Post on 21-Jul-2018
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
(2015) Chemical Kinetics by M Lim 2
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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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