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物理化學(三) 應用化學系朱超原老師 1
• Collision theory of bimolecular reactions• Arrhenius formula (again)• Fraction number in bimolecular reactions • Unimolecular reactions
VIII. The chemical reaction mechanismsVIII. The chemical reaction mechanisms
物理化學(三) 應用化學系朱超原老師 2
VIIIVIII--1. Collision theory of bimolecular reactions1. Collision theory of bimolecular reactions
bBaA products
dt
tBdbdt
tAda
tr 11
Two reactants
For simplicity (a=b=1)
products
products
A A
物理化學(三) 應用化學系朱超原老師 3
Reaction mechanisms
Kinetic energy
Internal energy Rotational energyVibrational energyElectronic energy
No kinetic energy change Elastic collision
Internal energy change inelastic collision
Bond forming or/and breaking Reactive collision
collision scattering
物理化學(三) 應用化學系朱超原老師 4
Total collision rate
22
VN5.0
21
dv
VNzZ rel
mTk
vv Brel 16
2
Number of collision per unit volume +per unit time
scollisonsofnumber3m
Fraction number of reactions = f fZReaction rate =
fZN Av
1Reaction rate in mole =
物理化學(三) 應用化學系朱超原老師 5
AAA 2 products
22
AvV
N/NA
22VN5.01
21
dv
Nf
dtAd
relAv
225.021 AdvfN
dtAd
relAv
Rate constant
AvB Nm
Tkdfk
42
(second-order)
Only dependent on temperature
(Ideal case = elementary)
物理化學(三) 應用化學系朱超原老師 6
BA products
dtBd
dtAdfZ
N Av12
1Reaction rate in mole =
212
121212 dV
NVN
vZ 12
128
Tkv B
BA
V/NN
V/NN Av2Av1
BAdvfNdt
AdAv
21212
AvB N
Tkdfk
12
212
8
Rate constant
物理化學(三) 應用化學系朱超原老師 7
Example 2HIIH 22
1115 smolL1074.8 fk
At T = 373.15K
Calculate fraction number f
Rate constant
AvB N
Tkdfk
12
212
8
Table A15
6.35397I2
2.72294H2
d×1010/mT/K
mmd 101012 1054.41035.672.221
kgkgmm
mm 272721
2112 103.31066.12542
2542
物理化學(三) 應用化學系朱超原老師 8
smolL
smolm
NTk
d AvB
11
38
12
212
1077.7
1077.7
8
-123 JK10380.1 Bk
molN Av /10022.623
At T = 373.15K
md 1012 1054.4
kg2712 103.3
1115 smolL1074.8 fk2611
15101.1
1077.71074.8
f
If T = 473.15K 1110 smolL1053.9 fk
smolL
smolL
NTkd AvB
11
11
12
212
1075.8
15.37315.4731077.7
8
2111
10101.1
1075.81053.9
f
物理化學(三) 應用化學系朱超原老師 9
VIIIVIII--2. Arrhenius formula (again)2. Arrhenius formula (again)
Kinetic energy
212122
1 vK
Classical picture
aEK
No reaction aEK
Reactions occur
K
aE
物理化學(三) 應用化學系朱超原老師 10
Arrhenius formula
RTE
Ak aexp
Activation energy
Arrhenius preexponential factor
A and Ea are very slow change with respect to temperature
dTkdRTEa
ln2
Activation energy is measured through experiment reaction rate cActivation energy is measured through experiment reaction rate constant onstant
Reactants aE
Products
Activated Complex
aE
Path of a reaction
ΔH
物理化學(三) 應用化學系朱超原老師 11
Example 2HIIH 22
1115 smolL1074.8 fkAt T = 373.15K
Rate constant
At T = 473.15K 1110 smolL1053.9 fk
Calculate activation energy and pre-exponential factor
11 exp RT
EAk a
22 exp RT
EAk a
15
2
1
21
21 molJ10703.1ln
kk
RTT
TTEa
11mol8.314JK R
3.432
RTEa 1192 smolL1008.63.43exp kA
物理化學(三) 應用化學系朱超原老師 12
PCIIIweek16-1作業
Problems 12.712.8
Page 539
物理化學(三) 應用化學系朱超原老師 13
VIIIVIII--3. Fraction number in bimolecular reactions3. Fraction number in bimolecular reactions
Total collision rate
VN
VNdvZ 122121212 12
128
Tkv B
vgMaxwell–Boltzmann distribution 1311 vdvgN number of A particles in 111 vdvv
1311 vdvgN number of B particles in 222 vdvv
Differential collision rate
V
vdvgNV
vdvgNddZ 1
3112
3222
121212 vv
13 vdvg
物理化學(三) 應用化學系朱超原老師 14
Maxwell–Boltzmann distribution
Tkmv
Tkmvg
BB 2exp
2
23
222
211 2
121 vmvmH
Center-of –mass coordinate
12 vvv
21
1122M
vvV
mmmm
2221
21 vMVH M
vdvgVdVgM
mmV
NNddZ MM
33212
1221212 v
1
物理化學(三) 應用化學系朱超原老師 15
Integral d3VM vdvg
VNN
ddZ 32122
1212 v
If we integral d3v 2122
121212 vV
NNdZ (no new)
Total reaction rate
cv
Classical pict ure
v ( relative speed)
Reaction probability
0
1
cvv All reactions
cvv no reaction
物理化學(三) 應用化學系朱超原老師 16
Total reaction rate vdvvgVNN
dreactionZ 32122
1212
cv BBdvv
Tkv
TkVNNdreactionZ 3
212
312
2122
1212 2exp4
2
2121
2exp 23
212 c
c
avc
v Be
av
advv
Tkv
Tka
B212
F ract ion number in bimolecul ar re actionsF ract ion number in bimolecul ar re actions
RTE
cTk
B
cTkv
B
cc
B
c
B
c
eRTE
eTk
eTk
vf
11
21 2
212
212
物理化學(三) 應用化學系朱超原老師 17
Example 2HIIH 22 At T = 373.15K
26101.1 fFraction number of reaction
Tk
B
cTkv
B
c Bc
B
c
eTk
eTk
vf
1
21 2
212
212
26101.11 xex 10ln261.1ln)1ln( xxx = 63.9454499236402
Txk Bc
eVmolkJmolJxRTEc 2/198/1098.15
11mol8.314JK R
物理化學(三) 應用化學系朱超原老師 18
new4
BA products
Elementary bimolecular reaction (two reactants)
BAkdt
Ad
RTE
cAv
BC
eRTE
NTkdk
18
12
212
RTE
Ak aexp ac EE
Compare with Arrhenius formula
Rate constant
物理化學(三) 應用化學系朱超原老師 19
Example 2HIIH 22
molJEc /1098.15
T1 = 293.15K T2 = 303.15K
11mol8.314JK R
KREc 41038.2
14exp
exp
1
2
RTERTE
C
C
983.0
1
1
2
1
11
22
1
2
TT
RTE
T
RTE
T
TATA
c
c
Change fast
Change slow
物理化學(三) 應用化學系朱超原老師 20
v (relative speed)
Reaction probability
cc
c
vvv
vvv
p1
0
Total reaction rate
cv
c
BBdv
vv
vTk
vTkV
NNdreactionZ 12
exp42
32
123
122
1221212
RTE
TkTkv c
B
c
B
c
eeef
2
212
Rate constant
fraction number
RTE
AvB
C
eNTkdk
12
212
8
0
1
cv
物理化學(三) 應用化學系朱超原老師 21
Example 2HIIH 22 At T = 373.15K
26101.1 fFraction number of reaction
262 101.1
212
TkTkv
B
c
B
c
eef
1.1ln10ln26 x x = 59.77Txk Bc
eVmolkJmolJxRTEc 93.1/186/1086.15
11mol8.314JK R
Better than …
15 molJ10703.1(exp) aE
物理化學(三) 應用化學系朱超原老師 22
Example 2HIIH 22 At T = 373.15K1115 smolL1074.8 fkRate constant
15 molJ10703.1(exp) aEActivation energy
Calculate effective collision diameter
RTE
AvB
C
eNTkdk
12
212
8
904.54RTEa
smolmN
TkAv
B
2612
10128
242721218 1043.1102.11074.8 dCross section 221212 10093.5 md
A4.0104 1112 md
物理化學(三) 應用化學系朱超原老師 23
Steric factor in bimolecular reactions
If two molecules are not in right orientation in collision, thereis no reaction no matter how large kinetic energy.
Simple way to consider this:
RTEc
ef
Rate constant
fraction number
RTE
AvB
C
eNTkdk
12
212
8
Steric factor
物理化學(三) 應用化學系朱超原老師 24
Example 2HIIH 22
At T = 373.15K
11mol8.314JK R
RTE
Ak aexp
1115 smolL1074.8 k 15 molJ10703.1 aE 119 smolL100.6 A
experiment
Calculate steric factor RTE
AvB
C
eNTkdk
12
212
8
smolL
NTkd AvB
11
12
212
1077.7
8
Av
B NTk
dA12
212
8
0077.0
物理化學(三) 應用化學系朱超原老師 25
PCIIIweek16-2作業
Problems 12.1512.16
Page 540
物理化學(三) 應用化學系朱超原老師 26
BA products BAkdt
Ad
Rate constant
RTE
Ak aexpExperiment
RTEc
ef
Theory
fraction number
RTE
AvB
C
eNTkdk
12
212
8
2
1221
cAvC vNE
If A=B, kk 21
2
21 Ak
dtAd
物理化學(三) 應用化學系朱超原老師 27
VIIIVIII--4. 4. UnimolecularUnimolecular reactionsreactions
A CB
Akdt
Ad
2Akdt
Ad
Experiment found this reaction
neither nor
Lindemann mechanism (2 steps)
AA AA *
*A CB
(1)
(2)
物理化學(三) 應用化學系朱超原老師 28
(1) *A as a product AAkAk
dtAd
dtAd **
21
12
1
(2) *A as a reactant ** 2 Akdt
BddtAd
forward reverse
Compare two steps *** 2121 AkAAkAkdtAd
*2 AkdtBd
At equilibrium *A 0* dtAd Akk
AkA12
21*
Akk
Akkdt
Bd
12
212
物理化學(三) 應用化學系朱超原老師 29
rate =
AkkAkk
dtBd
dtAdtv
12
212
A CB
(a) 21 kAk
Ak
kkdt
Bddt
Adtv1
12
unik(b) 21 kAk
21 AkdtBd
dtAdtv
First-order
Second-order