Download - Liquid Phase Reactor
A. SUMMARY
The topic investigated in this experiment was liquid phase chemical reactors with the
effect of temperature on reaction rate constant. This is significant in Chemical
Engineering because of the underlying importance it has in understanding how a
chemical reaction works (i.e. chemical kinetics). In addit ion, knowing
the kinetics of a reaction wil l help chemical engineers in optimum
reactor design.
The major objective of this lab was to find the reaction rate constant in a batch
stirred tank reactor for the saponification ethyl acetate with dilute sodium hydroxide.
Another objective was to study the effect of temperature on reaction rate constant,
and also to find the values of the rate constant and the Arrhenius parameters;
activation energy, Ea and pre-exponential factor, A).
In carrying out the experiment, a chemical reactor service unit fitted with batch
chemical reactor was used (see figure 1 for the diagram of the experimental set up).
From the experiment, some key results were obtained. One of such result was that
for any given chemical reaction, the reaction rate is temperature dependent. Thus,
an increase in temperature causes an increase in the reaction. Also, the conductivity
of the reactants decreases with time as the reactants loses their ions and become
less conductive. Another important finding was that as the concentration of the
hydroxide reduces, the reaction rate increases.
Going by the objectives of the lab, the Arrhenius parameters were estimated to be
197.87 and 501.625 kJ/mol respectively (i.e. the pre-exponential factor and
activation energy). In addition, the reaction rate constant (k) for the reactions were
estimated to be 0.0101 M-1s-1 at 25°C, 0.2853 M-1s-1 at 30°C and 0.0089 M-1s-1 at
40°C respectively.
From the experiment, it can be concluded that temperature plays a major part in
chemical kinetics (rate increases as temperature increases). Also, in a chemical
reaction, as the reactant (s) are been converted into products, the conductivity
changes. Finally, in homogenous (same phase) reaction that is second order overall
(first order in both components) like the one done in the lab, the concentration of the
reactants also affects the reaction rate.
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B. INTRODUCTION:
One of the major objectives of this lab was to find the reaction rate constant using a
batch stirred tank reactor for the saponification ethyl acetate with dilute sodium
hydroxide. Another objective was to study the effect of temperature on reaction rate
constant, and also to find the values of the rate constant and the Arrhenius
parameters; activation energy, Ea and pre-exponential factor, A). In the course of the
experiment, the effect of concentration of reactants on a homogenous reaction was
also considered.
One of the three types of reactors in chemical processes is the batch reactor. In this
type of reactor, the total feed is introduced at the beginning and no withdrawal is
made until the reaction has reached the degree of completion desired; hence it is a
closed system reactor. It differs from a continuous stirred tank reactor (CSTR) which
has material exchange taking place during the reaction.
For this experiment, a stirred tank batch reactor was used; meaning it has a stirrer to
ensure continuous mixing of the reactants to aid in a homogenous concentration
throughout the mixture. Another important thing to note about this type of reactor is
that it works with an unsteady process (that is all variables change with time).
Also, the mixture in the volume is assumed to be perfectly mixed (that is there will be
uniform concentrations). In addition, temperature will be uniform throughout the
reactor; however it may change with time (Basu, 2012). Also, batch reactors are
often used for liquid-phase reactions particularly when the required production is
small (Smith, 1981).
Generally, the mass balance for a stirred tank reactor can be written as:
Rate of change within the reactor = Input – Output – Loss by reaction. For any liquid
phase chemical reactor with a constant volume such as the batch stirred tank
reactor, this can be rearranged to give: Rate of change within the reactor = loss by
reaction.
Thus for any given reaction in constant volume, the rate equation can be given as:
−dC A
dt=r A (1)
Where:
r A is the rate of disappearance of reactant ‘A’ among the reacting species
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C A is the concentration of reactant ‘A’ in the exit stream
t is the time in seconds it takes for reactant ‘A’ to disappear
For a bimolecular reaction like the one in the experiment; the saponification of ethyl
acetate with dilute sodium hydroxide which is given as:
NaOH+CH 3COOC 2H 5→CH 3COONa+C2H 5OH
The rate law for such reaction can be written as:
−r A=k C An CB
m (2)
Where:
k is the rate constant
n and m are appropriate powers based on experimental result
C A is the concentration of reactant ‘A’ in the exit stream
CB is the concentration of reactant ‘B’ in the exit stream
Generally several factors could influence the rate of a chemical reaction. Some of
these factors include:
(i) Temperature
(ii) Concentration (if homogenous)
(iii) State of reactants (that is if they are solid, liquid or gas)
(iv) Order of reaction
(v) Pressure
Out of the above mentioned factors, the effect of temperature on the reaction rate
was the one studied. Though, the effect of concentration was also observed because
the reaction that was studied was a homogenous reaction. The relationship between
reaction rate and temperature is explained by Arrhenius equation which is given as:
k=A∗e−EaRT
(3)
Where:
k is the reaction rate constant
R is the universal gas constant (8.314 J mol-1K-1)
T is temperature (K)
Ea is the activation energy (J mol-1)
A is Arrhenius constant or pre-exponential factor (s-1) for a first order reaction
By applying natural logarithm to both sides, equation (3) can be re-written as:
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¿k=¿ A−EaRT
(4)
From equation (4), a plot of ¿k against 1/T would yield a straight line graph from
which ‘A’ can be obtained as the intercept of the line at 1/T = 0. The activation
energy (Ea) can be obtained from the slope of the graph which is given as−EaRT
.
Thus if the slope, S =−EaRT
, then the activation energy can be estimated as:
Ea=−R∗slope (5)
It is noteworthy to mention here that reactions with low activation energy are
relatively temperature-insensitive while those with high activation energies are very
temperature sensitive. Therefore, any given reaction is much more temperature-
sensitive at a low temperature than at a high temperature (Levenspiel, 1999).
From the above, it shows that the reaction rate constant has to be obtained first
before applying Arrhenius equation to find the Arrhenius parameters. This can be
done by referring to reaction to be studied:
NaOH+CH 3COOC 2H 5→CH 3COONa+C2H 5OH
The rate of the reaction can be said to depend on the concentrations of both reactant
‘A’ (NaOH ¿and reactant ‘B’ (CH 3COOC 2H 5 ¿. The order of the reaction studied is
known to be first order with respect to both ‘A’, and ‘B’ , hence second order overall.
Thus by combining equation (1) and (2), an expression for the reaction rate constant
in terms of the concentration of A and B can be obtained as:
dC A
dt=kC ACB
(6)
Where:
All the parameters are as defined in equation (2)
If the initial concentration of reactant A (CA0) and reactant B (CB0) are made to be
equal, then equation (6) can be reduced to:
dC A
dt=kC A
2 (7)
Integrating equation (7) yields:
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kt= 1C A
− 1C A 0
(8)
Where:
k , t , C A and C A0are as defined before.
From equation (8), it can be seen that a graph of 1CA
against t will give a straight line
graph with slope equal to k (reaction rate constant) and intercept 1CA 0
For the experiment, to calculateC A, the conductivity of the one of the reactants; in
this case reactant ‘A’ (Sodium hydroxide) can be measured at various time intervals.
With this, the concentration of the hydroxide can be calculated as:
C A(t)=CA 0k (t )−k∞k 0−k∞
(9)
Where:
C A is the concentration of reactant ‘A’ in the exit stream at time t
C A0 is the initial concentration of NaOH
k (t ) is the conductivity of the solution at time t
k∞ is the conductivity of the solution at the end of reaction
k 0 is the initial conductivity at time t = 0
Note:
k 0 can be found by plotting a graph of the measured conductivity (k) against time and
extrapolating to t = 0.
k 0 can also be found from the same graph by extrapolating to large t.
The rationale for calculating the concentration of the hydroxide by evaluating
conductivity is that the degree of conversion of reactants affects the conductivity of
the reactant contents, so that recording the conductivity with respect to time helps to
calculate the amount of conversion (Denbihh and Turner, 1971).
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C. EXPERIMENTAL EQUIPMENT
The major equipment used in the experiment was a chemical reactor service unit
fitted with batch chemical reactor. A diagram of the experimental set up is shown in
figure 1. Other equipment used include; thermostatic bath to control the temperature
stability of the two reactants to be added in at any time, 1 litre glass flasks containing
the reactants, conductivity meter to measure the conductivity of the solution,
stopwatch and stock solutions of 0.1M solution of sodium hydroxide and 0.1M of
ethyl acetate.
A batch reactor is one of the three types of reactors in chemical processes. It is
similar to the continuous stirred tank reactor in the sense that the mixture in the
volume is stirred but unlike the continuous stirred tank reactor where there is a
continuous supply of feed while products are continually removed, in the case of the
batch reactor; there is no inflow or outflow of material. The total feed is introduced at
the beginning and no withdrawal is made until the reaction has reached the degree
of completion desired.
This type of reactor is mostly used for liquid-phase chemical reactions, especially on
a small scale. Thus when used for liquid-phase reactions, the reactor volume does
not change significantly with the extent of reaction. For a gas-phase reaction, it may
be constant pressure sometimes. In addition, since the mixture in the tank is
assumed to be perfectly mixed, there will be uniform concentrations, and
temperature will also be uniform throughout the reactor; however with time it may
change. See figure 1 and 2 for a schematic diagram of a batch stirred tank reactor
and the experimental set-up respectively. The picture of the experimental set up is
also shown in figure 3.
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Figure 1: Schematic diagram of a batch stirred tank reactor
Source: http://www.rpi.edu/dept/chem-eng/Biotech-Environ/IMMOB/stirredt.htm
Figure 2: Schematic diagram of the experimental set up
Stirrer
Reactant components
Figure 3: Diagram of the experimental set-up
D. EXPERIMENTAL PROCEDURE AND OBSERVATIONS
For safety reasons safety goggles and protective gloves were worn
during the course of the experiment advised to wear safety goggles and
protective gloves. After this, 0.1M sodium hydroxide and 0.1 M ethyl acetate
were provided to run the experiment. Then the reaction temperature was set to 25°C
on the thermostatic bath.
Then the two 1 l i tre f lasks were fi l led to the mark with sodium hydroxide
solution and ethyl acetate solution respectively and placed in a bath.
The reaction temperature was then set on the reactor control panel.
After this, the conductivity meter was set and the probe end was placed
in the bath to get to get to the reaction temperature. The flasks were
also allowed to reach the reaction temperature.
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Conductivity probe
Reaction vessel
Conductivity meter
Temperature probe
Ethyl acetate NaoH
Temperature adjuster
The 1 l i tre of sodium hydroxide solution was added to the reactor,
fol lowed by the 1 l i tre of ethyl acetate solution, and the clock was
started when ca. 50% of ethyl acetate solution was added. After wait ing
for about 30 seconds, ca. 200ml was withdrawn and the conductivity
was measured, and then the sample was returned to the reactor while
the probe was returned to the bath.
The conductivity readings were taken every 30 seconds for about 10
minutes. It was then allowed to run for further 20 minutes and the
readings were taken after every 3 minutes.
The experiment was then repeated for reaction temperatures of 30°C
and 40°C. Some observations were then made, one of which was that
with t ime the conductivity of the solution decreases. This could be as a
result of loses of ions in the solution, thereby making it less conductive.
E. RESULTS AND CALCULATIONS
The results (both experimental and calculated, and extrapolated results) obtained in
the experiment are shown in table 1- 4 below. The graphs are shown in figures 3 - 9
Table 1: Measured conductivity values at different reaction temperatures
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t (s)Conductivity, k @ 25°C (S/m)
Conductivity, k @ 30°C (S/m)
Conductivity, k @ 40°C (S/m)
30 1.511 0.601 1.69860 1.398 0.544 1.51190 1.308 0.498 1.386
120 1.246 0.462 1.304150 1.188 0.431 1.246180 1.140 0.407 1.199210 1.100 0.387 1.161240 1.066 0.37 1.13270 1.037 0.355 1.105300 1.011 0.343 1.084330 0.988 3.33 1.065360 0.968 0.324 1.049390 0.950 0.317 1.035420 0.934 0.31 1.022450 0.918 0.305 1.011480 0.906 0.3 1.001510 0.893 0.296 0.984540 0.882 0.292 0.976570 0.871 0.289 0.969600 0.862 0.287 0.955780 0.818 0.276 0.936960 0.787 0.271 0.9131140 0.765 0.268 0.8961320 0.748 0.266 0.8821500 0.735 0.265 0.87
Table 2: Calculated hydroxide concentration CA at different temperatures
t (s) CA @ 25°C CA @ 30°C CA @ 40°C
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30 0.1250 0.1383 0.132260 0.1156 0.0710 0.117790 0.1082 0.0593 0.1079
120 0.1031 0.0501 0.1015150 0.0983 0.0422 0.0970180 0.0943 0.0361 0.0934210 0.0910 0.0310 0.0904240 0.0882 0.0267 0.0880270 0.0858 0.0229 0.0860300 0.0836 0.0198 0.0844330 0.0817 0.0173 0.0829360 0.0801 0.0150 0.0817390 0.0786 0.0132 0.0806420 0.0773 0.0115 0.0796450 0.0759 0.0102 0.0787480 0.0749 0.0089 0.0779510 0.0739 0.0079 0.0766540 0.0730 0.0069 0.0760570 0.0720 0.0061 0.0754600 0.0713 0.0056 0.0744780 0.0677 0.0028 0.0729960 0.0651 0.0015 0.0711
1140 0.0633 0.0008 0.06981320 0.0619 0.0003 0.06871500 0.0608 0.000 0.0677
Table 3: Calculated reciprocal of hydroxide concentration (1/CA) at different
temperatures.
t (s) 1/CA @ 25°C 1/CA @ 30°C 1/CA @ 40°C30 8.001 7.231 7.564
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60 8.648 14.086 8.50090 9.243 16.867 9.266
120 9.703 19.949 9.849150 10.177 23.675 10.307180 10.605 27.676 10.711210 10.991 32.213 11.062240 11.341 37.429 11.365270 11.659 43.667 11.623300 11.958 50.385 11.848330 12.237 57.794 12.059360 12.490 66.610 12.243390 12.726 75.577 12.409420 12.944 87.333 12.567450 13.170 98.250 12.703480 13.344 112.286 12.830510 13.539 126.774 13.052540 13.707 145.556 13.159570 13.881 163.750 13.254600 14.026 178.636 13.448780 14.780 357.273 13.721960 15.362 655.000 14.0671140 15.804 1310.000 14.3341320 16.163 3930.000 14.5611500 0.000 0.000 0.000
Initial conductivity,k0
@ 25°C (S/m)
Initial conductivity,k0
@ 30°C (S/m)
Initial conductivity,k0
@ 40°C (S/m)
Conductivity at end of
reaction, k∞
@ 25°C (S/m)
Conductivity at end of reaction, k∞
@ 30°C (S/m)
Conductivity at end of
reaction, k∞
@ 40°C (S/m)
1.209 0.4346 1.2843 0 0 0
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Table 4: Extrapolated data
k0 was extrapolated to t = 0 from a graph of measured k against t in figure 4, 5 and 6
k∞ was extrapolated to large t from a graph of measured k against t in figure in figure
4, 5 and 6.
Table 5: Reaction rate constants at different temperatures
Reaction rate constant, k@ 30°C ( M-1s-1 )
Reaction rate constant, k@ 30°C ( M-1s-1 )
Reaction rate constant, k@ 40°C ( M-1s-1 )
0.0101 0.2853 0.0089
These values were obtained from figures 7, 8 and 9.
0 200 400 600 800 1000 1200 1400 16000.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
f(x) = − 0.000432987654320987 x + 1.20903407407407
Time, t (seconds)
Mea
sure
d co
nduc
tivity
, k (S
/m)
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Figure 4: Graph of conductivity against time at reaction temperature of 25 °C
0 200 400 600 800 1000 1200 1400 16000.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
f(x) = − 0.000172329218106996 x + 0.434598024691358
time, t (seconds)
Mea
sure
d Co
nduc
tivity
, k (S
/m)
Figure 5: Graph of conductivity against time at reaction temperature of 30 °C
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0 200 400 600 800 1000 1200 1400 16000.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
f(x) = − 0.000393218106995884 x + 1.28426469135802
time, t (seconds)
Mea
sure
d Co
nduc
tivity
, k (S
/m)
Figure 6: Graph of conductivity against time at reaction temperature of 40 °C
0 100 200 300 400 500 600 7000
2
4
6
8
10
12
14
16
f(x) = 0.0100635628274733 x + 8.54951503276483
time, t (seconds)
1/CA
(M)
Figure 7: Graph of 1/CA against time at reaction temperature of 25 °C
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0 100 200 300 400 500 600 7000
20
40
60
80
100
120
140
160
180
200
f(x) = 0.285281895218509 x − 20.5766175931413
time, t (seconds)
1/CA (M)
Figure 8: Graph of 1/CA against time at reaction temperature of 30 °C
0 100 200 300 400 500 600 7000.000
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
f(x) = 0.00892611933035733 x + 8.67920958875541
time, t (seconds)
Mea
sure
d co
nduc
tivity
, k (S
/m)
Figure 9: Graph of 1/CA against time at reaction temperature of 40 °C
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0.00329
0.0033
0.00331
0.00332
0.00333
0.00334
0.00335
0.00336
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
f(x) = − 60334.5561617578 x + 197.869733707811
Series2Linear (Series2)
1/T (K)
In k
Figure 10: Graph of In (k) against 1/T showing the effect of temperature on reaction
rate constant.
Note: When plotting the graph of ln (k) against 1/T, the value of the reaction rate
constant (k) gotten when the reaction temperature was 40 °C as shown in figure 9
was not used. This was because from the readings gotten from the experimental as
shown in table 1, an experimental error was suspected to have occurred thereby
giving wrong readings. This error could possibly be in the reading of the conductivity
meter.
SAMPLE CALCULATIONS:
(A) Sample calculation for the concentration of the hydroxide.
Hydroxide concentration at 25°C in 30 seconds.
Using equation (9) C A(t)=CA 0k (t )−k∞k 0−k∞
When CA0 = 0.1 M, k (t) = 1.511 S/m, k∞ = 0, k0 = 1.209
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∴C A( t)=0.11.511−01.209−0 = 0.1250 M
→ 1/CA = 1/0.1250 = 8.001
Using same procedure, the hydroxide concentration (CA) and its reciprocal (1/CA) at
30°C and 40°C at various time intervals were also calculated.
(B) Calculation of Arrhenius parameters (A and Ea)
From equation (4): ¿(k )=¿ A−EaRT
A graph of In (k) against 1/T as shown in figure 8 will yields a straight line with
intercept ‘A’
∴ Arrhenius parameter (A) = 197.87
Activation energy (Ea):
From equation (5): Ea=−R∗slope
Where slope in figure 8 = - 60335, R = 8.314 *10-3 kJ mol K-1
∴ Ea=−60335 ¿8.314 *10-3) = 501.625 kJ/mol = 501625.19 J/mol
F. DISCUSSION OF RESULTS:
From the results obtained in the experiment, it shows that reaction rate is dependent
on temperature, through the dependence of reaction rate constant on ‘k’ on
temperature ‘T’. This can be seen from figure 9 where a plot of In (k) against 1/T
gave a straight line graph. This can also be seen from table 1 where at a
temperature of 25 °C, the reaction rate constant was 0.010 M-1s-1, while at 30 °C it
was 0.2853 M-1s-1 . At 40 °C, the reaction rate constant was 0.0089 M-1s-1.
Thus reaction rate increases with an increase in temperature. This is because as
temperature increases, the reactants will acquire a lot of kinetic energy; hence there
will be more collision between the reacting molecules. In addition, this temperature
rise will also bring the reaction closer to its activation energy which is the minimum
amount of energy needed for a chemical reaction to occur.
It is noteworthy to mention here that even though there is suppose to be an
increasing trend in the reaction rate with time, at 40 °C there was a decrease. The
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reason could be because of an experimental error. This could be due to the readings
of the conductivity meter.
Thus when a graph of In (k) was plotted against 1/T to estimate the Arrhenius
parameters, the values of the reaction rate constant (k) obtained when the
temperature was 40 °C was not used so as to obtain a straight line (linear) graph.
From figures 3, 4 and 5, it shows that conductivity decreases with time. This is could
be due to loses of some ions. This can also explain why at the start, only sodium
hydroxide would contribute to the conductivity. As reaction proceeds, sodium acetate
would start forming after consumption of sodium hydroxide resulting in different
conductivity results (Fogler, 1999).
Hence in the experiment carried out, there was a reduction in the concentration of
the hydroxide (NaOH) at various time intervals. The reason for this could be that
since it is a batch reactor, the reactants would be converted into products while
remaining in the reactor since there is no inflow or outflow; thus as the reactants are
been converted into products, there would be less and less reactant and more and
more products.
It can then been inferred that close to time t = 0, there would be a lot of reactant and
little product while close to time = infinity, there would be more product and less
reactant (Missen et al, 1999).
Finally, this goes to show that for a second order reaction (first order in each reacting
components) like the saponification of ethyl acetate with dilute sodium hydroxide, the
reaction rate is also dependent on one or both of the reactants concentrations; in this
case that of the sodium hydroxide. For the reaction studied in this experiment, a
decrease in one of the reactant concentrations; in this case sodium hydroxide
causes and increase in the reaction rate. This is in line with the collision theory.
G. CONCLUSIONS:
From the experiment, the following conclusions can be drawn.
(i) The rate of a chemical reaction is temperature dependent. It increases
with an increase in temperature and vice versa.
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(ii) In a batch reactor, since there is no inflow or outflow, the reactants
concentration reduces with time.
(iii) For an overall second order reaction (first order in both components) like
the one that was done in the lab, the reaction rate is also dependent on
the concentration of the reactants unlike a zero order reaction that is
independent of the concentrations of the reactants.
(iv) Conductivity of a solution reduces with time as the solution loses it ions
and become less conductive.
Nomenclature
Symbols Units Meaning
A Arrhenius parameter (pre-exponential factor)
CA M exit concentration of reactant ‘A’ in the exit stream
CA0 Minput concentration of ‘A’ in the
input stream
CB M concentration of reactant ‘B’ in the exit stream
Ea kJ/mol Arrhenius parameter (activation energy)
k M-1s-1 Reaction rate constant
k S/mConductivity of solution at various time intervals
k0 S/m initial conductivity at time t = 0
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k∞ S/m conductivity of the solution at
the end of reaction
mOrder of reaction of reactant
component ‘A’
nOrder of reaction of reactant
component ‘B’
T °C Reaction temperature
References:
Denbihh, K. G., and Turner, J. C. R. (1971) Chemical Reactor Theory. 2nd ed.
Cambridge: Cambridge University Press.
Fogler, H.S. (1999) Elements of Chemical Reaction Engineering. 3rd ed .New Jersey:
Prentice Hall.
Levenspiel, O. (1999) Chemical Reaction Engineering. 3rd ed. New York: John
Wiley & Sons, Inc.,
Missen, R. W., Charles, A. M. and Bradley, A. S (1999) Introduction to Chemical
Reaction Engineering and Kinetics. 3rd ed. New York: John Wiley & Sons, Inc.,
Smith, J.M. (1981) Chemical Engineering Kinetics. 3rd ed .New York: McGraw-Hill.
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