger
• A rate constant is constant only for a giving
  reaction and a given temperature

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The Arrhenius Equation
where k is the kinetic rate constant at T
Ea is the activation energy
R is the energy gas constant 8.314 J/mol K
T is the Kelvin temperature
ln k ln A - Ea/RT
A is the collision frequency factor
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ln k -Ea/R (1/T) ln A
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has rate constants of 9.51x10-9L/mols at 500. K
and 1.10x10-5 L/mols at 600. K. Find Ea.
PLAN
Use the modification of the Arrhenius equation to
find Ea.
SOLUTION
Ea 1.76x105J/mol 176kJ/mol
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Elementary Step
Molecularity
Rate Law
Unimolecular
Rate k A
Bimolecular
Rate k A2
Rate k AB
Bimolecular
Termolecular
Rate k A2B
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(a) Write the overall balanced equation.
(b) Determine the molecularity of each step.
(c) Write the rate law for each step.
PLAN
(a) The overall equation is the sum of the steps.
(b) The molecularity is the sum of the reactant
particles in the step.
SOLUTION
rate2 k2 NO2ClCl
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The Rate-Determining Step of a Reaction Mechanism
The overall rate of a reaction is related to the
rate of the slowest, or rate-determining step.
Correlating the Mechanism with the Rate Law
The elementary steps must add up to the overall
equation.
The elementary steps must be physically
reasonable.
The mechanism must correlated with the rate law.
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