Chap. 8 Reaction Kinetics
(1) Definition of reaction rate
The change of number of component i with time is define as the rate
of reaction:
ri =
1 dN i
*
(Based on unit volume of reactor)
V dt
=
dCi
(V = constant)
dt
e.g. A + 2 B → C , V = cons.
rC =
dCC
dC
dC
, rB = − B , rA = − A
dt
dt
dt
(2) Homogeneous reactions
ri = f ( state of system ) = f ( T, P, component )
∵ homogeneous, P = constant
→ ri = f ( T, component )
(3) Rate equation
1. Single & multiple reactions:
a. single rxn: A → B or A + B → C + D
b. multiple rxn:
(i) Series rxn: A → B → C
(ii) Parallel rxn: A → B
A→C
2. Elementary & nonelementary rxns:
Elementary reactions: rate equation corresponds to the
stoichiometic equation.
K
e.g. A + 2 B ⎯⎯→
C , − rA = k * C 1A * C B2 , where k: rate constant
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Edited by Prof. Yung-Jung Hsu
Nonelementary reactions: rate equation isn’t related to the
stoichiometic equation.
K
3B , − rA = k
e.g. 2 A ⎯⎯→
C A2
, where k: rate constant
CB
3. Order of reaction:
− rA = k * C Aa * C Bb * CCc * C Dd , a + b + c + d = n
For A: of order a, for B: of order b
Overall: of order n
4. Expression of rate equation:
a. elementary rxns: A → B or A + B → C + D
K
A + 2 B ⎯⎯→
3C
− rA = k * C A * C B2 , − rB = k * C A * C B2 , rC = k * C A * C B2
→ − rA = −rB = rC (wrong!!)
∵ stoichiometic equation.
→ − rA = k * C A * C B2
− rB = k ' * C A * C B2 , k ' = 2k
rC = k '' * C A * C B2 , k '' = 3k
b. nonelementary rxns:
Choose suitable mechanism
By rate-limiting step method. 速率決定步驟
1 is at equilibrium, K =
∵○
[O ]
[O2 ][O]
⇒ [O] = K 3
[O3 ]
[O2 ]
2 is the rate-determine step, − RO 3 = k3 [O][O3 ] = k '
∵○
2
[O3 ]2
[O2 ]
Edited by Prof. Yung-Jung Hsu
(4) Temperature dependence
1. Rate equation: ri = f (T, component), P=const.
= k* f (component)
By Arrhenius Law:
k = k0 * exp[− E
RT
→k~T
] , where k0: frequency factor
E: activation energy
2. How to find E, k0?
From k = k0 * exp[− E RT ]
→
ln k = ln k0 −
E
RT
Plot lnk vs. 1/T
(5) Equilibrium constant & rate constant
Consider a “reversible” reaction at constant volume:
− rA = −
dC A
= kC A − k −1CB * CC (A 濃度隨時間變化之量)
dt
If the reaction is at equilibrium, the rate of change of concentration of
A will be zero ⇒
dC A
= 0 帶入上式
dt
⇒ kC A, E − k −1CB , E * CC , E = 0
⇒
C * CC , E
k
= B, E
=K
−1
k
C A, E
⇒K
CB , E * CC , E
k
, where K is equilibrium constant & K = −1
k
C A, E
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(6) Interpretation of reaction data → to find k
1. Unimolecular irreversible 1st-order reaction:
k
A⎯
⎯→
P , V=constant
− rA = −
dC A
dC A
= kC A ⇒
= k * dt
CA
dt
t
dC A
C
= ∫ k * dt ⇒ − ln A = kt
0
C A0 C
C A0
A
⇒ −∫
CA
2. Pseudo 1st-order reaction:
k
A+ B ⎯
⎯→
P , with B excess (V=const.)
− rA = −
dC A
= kC A * CB
dt
If B is excess ⇒ CB ≅ CB 0 >> C A (超過 20 倍)
dC A
= kC A * CB 0
dt
C
− ln A = kCB 0 * t
C A0
−
ln C A = − kCB 0 * t + ln C A0
3. Irreversible 2nd-order reaction:
k
Type I: 2 A ⎯
⎯→
P
− rA = −
dC A
2
= kC A
dt
t
dC A
= − k ∫ dt
2
0
C A0 C
A
⇒∫
CA
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⇒
1
1
=
+ kt
C A C A0
k
Type II: A + B ⎯⎯→
P
dC A
= kC A * C B
dt
Q C A − C A0 = C B − C B 0
⇒ C B = C A + C B 0 − C A0
− rA = −
a. if C A0 = C B 0 ⇒ C A = C B
− rA = −
dC A
2
= kC A ……type I
dt
b. if C A0 ≠ C B 0
dC A
= kC A * (C A + C B 0 − C A0 )
dt
C
C
⇒ ln A − ln B = −k (C B 0 − C A0 )t
C A0
CB 0
− rA = −
⇒ ln[
C A CB0
*
] = −k (C B 0 − C A0 )t
C B C A0
4. Irreversible nth-order reaction & n ≠ 1 :
k
nA ⎯
⎯→
P
dC
n
− rA = − A = kC A
dt
⇒ ln(−rA ) = ln k + n ln C A
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Then plot ln(−rA ) vs. ln C A :
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