Chap 21. The rates of chemical reactions

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• Reaction rate: depends on [R] and [P]

• Rate raw: reaction rates expressed in terms of differential equation. - Predict [R(t)] and [P(t)]- Provides insight into the series of elementary steps by which a

reaction takes place: (proposed) mechanisms of reactions- the key test for the mechanism → construction of a rate law

→ reproduce experimental measurements.

• Chemical kinetics (the study of reaction rates) - leads to an understanding of the mechanisms of reactions- Rates of chemical reaction:

might depends on p, T, and the presence of catalyst

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Chapter 21 in the 9th edition

• Numerical Problems: 21.2, 21.5, 21.13, 21.15, 21.16, 21.18, 21.19, 21.21

• Theoretical Problems: 21.23, 21.27, 21.28, 21.30, 21.31, 21.34

• Applications: 21.37, 21.38, 21.40

Assigned Problems

Empirical chemical kinetics

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Steps in the kinetic analysis of reactions:1. establish the stoichiometry, identify any side reactions2. obtain [R(t)], [P(t)]3. typically keep T constant.

21.1 Experimental techniques1. Pressure change: involving a gas

2. Spectrometry: ex, H2(g) + Br2(g) → 2HBr(g) ([Br2] change by visible)3. Conductivity: (if the number or types of ions changes)4. pH: [H+] changes

5. Emission spectroscopy, mass spectrometry, gas chromatography, NMR, ESR

(a) Monitoring the progress of a reaction

( ) ( ) ( ) ( ) ( ) ( ) ( )3 2 33 3CH CCl g H O l CH COH aq aq lH C aq+ −+ → + +

( ) ( ) ( )2 4 2 22 4N O g NO g O g→ +

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21.1(b) Application of techniques1. Real time analysis

• Flow method: require large quantity, hard for fast techniques

→ Stopped-flow techniques• Flash photolysis: very fast reactions

ex, time-resolved spectroscopy

2. Quenching methods: for slow reaction• Chemical quench flow method• Freeze quench method

( ) ( ) ( )2 4 2 22 4N O g NO g O g→ +Ex 21.1 predict how p varies as progresses in a constant volume

( ) ( ) ( )

( )

2 4 2 2

0 0 2 4

2 4 Total

1 3: (1 ) 2 12 2

3 1 where is the initial amount of 2total

N O g NO g O g

Amount n n n n

p n p p N O g

α α α α

α

→ +

− +

∴ = +

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• Time-resolved spectroscopy

1. Pump-probe spectroscopy2. Continuum generation

21.2 The rates of reactions

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• Rate of reaction:

: stoichiometric coefficient

1 [ ]

νν

≡

J

J

d Jvdt

• Rate law: 1 1[ ] [ ] for = + →v k A B A B k: rate constantreaction order superscript

[ ][ ][ ] [ ] [ ] [ ] [ ]

112

3 22 2

2 2'2

1 3[ ] [ ] order for [ ], overall order: 2 2

1st for , indefinite for ,

v k A B A

k H Brv H Br HBr

Br k HBr

=

=+

, 2 3[ ] 1 [ ] 1 [ ] [ ]

2 3

+ → +

= − = − = =

ex A B C Dd A d B d C d Dv

dt dt dt dt

( )( )[ ],[ ],

, , [ ]

= ⋅⋅ ⋅

→ ⋅⋅ ⋅ =A B J

v f A B

f p p p RT J

21.2 The rates of reactions

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The rate law of a reaction is determined experimentally1. Determine rate law and rate constants experimentally2. Construct a reaction mechanism consistent with the rate law

2 5 2 2 2 51, 2 ( ) 4 ( ) ( ) [ ]→ + =ex N O g NO g O g v k N O2

2 2 22, 2 ( ) ( ) 2 ( ) [ ] [ ] "coincidence"

+ → =ex NO g O g NO g v k NO O

21.2 The rates of reactionsexperimental investigation

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• Isolation method: all the [R]s except one are in large excess

1. Pseudofirst-order rate law:

2. Pseudosecond-order rate law:

• Initial rate

0 0

0 0

[ ][ ]

log log log[ ]

a

a

v k Av k A

v k a A

=

== + Otherwise [A] change has to be measured

1 1 10[ ] [ ] '[ ] '= [ ]v k A B k A k k B= ≈

[ ]0for excess B

[ ] [ ][ ] [ ] [ ]

[ ]

2 1 2 1 221 1 0

2 3 2 3 0

' '=k A B k B

v k A kk k B k k B

= ≈+ +

21.3 Integrated rate laws

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An expression for the concentration of a reactant or product as a function of time

Integrate rate laws written in differential equations

21.3(a) First-order reactions

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[ ] [ ]= −d A

k Adt ( ) ( )

( ) ( )

( ) 1 2

0 00 0

0

00

1 2 0 0

1 2 1 2

=

ln

ln ln 0

ln

12

1 ln 2 0.693ln 2

−

−

− = −

= − = −

− = − −

= − =

= =

= − = =

∫ ∫s s s s

kt

kt

dx dxkx kdtdt x

dx kdt x ktx

x s x k s

x sks x t x e

x

x t x x e

kt tk k

large small3=k k

1 2half-life: 2 ln=t

k( )11unit of : −− =k Mss M

0[ ] [ ] −= ktA A e

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[ ]

( )

2

0

1 20

1 1 1 2

1 1[ ] [ ] [ ]

1half-life: [ ]

unit of :

d Ak A kt

dt A A

tk A

k M s Ms M− − −

= − − =

=

=

( ) ( )

( )

( )

22

2 00 00

0

0

1 20 0 0 01 2

1 20

=

1

1 1 0

1 1

1 1 1 1 12

1

− = −

= − − = −

− = − =

− =

− = − = =

=

∫ ∫s

s s s

dx dxkx kdtdt x

dx kdt ktx x

k s ksx s x

ktx t x

ktx x x xx t

tkx

21.3(c) Second-order reactions

large small3=k k

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( ) ( )

( ) ( )

( )

( )

1 00 00

1 10

1 10

1

1 21 1 10 00

1

1 2 10

=

1

1 1 11

1 1 1

1 1 2 12

2 11

−

− −

− −

−

− − −

−

−

− = −

= − = −

− = − − −

− = −

−− = =

−=

−

∫ ∫

nn

ss s s

n n

n n

n n

n

n n n

n

n

dx dxkx kdtdt x

dx kdt ktx x

ksn x s x

n ktx s x

ktx xx

tn kx

21.3(c) nth-order reactions[ ] ( )

( )( )

1 10

1

1 2 10

1 1 1

1 1[ ] 1[ ] [ ]

2 1half-life: 1 [ ]

unit of :

− −

−

−

− − −

= − − = −

−=

−

=

nr rn n

n

nr

n n

d Ak A n k t

dt A A

tn k A

k M s Ms M

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21.3 Integrated rate laws

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Review 21-1

Rate of reacti 1o [ ]n: J

d Jvdtν

≡

• Experiments: Real time analysis, Quenching methods

Rate law: [ ] [ ]m nv k A B=

• Isolation method, Initial rate

[ ]

( )

0

1 2

1 1

[ ]

half-life:

unit of

[ ]

[

:

]

ln 2

−

−

−

=

=

= −

=

ktd Ak A

dt

k Ms

A A e

tk

s M

[ ]

( )

0

1 20

1

2

1 1 2

[ ]

half-life:

unit o

1 1[ ] [ ]

1[ ]

f : −− −

=−

=

−

=

=

d Ak A

dt

k Ms

ktA A

tk A

s MM