Lecture 14
description
Transcript of Lecture 14
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Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of
chemical reactions and the design of the reactors in which they take place.
Lecture 14
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Lecture 14 – Thursday 2/24/2011Pseudo Steady State Hypothesis (PSSH)
Net Rate of Reaction of Active Intermediates is Zero
Hall of Fame Reaction: 2NO +O2 2NO2Introduction to Enzyme KineticsBegin Non-Isothermal Reactor Design
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An active intermediate is a molecule that is in a highly energetic and reactive state It is short lived as it disappears virtually as fast as it is formed. That is, the net rate of reaction of an active intermediate, A*, is zero.The assumption that the net rate of reaction is zero is called the Pseudo Steady State Hypothesis (PSSH)
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Example
CBA
The rate law for the reaction
A
AA Ck
kCr
1
2
is found from experiment to be
How did this rate law come about? Suggest a mechanism consistent with the rate law.
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For reactions with active intermediates, the reaction coordinated now has trough in it and the active intermediate, A*, sits in this trough
A*k1
k2
k3
A+A B+C
A+A
+A
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AAA*A 2 2k AAA CCkr *2*2
CB*A 3 3k *3*3 AA Ckr
A*AAA 1 1k 21*1 AA Ckr
Solution
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Rates:Rate laws:
21*1 AA Ckr Reaction (1)
(1)*2*2 AAA CCkr Reaction (2)
(2)
*3*3 AA Ckr Reaction (3)(3)
*33*11 , ABAA rrrr Relative Rates:But C*A cannot be measured since it is so small
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k3 is defined w.r.t. A*
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A
AA Ckk
CkC23
21
*
Net Rates: Rate of Formation of Product
*3*33 AABB Ckrrr (4)
*3*2*1** AAAAA rrrrr (5)
0*3*22
1 AAAA CkCCkCk (6)
*ACSolving for
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Pseudo Steady State Hypothesis r*A = 0
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Substituting for in Equation (4) the rate of formation of B is
CA*
A
AB Ckk
Ckkr23
231
(8)
11BA rr
CBA
Relative rates overall
A
ABA Ckk
Ckkrr23
231
(9)
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For high concentrations of A, we can neglect with regard to , i.e.,
3kACk2
32 kCk A
and the rate law becomes
Apparent first order.
AAA kCCkkkr 2
31 (10)
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ACkk 23
For low concentrations of A, we can neglect with regard to k3, i.e.,
and the rate law becomes
21
2
3
13AAA CkC
kkkr (11)
Apparent second order.Dividing by k3 and letting k’=k2/k3 and k=k1 we have the rate law we were asked to derive
A
AA Ck
kCr
1
2
(12)
A2Ck
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What about AA kCr
I
A
k
k
k
CkkCkk
CBA
IAIA
IAIA
22
31Ar-
)3(
* )2(
* )1(
3
2
1
Active Intermediates
)(`1
InertICk
kCrI
AA
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Why so many Reactions Follow Elementary Rate Laws
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2ONONO CkCr
The reaction 2NO +O2 2NO2
has an elementary rate law
However… Look what happens to the rate as the temperature is increased.
Active Intermediates / Free Radicals (PSSH)
-rNO2
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Hall of Fame Reaction
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Why does the rate law decrease with increasing temperature?
Mechanism:*3
k2 NOONO 1 (1)
2k*
3 ONONO 2 (2)
2k*
3 NO2NONO 3 (3)
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Write Rate of formation of Product rNO2
Note: k3 is defined w.r.t. NO2
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Assume that all reactions are elementary reactions, such that:
Define k w.r.t. NO3*
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The net reaction rate for NO3* is the sum of the individual reaction rates for NO3*:
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rNO3
* 0
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Pseudo Steady State Hypothesis (PSSH)The PSSH assumes that the net rate of species A* (in this case NO3
*) is zero.
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NOkk
ONOkNO
23
2
21*3
Pseudo Steady State Hypothesis (PSSH)
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Pseudo Steady State Hypothesis (PSSH)
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2
312
2
2
31312
2ONOe
AAAONO
kkkr RT
EEE
NO
312 EEE
The result shows why the rate decreases as temperature increases.20
-rNO2
T
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End of Lecture 14
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