che441 analysis of rate data-1
TRANSCRIPT
![Page 1: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/1.jpg)
Ch E 441 - Chemical Kinetics and Reaction Engineering
Analysis of Rate Data
![Page 2: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/2.jpg)
Extracting Kinetic Constants• To design reactors, rate equation must be known.• Determining the rate equation and its associated
constants requires analysis of experimental data.
Experimental reactor types:
• batch• differential
Experimental methods used to collect data:
• half-lives• initial rates
• differential• Integral• linear regression• non-linear
regression
Analysis & interpretation techniques:
![Page 3: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/3.jpg)
Batch Reactor Data• Differential Method of Analysis• Consider the following reaction that occurs in a
constant volume batch reactor productsA
AA r
dtdN
V1
AA kCr
Mole Balance Rate Law Stoichiometry
oVV
Combine A
A kCdt
dC
take the natural log of the combined equation
![Page 4: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/4.jpg)
Batch Reactor Data• Differential Method of Analysis• Consider the following reaction that occurs in a
constant volume batch reactor
xm b y
Clnklndt
dCln A
A
fit by least squares regression
productsA
AA kC
dtdC
![Page 5: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/5.jpg)
Differential method example• When arterial blood enters a tissue capillary, it exchanges oxygen and
carbon dioxide with its environment. The kinetics of this deoxygenation of hemoglobin in blood was studied with the aid of a tubular reactor by Nakamura and Staub [J. Physiol., 173, 161 (1967)].
• Although this is a reversible reaction, measurements were made in the initial phases of the decomposition so that the reverse reaction could be neglected. Consider a system similar to the one used by Nakamura and Staub: the solution enters a tubular reactor (0.158 cm diameter) that has oxygen electrodes placed at 5-cm intervals down the tube. The solution flow rate into the reactor is 19.6 cm3/s.
Electrode position 1 2 3 4 5 6 7% decomposition of HbO2 0.00 1.93 3.82 5.68 7.48 9.25 11.0
22 OHbHbO
![Page 6: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/6.jpg)
Differential method example• For a tubular reactor assuming rate equation is
nth order in CA: nn
AoAo X1kCdVdX
F
n
Ao
cnAo X1F
AkCdzdX
X1lnnF
AkCln
dzdX
lnAo
cnAo
![Page 7: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/7.jpg)
Batch Reactor Data• Experimental Technique: Method of Excess• Consider the following reaction that occurs in a
constant volume batch reactor
BAAA CCkr
Rate Law
component A in excess such that [A] constant
BA C"kr
AA C'kr component B in excess such that [B] constant
kA can now be determined
AA Cln vs. rln
BA Cln vs. rln
BAAA CCrk
productsBA
![Page 8: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/8.jpg)
Batch Reactor Data• Experimental Technique: Method of Initial Rates• used when differential method is ineffective: e.g.,
– Competing reactions,– Reverse reactions, and/or– Pressure changes due to reaction.
• series of reactions at different Ci,o performed• initial rate: differentiate data, extrapolate to t = 0• relate –rAo to CAo, to find appropriate rate law.
![Page 9: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/9.jpg)
Batch Reactor Data• Protocol for analyzing Rate Data:
1. Postulate a rate law.2. Process data in terms of the measured variable.3. Look for simplifications.4. Calculate –rA as a function of reactant concentration
to determine reaction order.• Batch: -dCA/dt• Differential PBR: -rA = FAoX/W
5. Determine specific reaction rate, k.
![Page 10: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/10.jpg)
Batch Reactor Data• Integral Method of Analysis
– Assume order– integrate rate law/design equation– Linearize result
• Consider reaction in constant V batch reactor
productsA
AA r
dtdC
kdt
dCA
Zero Order Reaction
ktCC AoA
Thus, a plot of CA vs. t will be linear with a slope of k and an intercept of CAo if the rate law is correct
![Page 11: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/11.jpg)
Batch Reactor Data• Integral Method of Analysis
– Assume order– integrate rate law/design equation– Linearize result
• Consider reaction in constant V batch reactor
productsA
AA r
dtdC
AA kC
dtdC
1st Order Reaction
ktCC
lnA
Ao
Thus, a plot of ln(CAo/ CA) vs. t will be linear with a slope of k if the rate law is correct
![Page 12: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/12.jpg)
Batch Reactor Data• Integral Method of Analysis
– Assume order– integrate rate law/design equation– Linearize result
• Consider reaction in constant V batch reactor
productsA
AA r
dtdC
2A
A kCdt
dC kt
C1
C1
AoA
Thus, a plot of 1/ CA vs. t will be linear with a slope of k if the rate law is correct
2nd Order Reaction
![Page 13: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/13.jpg)
Integral method of analysis• Penicillin G reacts with hydroxylamine (NO2OH) to form
hydroxamic acid, producing a colored complex with iron(III).• To determine overall reaction order, equal concentrations of
penicillin and NH2OH were mixed together in a 250-mL flask [J. Chem. Educ., 49, 539 (1972)]. – Samples were withdrawn every 10 minutes and added to a solution
containing iron(III) chloride. – Using a colorimeter, concentration of the colored complex (hence
concentration of hydroxamic acid) was obtained as function of time (absorbance is directly to hydroxamic acid concentration).
Time(min) 0 10 20 30 40 50 Absorbance 0.00 0.337 0.433 0.495 0.539 0.561 0.665
![Page 14: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/14.jpg)
Integral method of analysisHAOHP
1X when AA
constant analyticalKabsorbanceA
acid hydroxamicHAinehydroxylamOH
penicillinP
Mole Balance Rate Law Stoichiometry
PP r
dtdC
XCC
X1CC
PoHA
PoP
n
PP kCr
define relationship tomeasured variable
AKCHA
Combine
nnPoPo X1kC
dtdX
C
nnPo
Po
A
A1kC
dtdA
AC
nAAKdtdA
1nnPo
AC
kK
![Page 15: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/15.jpg)
Integral method of analysis
IntegralMethod nAAK
dtdA
1nnPo
AC
kK
0AAKdtdA
Zero
Order KtdAA
0
1AAKdtdA
First
Order
t
0
A
0dtK
AAdA
KtA
AAln
2AAKdtdA
SecondOrder
t
0
A
0 2 dtKAA
dA Kt
A1
AA1
KtA
HAOHP
![Page 16: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/16.jpg)
Express in terms of measured variable• Do not convert measured data into conversion.
Express design equation in terms of measured variable.• Consider constant V & T, gas-phase, batch reaction for
which total pressure vs time is measured
X1CC AoA
o
o
o T
TX1
PP
VV
oAo
ooAo
oo
PPP1
PPPy
1PP
P1
X
RT
PPPC oo
A
substituting
![Page 17: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/17.jpg)
• Do not convert measured data into conversion. Express design equation in terms of measured variable.
• Consider constant V & T, gas-phase, batch reaction
Express in terms of measured variable
RT2
PP3RT
2PPPRT
PPPC ooooo
A
C2BA .,g.e 2121
A
AA kC
tC
r
PP3'ktP
o PP3ln'kln
tP
ln o
![Page 18: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/18.jpg)
Batch Reactor Data• Integral Method of Analysis
– Assume order– integrate rate law/design equation– Linearize result
• Consider reaction in constant V batch reactor
C2BA
AA r
dtdC
PP3'ktP
o
assume = 1
t'kPP3
P2ln
o
o
![Page 19: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/19.jpg)
Batch Reactor Data• Experimental technique: Method of Half Lives• Half life is the time required for concentration of
the reactant to fall to half of its initial value.• By determining half life as a function of initial
concentration, order and specific rate can be determined.
![Page 20: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/20.jpg)
• Experimental technique: Method of Half Lives
Batch Reactor Data
AA kCr
productsA
AA kC
dtdC
1
Ao1
A C1
C1
1k1
t
1CC
1kC1
t1
A
Ao1
Ao
![Page 21: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/21.jpg)
• Experimental technique: Method of Half Lives
Batch Reactor Data
AoA
½
C½Ctt
1Ao
1
½ C1k12
t
Ao
1
½ Cln11k12
lntln
obtain order from slopeobtain k from intercept after obtaining
AA kCr
productsA
1CC
1kC1
t1
A
Ao1
Ao
![Page 22: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/22.jpg)
Method of Half Lives Example• Nitrogen oxide is a pollutant in automobile exhaust that
can react with oxygen to form nitrogen dioxide:
• At 298 K the specific reaction rate is:
Find t½ of 3000 ppm NO (typical pre-control exhaust level) in air?
What is t½ of 1 ppm NO (a typical polluted atmosphere value)?
2k
2 NO2ONO2 2minppm104.1k 29
2
since oxygen is highly in excess,
NO2ONONO CkCkCr
![Page 23: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/23.jpg)
Method of Half Lives Example• Nitrogen oxide is a pollutant in automobile exhaust that
can react with oxygen to form nitrogen dioxide:
• At 298 K the specific reaction rate is:
Find t½ of 3000 ppm NO (typical pre-control exhaust level) in air?
What is t½ of 1 ppm NO (a typical polluted atmosphere value)?
2k
2 NO2ONO2 2minppm104.1k 29
2
3NO2NO2ONONO CkCkCkCr
units on specific reaction rate imply = 3
![Page 24: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/24.jpg)
Method of Half Lives Example• Nitrogen oxide is a pollutant in automobile exhaust that
can react with oxygen to form nitrogen dioxide:
• At 298 K the specific reaction rate is:
Find t½ of 3000 ppm NO (typical pre-control exhaust level) in air?
What is t½ of 1 ppm NO (a typical polluted atmosphere value)?
2k
2 NO2ONO2 2minppm104.1k 29
2
2Ao
913Ao
13
1Ao
1
½ C108.23
C13k12
C1k12
t
substituting = 3 into half-life expression:
![Page 25: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/25.jpg)
Method of Half Lives Example• Nitrogen oxide is a pollutant in automobile exhaust that
can react with oxygen to form nitrogen dioxide:
• At 298 K the specific reaction rate is:
Find t½ of 3000 ppm NO (typical pre-control exhaust level) in air?
What is t½ of 1 ppm NO (a typical polluted atmosphere value)?
2k
2 NO2ONO2 2minppm104.1k 29
2
substituting CNO = 3000 ppm:
min 1.119
3000108.23
t 29½
substituting CNO = 1 ppm:
min 10071.1
1108.23
t 929½
![Page 26: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/26.jpg)
Differential Reactors• Used to determine rate for heterogeneous catalytic
reactions as a function of Ci or Pi.• Uses a method similar to initial rates.• Reactor is a tube with a small (differential) wafer of
catalyst, causing a small conversion of reactant.
FAo FAe
L
inert packingcatalyst
![Page 27: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/27.jpg)
Differential Reactors• Known, controlled, or measured:
– Volumetric flow rate ()– Concentrations (Cao, CA)– Catalyst weight (W)
FAo, FA
0W'rFF AAeAo
WF
WXF
WFF
'r PAoAeAoA
FAo FAe
L
WC
WCC
'r PoAeAooA
for constant o
![Page 28: ChE441 Analysis of Rate Data-1](https://reader034.vdocuments.site/reader034/viewer/2022052117/553740644a795936258b4caa/html5/thumbnails/28.jpg)
Differential Reactors• By using very little catalyst and operating at high
volumetric flow rates, (CAo - CAe) can be made small.• Catalyst bed is approximated as being gradientless.
AbAA C'r'r 2
CCC AeAo
Ab
AoAb CC
FAo FAe
L
WC
WCC
'r PoAeAooA
for constant o