ChE 452 Lecture 03 Variations In Rate With Temperature 1
Dec 28, 2015
ChE 452 Lecture 03
Variations In Rate With Temperature
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Objectivge For Today
Review Arrhenius’ law Develop some rules of thumb that
allow one to estimate activation barriers from very little data.
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Variations in Rate With Temperature Huge
Rate variations with temperature are much larger than variations in rate with concentration Factor of two in concentration gives
factor of 2-4 in rate Factor of 2 in temperature gives 107
variation in rate
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Homogeneous Reactions
Rate increases with increasing temperature
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3.1 3.2 3.3 3.4 3.5 3.61
10
100
1000 10 °C20 °C30 °C40 °C
Gro
wth
Rate
, #/h
r
1000/T, K-1
Figure 2.10 The rate of E. Coli growth as a function of temperature adapted from
Bailey and Ollis [1977].
Heterogeneous Reactions
Rate has a maximum at intermediate temperatures
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Rat
e, M
olec
ules
/cm
-se
c2
Temperature, KTemperature, K
1E+13
1E+12
1E+11
600400 800600 800400
P =2.E-7 torrCO
A
B
C
2P =2.5E-8 torrO
DEF
Figure 2.18 The rate of the reaction CO + 2 O2 CO2 on Rh(111). Data of Schwartz, Schmidt and
Fisher[1986].
Models For Variations In Rate With Temperature
Key processes• Molecules get hot• Cross a barrier
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Reaction Cordinate
En
erg
y
ReactantsProducts
Barrier
A‡
Figure 7.5 Polanyi’s picture ofexcited molecules.
Models For Variations In Rate With Temperature
Key processes• Molecules get hot• Cross a barrier
Models• Perrin’s Model: energy transfer
dominates• Arrhenius’ Model: barrier dominates
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Perrin’s Model
Assume energy transfer dominates.
k = kT Tn
k = rate constant
kT = preexponential
n = constant between 1 and 4
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(2.24)
Arrhenius’ Model
Assume barrier dominates
k = koexp(-Ea/kBT)
ko = preexponential
Ea = activation barrier, kJ/molecule
kB = Boltzman’s constant, 1.381x10-23
J/K
T = temperature (K)9
(2.26)
Arrhenius’ Model In Kcal/mole
Assume barrier dominates
k = koexp(-Ea/RT)
ko = preexponential
Ea = activation barrier, kcal/molecule
R = Gas law constant, 1.98x10-3
kcal/mole/K
T = temperature (K)10
Real Data Somewhere In Between
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0.5 1 1.5 2 2.5 3 3.5 40.1
1
10
100
1000 3004005006001000 800 700
620 torr
100 torr
20 torr
1000/T, K
Rat
eTemperature,K
-1
Figure 2.6 The rate of the reaction CH + N2 HCN + N as a function of the temperature. Data of Becker, Gelger and Wresen[1996].
Best Fit Of Real Data Uses A Combined Expression
Tk/E-m0
m1BAe(T)k=k
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Arrhenius’ effect much larger than Harcourt and Essen
(2.28)
Rates Double Or Triple When The Temperature
Rises By 10 K
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Reaction Temperature range, C
Rate Change with a 10-K Temperature
Change
3.6-30.4 2.03
23.5-43.6 2.87
24.5-43.6 2.68
0-61 3.0
CH COOCH CH H O
CH COOH CH CH OH3 2 3 2
H
3 3 2
CH
C = CH3
2
CH Cl NaOH
H NaCl H O2
2 2
CH CH CH Cl NaOH
CH CH CH NaCl3 2 2
3 2
HPO3 H O H PO2 3 4
Table 2.6 The variation in rate of a series of reactions with a 10-K change in temperature
Also Works For Biological Processes
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Table 2.7 The variation in the respiration rate of plants with a 10 change in temperature. Data of Clausen[1890].
Wheat 2.47
Lilac 2.48
Lupine 2.463.1 3.2 3.3 3.4 3.5 3.61
10
100
1000 10 °C20 °C30 °C40 °C
Gro
wth
Rate
, #/h
r
1000/T, K-1
Figure 2.10 The rate of E. Coli growth as a function of temperature adapted from
Bailey and Ollis [1977].
Crickets Chirping Example
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3.3 3.35 3.4 3.45 3.5 3.553000
4000
5000
6000
7000
8000
9000
10000
1000/T, KC
hirp
Rat
e, C
hirp
s/hr
10 °C15 °C20 °C25 °C
3.3 3.35 3.4 3.45 3.5 3.551000
10000
2000
3000
4000
5000
6000
7000
80009000
1000/T, K
Chi
rp R
ate,
Chi
rps/
hr
10 °C15 °C20 °C25 °C
-1-1
Figure 2.11 The rate that crickets chirp as a function of temperature. Data for field
crickets (Gryllys pennsylvanicus)
Examples From You Own Life
Why does bread taste better warm? Why does beer taste better cold? Why do you refrigerate, freeze food? Why do you maintain a body
temperature? Why do amphibians stop moving when
it is cold Why a fever?
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Next Key Implications Of Arrhenius’ Law
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(2.32)
(2.33)Figure 2.8 A plot of ½ vs. EA at 100, 200, 300,
400, and 500 K.
0 10 20 30 40 501E-6
1E-2
1E+2
1E+6
1E+10
1E+14 1,000,000 yrs
100 yrs
1 yr
1 day1 hr1 min
1 sec
Ea, Kcal/mole
Hal
f Life
, sec
onds
500K
400K300K200K100K
utemina T)Kkcal15/1(E (2.31)
ondseca T]K)molkcal06.0[(E
autemin Ekcal
molK15T
Example Question
Assume that you are measuring the kinetics of sponification of ethyl acetate in the unit ops lab, and you find that you get 50% conversion in 20 minutes at 25 C. What is the activation energy of the reaction?
How long should it take to get to 50% conversion at 35 C.
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Example
Assume that a reaction has an activation barrier of 35 kcal/mole. Approximately what temperature do we want to run it?
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Summary: Cont
Arrhenius’ law and Perrin’s model Arrhenius: barrier dominates Perrin: energy transfer dominates
Truth in between Biological processes follow the same
rate laws as chemical processes Leads to simple ways to estimate
activation barriers
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