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Transcript of Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 10: Chemical Kinetics: The Rates of...
Atkins & de Paula: Atkins & de Paula: Elements of Physical Chemistry: Elements of Physical Chemistry:
5e5e
Chapter 10: Chemical Kinetics:
The Rates of Reactions
End of chapter 10 assignments
Discussion questions:• 2, 3, 4, 5, 7
Exercises:• 1, 2, 4, 5, 7, 9, 12, 13, 19,
20
Use Excel if data needs to be graphed
Homework assignmentsHomework assignments
• Did you:– Read the chapter?– Work through the example problems?– Connect to the publisher’s website &
access the “Living Graphs”?– Examine the “Checklist of Key Ideas”?– Work assigned end-of-chapter
exercises?
• Review terms and concepts that you should recall from previous courses
Empirical chemical kineticsEmpirical chemical kinetics
In order to investigate the rate and mechanism of a reaction:
1. Determine the overall stoichiometry of the rxn and any side rxns
2. Determine how the concentrations of reactants and products change over time
– Spectrophotometry, conductivity, pH, GC/MS, NMR, polarimetry, etc
SpectrophotometrySpectrophotometry
• Beer-Lambert law
log = [J] l
– Io = incident light– I = transmitted light– l = length of light path = molar absorption coefficient– [J] = molar concentration of J
• I = Io 10–[J]l
IoI
Molar extinction coefficient?
•Molar absorption coefficient () was known as the “molar extinction coefficient”
•Use of the term “molar extinction coefficient” has been discouraged since the 1960s
Preferred terminology of Preferred terminology of
Molar absorption coefficient (ε)Synonyms: Molar extinction coefficient, molar absorptivity
"The recommended term for the absorbance for a molar concentration of a substance with a path length of 1.0 cm determined at a specific wavelength. Its value is obtained from the equation ε = A / cl
-- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.
Preferred terminology of Preferred terminology of
Molar absorption coefficient (ε)
“Strictly speaking, in compliance with SI units the path length should be specified in meters, but it is current general practice for centimeters to be used for this purpose.”
-- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.
Preferred terminology of Preferred terminology of
Molar absorption coefficient (ε)
“Under defined conditions of solvent, pH, and temperature the molar absorption coefficient for a particular compound is a constant at the specified wavelength."
-- R.C. Denney, Dictionary of Spectroscopy, 2nd ed. (Wiley, 1982), p.119-20.
SpectrophotometrySpectrophotometry
• Beer’s law: [J] =
• Thus, absorbance is directly proportional to the molar concentration
• A = [J] l (notice A is dimensionless)
• Absorbance a/k/a “optical density”
• What is max?
• Do we always use max?
• Is specific to a compound? To a ?
A l
Table 10.1 Table 10.1 Kinetic techniques for fast reactionsKinetic techniques for fast reactions
SpectrophotometrySpectrophotometry
Fig 10.1 (231)The intensity of the absorbed light increases exponentially with path length
SpectrophotometrySpectrophotometry
Fig 10.2 (231)Two concentrations of two absorbing species can be determined from their at two different ’s within their joint absorption region
SpectrophotometrySpectrophotometry
• Fig 10.3 (232)• An isosbestic point
is formed when two unrelated absorbing species are present in the rxn solution
• The curves repre-sent different stages of the rxn
Applications of SpectrophotometryApplications of Spectrophotometry
We can use spectrophotometers
to follow the progress of a reaction in “real time”
Applications of spectrophotometryApplications of spectrophotometry
• Fig 10.4 (232)• Flow technique
• Fig 10.5 (232)• Stopped-flow
technique
Applications of spectrophotometryApplications of spectrophotometry
• Flash photolysis• Quenching methods
– Rapid cooling– Adding a large volume of solvent– Rapid neutralization– Applicable to relatively slow rxns
Reaction rateReaction rate
Reaction rate is the change in the concentration of a reactant or a product with time (M/s).
A B
rate = –[A]t
rate = [B]t
[A] = change in concentration of A over time period t
[B] = change in concentration of B over time period t
Because [A] decreases with time, [A] is negative.
Review from Gen Chem
Reaction Rates and Stoichiometry
2A B
Two moles of A disappear for each mole of B that is formed.
rate = [B]t
rate = –[A]t
12
Review from Gen Chem
Reaction Rates and Stoichiometry
2A B
Two moles of A disappear for each mole of B that is formed.
rate = [B]t
rate = –[A]t
12
aA + bB cC + dD
rate = –[A]t
1a
= –[B]t
1b
=[C]t
1c
=[D]t
1d
Another generic chemical reaction
Review from Gen Chem
Definition of reaction rateDefinition of reaction rate
• Rate =
• More precisely, Rate =
• Partial pressures can be used instead of molar concentrations
|[J]|
t
d[J]
dt
Notice Atkins/de Paula use the absolute value
t is infinitesimally
small
Definition of reaction rateDefinition of reaction rate
• Fig 10.6 (233)• Concentration of
reactant vs time• The rxn rate
changes as the rxn proceeds
• Slope is the instantaneous rate at that time
Rate laws and rate constantsRate laws and rate constants
• The rate of a rxn is often (usually?) found proportional to the product of the molar concentrations raised to a simple power:
Rate = [A]x [B]y
• The units of the rate constant are determined by the form of the rate law (p.234)
Rate laws and rate constantsRate laws and rate constants
• The rate law allows us to predict the concentrations of reactants and products at time t
• Proposed mechanisms must be consistent with the rate law
Classification according to Classification according to orderorder
• The power to which a concentration is raised in the rate law is the order with respect to that species
• The overall order of a reaction is the sum of the orders of all the reactants
• The order may be a fraction, zero, or indefinite
• The rate law is determined empirically and cannot be inferred from the stoichiometry of the chemical eqn
Determination of the rate lawDetermination of the rate law
• The rate law is determined empirically
• Two common methods:– The isolation method
(as performed in Gen Chem lab; all reactants except one present in great excess, so their concentrations do not change much)
– The method of initial rates
The method of initial ratesThe method of initial rates
• log rate0 = log k’ + a log[A]0
• This equation is of the form:• y = intercept + slope x • So, for a series of initial
concentrations, a plot of the log rate0 vs log[A]0 should be a straight line, with the slope = a, the order of the rxn with respect to A
• Let’s look at an example
Determination of the rate lawDetermination of the rate law
• Fig 10.7 (237)• The slope of a
graph of log(rate0) vs log[A]0 is equal to the order of the reaction
The method of initial ratesThe method of initial rates
You should work through Example 10.1, pp.237f
Integrated rate lawsIntegrated rate laws
• First order rxns:
• ln = kt
• ln[A] = ln[A]0 – kt OR [A] = [A]0 e–kt
• In 1st order rxns, the [reactants] decays exponentially with time
[A]0
[A]
Integrated rate lawsIntegrated rate laws
• Fig 10.10 (239)
• The exponen-tial decay of reactant in a 1st order rxn.
• The larger the rate constant, the faster the decay
Integrated rate lawsIntegrated rate laws
• Fig 10.11 (240)• Part of Ex 10.2
• You should work through Example 10.2
Integrated rate lawsIntegrated rate laws
• Fig 10.12 (241)• Variation with
time of the [reactant] in a 2nd order rxn
Integrated rate lawsIntegrated rate laws
• Fig 10.13 (241)• The
determination of the rate constant of a 2nd order rxn
• The slope equals the rate constant
Table 10.2 Table 10.2 Kinetic data for first-order reactionsKinetic data for first-order reactions
Reaction Phase /°C k/s 1 t1/2
2 N2O5 4 NO2 O2 g 25 3.38 10 5 2.85 h
2 N2O5 4 NO2 O2 Br2(l) 25 4.27 10 5 2.25 h
C2H6 2 CH3 g 700 5.46 10 4 21.2 min
Cyclopropane propene g 500 6.17 10 4 17.2 min
The rate constant is for the rate of formation or consumption of the species in bold type. The rate laws for the other species may be obtained from the reaction stoichiometry.
Table 10.3 Table 10.3 Kinetic data for second-order reactionsKinetic data for second-order reactions
Reaction Phase /°C k/(dm3 mol 1 s 1)
2 NOBr 2 NO Br2 g 10 0.80
2 NO2 2 NO O2 g 300 0.54
H2 I2 2 HI g 400 2.42 10 2
D2 HCl DH DCl g 600 0.141
2 I I2 g 23 7 109
hexane 50 1.8 1010
CH3Cl CH3O CH3OH(l) 20 2.29 10 6
CH3Br CH3O CH3OH(l) 20 9.23 10 6
H OH H2O water 25 1.5 1011
The rate constant is for the rate of formation or consumption of the species in bold type. The rate laws for the other species may be obtained from the reaction stoichiometry.
Table 10.4 Table 10.4 Integrated rate lawsIntegrated rate laws
Order Reaction type Rate law Integrated rate law
0 A P rate k [P] kt for kt [A]0
1 A P rate k[A] [P] [A]0(1 e kt)
2 A P rate k[A]2 [ ][ ]
[ ]P
A
A
kt
kt02
01
A B P rate k[A][B] [ ][ ] [ ] ( )
[ ] [ ]
([ ] [ ] )
([ ] [ ] )PA B e
A B e
B A
B A
0 0
0 0
1 0 0
0 0
kt
kt
Half-lives and time constantsHalf-lives and time constants
• A half-life is a good indicator of the rate of a 1st order rxn
• The half-life is the time it takes for [reactant] to drop to ½[reactant]0
Half-lives and time constantsHalf-lives and time constants
• Useful for 1st order rxns• [A] = ½[A]0 at t½ substitute into next
eqn…
• ln = kt to get….
• kt½ = – ln = – ln ½ = ln 2
• For 1st order rxn, t½ of a reactant is independent of its concentration
[A]0
[A]
½[A]
0 [A]0
Using a half-lifeUsing a half-life
• Fig 10.15 (242)• Illustration 10.2
Using a half-lifeUsing a half-life
• Fig 10.16 (243)• Illustration 10.3
The Arrhenius parametersThe Arrhenius parameters
In the 1800s Arrhenius noticed that the rates of many different rxns had a similar dependence on temperature
• He noticed that a plot of ln k vs 1/T gives a straight line with a slope characteristic of that rxn
• ln k = intercept + slope 1/T
• ln k = ln A –
Ea
R1T
The Arrhenius parametersThe Arrhenius parameters
• ln k = ln A –
• k = Ae• The Arrhenius parameters:
– A is the pre-exponential factor– Ea is the activation energy, kJ/mol
• When Ea is high, the rxn rate is sensitive to temperature, steep slope
• When Ea is low, the rxn rate is less sensitive to temperature, less steep slope
Ea
RT–Ea/RT
Two common forms of the Arrhenius equation
The Arrhenius ParametersThe Arrhenius Parameters
Fig 10.17 (244)The general from of an Arrhenius plot
The Arrhenius ParametersThe Arrhenius Parameters
• Fig 10.18 (244)
• ln k vs 1/T• Notice the
rxn with a higher Ea has a steeper slope
The Arrhenius parametersThe Arrhenius parameters
Tables of Arrhenius parameters have values for A (in sec-1) and for Ea (in kJ mol-1)
Want to see some Arrhenius parameters??
Table 10.5 Table 10.5 Arrhenius parameters – First-order Arrhenius parameters – First-order
reactionsreactions
First-order reactions A/s 1 Ea/(kJ mol 1)
Cyclopropene propane 1.58 1015 272
CH3NC CH3CN 3.98 1013 160
cis-CHDCHD trans-CHDCHD 3.16 1012 256
Cyclobutane 2 C2H4 3.98 1015 261
2 N2O5 4 NO2 O2 4.94 1013 103
N2O N2 O 7.94 1011 250
Table 10.5 Table 10.5 Arrhenius parameters – Second-order reactionsArrhenius parameters – Second-order reactions
Collision theoryCollision theory
• For bimolecular, gas phase rxns• Collisions must have at least a
minimum energy in order for products to form
• (What is a “bimolecular” rxn?)
Collision theoryCollision theory
Fig 10.20 (246) A rxn occurs when two molecules collide with sufficient energy(a) insufficient energy(b) sufficient energy
Reaction profileReaction profile
• Fig 10.21 (247)• Relationship of
potential energy vs the progress of a rxn
• Is this rxn endo-thermic or exo-thermic?
Collision theoryCollision theory
• Fig 10.22 (247)
• The KE of the collision must be greater than the Ea
Collision theoryCollision theory
Fig 10.23 (248)Maxwell distribution of speeds of atoms or molecules
Collision theoryCollision theory
• Fig 10.24 (249)• Not only must the
KE of the collision be greater than the Ea
• But the molecules or atoms must also have the correct orientation
Transition state theoryTransition state theory
• Can be applied to rxns in solution as well as in the gas phase
• The “activated complex” may involve solvent molecules
• Empirical support for the existence of an “activated complex” comes from the relatively young branch of chemistry known as “femtochemistry” (see Box 10.1 pp.250f)
Transition state theoryTransition state theory
• Fig 10.25 (249)• As the reactants
approach, the PE rises to a maximum.
• The activated complex is not an intermediate that can be isolated
Transition state theoryTransition state theory
Fig 10.26 (250)The cluster of atoms that make up the activated complex may continue to products, or they may return to reactants
Key Key ConceptConcept
ss
Key Key ConceptConcept
ss
The EndThe End…of this chapter…”
The method of initial ratesThe method of initial rates
• Fig 10.8 (237)Fig 10.8 (237)• Part of Ex 10.1Part of Ex 10.1
The method of initial ratesThe method of initial rates
• Fig 10.9 (238)Fig 10.9 (238)• Part of Ex 10.1Part of Ex 10.1
• Box 10.1 (250f)Box 10.1 (250f)