Download - Atkins & de Paula: Elements of Physical Chemistry: 5e

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 kineticsIn order to investigate the rate and

mechanism of a reaction:1. Determine the overall stoichiometry of

the rxn and any side rxns2. Determine how the concentrations of

reactants and products change over time

– Spectrophotometry, conductivity, pH, GC/MS, NMR, polarimetry, etc

SpectrophotometrySpectrophotometry

• Beer-Lambert lawlog = [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.


• 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


Fig 10.1 (231)The intensity of the absorbed light increases exponentially with path length


Fig 10.2 (231)Two concentrations of two absorbing species can be determined from their at two different ’s within their joint absorption region


• 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 rateReaction 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 BTwo moles of A disappear for each mole of B that is formed.

rate = [B]trate = – [A]

t12


Reaction Rates and Stoichiometry

2A BTwo moles of A disappear for each mole of B that is formed.

rate = [B]trate = – [A]

t12

aA + bB cC + dD

rate = – [A]t

1a

= – [B]t

1b

= [C]t

1c

= [D]t

1d

Another generic chemical reaction


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]


• Fig 10.10 (239)

• The exponen-tial decay of reactant in a 1st order rxn.

• The larger the rate constant, the faster the decay


• Fig 10.11 (240)• Part of Ex 10.2

• You should work through Example 10.2


• Fig 10.12 (241)• Variation with

time of the [reactant] in a 2nd order rxn


• 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

AA

ktkt

02

01

A B P rate k[A][B] [ ][ ] [ ] ( )[ ] [ ]

([ ] [ ] )

([ ] [ ] )PA B eA 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?)


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?


• Fig 10.22 (247)

• The KE of the collision must be greater than the Ea


Fig 10.23 (248)Maxwell distribution of speeds of atoms or molecules


• 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)


• 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


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

The EndThe End…of this chapter…”


• Fig 10.8 (237)Fig 10.8 (237)• Part of Ex 10.1Part of Ex 10.1


• 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)

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