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

Spectrophotometry • Beer-Lambert law I log = I  [J]

l

• – –

I I o

= incident light = transmitted light – –

l

 = length of light path = molar absorption coefficient

I

– [J] = molar concentration of J =

I o

10 –  [J]

l

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 

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 / c  l -- R.C. Denney,

Dictionary of Spectroscopy

, 2nd ed. (Wiley, 1982), p.119-20.

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 

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.

Spectrophotometry • Beer’s law: 

A l

• 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  ?

Table 10.1 Kinetic techniques for fast reactions

Technique

Femtochemistry Flash photolysis Fluorescence decay Ultrasonic absorption EPR* Electric field jump Temperature jump Phosphorescence NMR* Pressure jump Stopped flow

Range of time-scales/s

 10  15  10  12 10  10 –10  6 10  10 –10  4 10  9 –10  4 10  7 –1 10  6 –1 10  6 –10 10  5 –1  10  5  10  3 * EPR is electron paramagnetic resonance (or electron spin resonance); NMR is nuclear magnetic resonance; see Chapter 21.

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

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

Spectrophotometry • 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 Spectrophotometry We can use spectrophotometers to follow the progress of a reaction in “real time”

Applications of spectrophotometry • Fig 10.4 (232) • Flow technique • Fig 10.5 (232) • Stopped-flow technique

Applications of spectrophotometry • Flash photolysis • Quenching methods – Rapid cooling – Adding a large volume of solvent – Rapid neutralization – Applicable to relatively slow rxns

Reaction rate

Reaction rate

is the change in the concentration of a reactant or a product with time (

M

/s).

A B rate = – D [A] D

t

D [A] = change in concentration of A over time period D

t

rate = D [B] D

t

D [B] = change in concentration of B over time period D

t

Because [A] decreases with time, D [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 =

–

1 2 D [A] D

t

rate = D [B] D

t

Review from Gen Chem

Reaction Rates and Stoichiometry 2A B Two moles of A disappear for each mole of B that is formed.

rate =

–

1 2 D [A] D

t

rate = D [B] D

t

Another generic chemical reaction

a

A +

b

B

c

C +

d

D rate = – 1

a

D [A] D

t

= – 1

b

D [B] D

t

= 1

c

D [C] D

t

= 1

d

D [D] D

t

Review from Gen Chem

Definition of reaction rate • Rate = |  [J] | 

t

Notice Atkins/de Paula use the absolute value  t is infinitesimally small • More precisely, Rate = d[J] d

t

• Partial pressures can be used instead of molar concentrations

Definition 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 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 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 order • 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 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 rates • • log rate 0 = 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 rate 0 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 law • Fig 10.7 (237) • The slope of a graph of log(rate 0 ) vs log[A] 0 is equal to the order of the reaction

The method of initial rates You should work through Example 10.1, pp.237f

Integrated rate laws • First order rxns: [A] • ln =

k



t

[A] • ln[A] = ln[A]

k



t

0 –

k



t

OR [A] = [A] 0 e – • In 1 st order rxns, the [reactants] decays exponentially with time

Integrated rate laws • Fig 10.10 (239) • The exponen tial decay of reactant in a 1 st order rxn. • The larger the rate constant, the faster the decay

Integrated rate laws • Fig 10.11 (240) • Part of Ex 10.2

• You should work through Example 10.2

Integrated rate laws • Fig 10.12 (241) • Variation with time of the [reactant] in a 2 nd order rxn

Integrated rate laws • Fig 10.13 (241) • The determination of the rate constant of a 2 nd order rxn • The slope equals the rate constant

Table 10.2 Kinetic data for first-order reactions

Reaction

2 N 2 O 5  4 NO 2 

O 2

2 N 2 O 5  4 NO 2 

O 2 C 2 H 6

 2 CH 3

Cyclopropane

 propene

Phase

g Br g g 2 (l) 

/°C

25 25 700 500

k/s



1

3.38  10  5 4.27  10  5 5.46  10  4 6.17  10  4

t

1/2

2.85 h 2.25 h 21.2 min 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 Kinetic data for second-order reactions

Reaction

2 NOBr  2 NO 

Br 2

2 NO 2  2 NO 

O 2 H 2

 I 2  2 HI

D 2

 HCl  DH  DCl 2 I 

I 2 CH 3 Cl

 CH 3 O 

CH 3 Br

 CH 3 O 

H

  OH   H 2 O

Phase

g g g g g hexane CH 3 OH(l) CH 3 OH(l) water 

/°C

10 300 400 600 23 50 20 20 25

k/(dm

0.80 0.54 2.42  10  2 0.141 7  1.8  10 10 2.29  10  6 9.23  10  6 1.5 10 

3

9

mol

10 11 

1 s



1 )

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 Integrated rate laws

Order

0 1 2

Reaction type

A  P A  P A  P A  B  P

Rate law

rate 

k

rate 

k

[A] rate 

k

[A] 2 rate 

k

[A][B]

Integrated rate law

[P] 

kt

for

kt

 [A] 0 [P]  [A] 0 (1  e 

kt

) 

kt

[ ] 0 2 1 

kt

0  [ ] 0  1  e 0 e 0  [ ] )

kt

) 0 

kt

Half-lives and time constants • A half-life is a good indicator of the rate of a 1 st order rxn • The half-life is the time it takes for [reactant] to drop to ½[reactant] 0

Half-lives and time constants • Useful for 1 st order rxns • [A] = ½[A] 0 at t ½ substitute into next eqn… [A] • ln =

k



t

to get….

•

k



t

½ = [A] – ln = – ln ½ = ln 2 [A] 0 • For 1 st order rxn, t ½ of a reactant is independent of its concentration

Using a half-life • Fig 10.15 (242) • Illustration 10.2

Using a half-life • Fig 10.16 (243) • Illustration 10.3

The 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

–

E

a

R

 1

T

The Arrhenius parameters • ln

k

= ln

A

–

E

a

RT

Two common forms of the Arrhenius equation •

k

=

Ae

–

E

a /

RT

• The Arrhenius parameters: –

A

is the pre-exponential factor –

E

a is the activation energy, kJ/mol • When

E

a is high, the rxn rate is sensitive to temperature, steep slope • When

E

a is low, the rxn rate is less sensitive to temperature, less steep slope

The Arrhenius Parameters Fig 10.17 (244) The general from of an Arrhenius plot

The Arrhenius Parameters • Fig 10.18 (244) • ln

k

vs 1/T • Notice the rxn with a higher E a has a steeper slope

The Arrhenius parameters Tables of Arrhenius parameters have values for

A

(in sec -1 ) and for

E a

(in kJ mol -1 ) Want to see some Arrhenius parameters??

Table 10.5 Arrhenius parameters – First-order reactions

First-order reactions

Cyclopropene  propane CH 3 NC  CH 3 CN

cis

-CHD  CHD 

trans

-CHD  CHD Cyclobutane  2 C 2 H 4 2 N 2 O 5  4 NO 2  O 2 N 2 O  N 2  O

A/s



1

1.58  10 15 3.98  10 13 3.16  10 12 3.98  10 15 4.94  10 13 7.94  10 11

E

a /(kJ mol



1 )

272 160 256 261 103 250

Table 10.5 Arrhenius parameters – Second-order reactions

Second-order reactions

Gas phase

O  N 2  NO  H OH  H 2  H 2  H Cl  H 2  HCl  H CH 3  CH 3  C 2 H 6 NO  Cl 2  NOCl  Cl

Solution

NaC 2 H 5 O  CH 3 I in ethanol C 2 H 5 Br  OH  in water CH 3 I  S 2 O 2 – 3 in water Sucrose  H 2 O in acidic water

A/(dm 3 mol



1 s



1 )

1  10 11 8  10 10 8  10 10 2  10 10 4  10 9 2.42  10 11 4.30  10 11 2.19  10 12 1.50  10 15

E

a /(kJ mol



1 )

315 42 23 0 85 81.6 89.5 78.7 107.9

Collision 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 theory Fig 10.20 (246) A rxn occurs when two molecules collide with sufficient energy (a) insufficient energy (b) sufficient energy

Reaction profile • Fig 10.21 (247) • Relationship of potential energy vs the progress of a rxn • Is this rxn endo thermic or exo thermic?

Collision theory • Fig 10.22 (247) • The KE of the collision must be greater than the E a

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

Collision theory • Fig 10.24 (249) • Not only must the KE of the collision be greater than the E a • But the molecules or atoms must also have the correct orientation

Transition 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 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 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 Concepts

Key Concepts

The End

…of this chapter…”

The method of initial rates • Fig 10.8 (237) • Part of Ex 10.1

The method of initial rates • Fig 10.9 (238) • Part of Ex 10.1

• Box 10.1 (250f)