DEPARTMENT OF CHEMICAL ENGINEERING, INDIAN INSTITUTE OF TECHNOLOGY KANPUR
CHE 391 – Chemical Engineering Laboratory 1 Experiment Title: Batch Reactor
Experiment No: 15 Date of Experiment: 10/01/13 Date of Submission: 17/01/13 Group No.: 5 Roll No.
Name
10589
Ranvijay Kumar
10579
Rajkumar Singh
10583
Ramavtar Meena
TA Name: Mr. Vidyasagar Aragonda
Contents 1
1. Introduction Introd uction …………………………………………………………………………………………..
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2. Objec Objective tive ………………… ………………………… ……………… ……………… ………………… ………………… ……………… ……………… ……………… ………………… ………….. 3. Theory
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4. Apparatus Apparat us
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5. Experimental Experi mental Set-u Set-up p …………………………………………………………………………………... 6. Procedure Proced ure
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7. Observations Observat ions and Calculations Calculat ions 8. Results
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10. Sources Source s of Errors
………………..………………………………………………..……………….. ………………..……………………………………………….. ………………..
11. Questions Question s and Answers 12. Nomenclature Nomencla ture
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9. Error Analysis
13.Refrences 13.Refre nces
7
17 18
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19
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21
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2
Introduction
A batch reactor is used for small scale operations, for testing new processes that have not been fully developed, for the manufacture of expensive products like fertilizers and pharmaceuticals and for the processes that are difficult to convert to continuous processes. The reactor is charged via two holes in the top of the tank. While reaction is carried out, nothing else is put in or taken out until the reaction is done. The tank can be easily heated or cooled by jacket. Batch reactors provide more flexibility and control. They have the advantage of high conversions that can be obtained by leaving the reactants in the reactor for long periods of time. Moreover the capital costs involved in a batch reactor is often less than for corresponding continuous processes when the desired rate of production is low. In operations where rapid fouling or contamination of fermentation cultures is to be avoided, batch reactors are preferred as they permit necessary cleaning and sanitation procedures. However, the operating costs of a batch reactor are more as it involves repeated filling and emptying of batches and also it is difficult for large scale production.
Objective The objective of this experiment is to determine experientially the rate equation between ethyl acetate and sodium hydroxide.
Theory The saponification reaction between ethyl acetate and sodium hydroxide is represented as: CH3COOC2H5 + NaOH
CH3COONa + C2H5OH
For simplicity the reaction is represented as: A+B
C +D
Assuming that the reaction is reversible and second order in both the directions, the specific reaction rate for the batch operation is given by 3
r =
1 dN V dt
=
da dt
=
k 1 [a ][b]
Where a, b, c and d are concentrations of A, B, C and D respectively. V = volume of the reaction mixture N = moles of the ethyl acetate present in the reactor at time t. k 1 = rate constants. INTEGRAL APPROACH:If the concentrations of the reactants are equal ([a] = [b]) and the reverse reaction is neglected (k2 is very small). da dt
= −k 1a 2
or
db dt
= −k 1b 2
…… (3)
Integrating the above equation, we get:
t =
1
k 1
1
b
−
1
bo
......... (4)
Where time (“t”) required to reduce the concentration of B (NaoH) from b o to b. Thus, a plot of t vs. (1 / b) would yield a straight line from which k 1 can be estimated.
DIFFERENTIAL APPROACH Plotting log [-(d[b] / dt)] and log [b] would yield a straight line
− db = log k + 2 log b 1 dt
log
…… (5) And, again k1 can be calculated.
The energy required to pass the reactant to activated complex is known as energy of activation or the activation energy as shown in Fig. A+B X C+D Reactant Activated complex Product
4
Effect of catalyst on activation energy:-
ARRHENIUS EQUATION The Arrhenius equation gives the quantitative basis of the relationship between the activation energy and the rate at which a reaction proceeds. From the Arrhenius equation, the activation energy can be expressed as
5
Where A is the frequency factor for the reaction,
R
is the universal gas constant, and
T
is the
temperature (in kelvin). While this equation suggests that the activation energy is dependent on temperature, in regimes in which the Arrhenius equation is valid this is cancelled by the temperature dependence of k . Thus
E a
can be evaluated from the rate constant at any
temperature (within the validity of the Arrhenius equation)
Thus a plot of log (k 1) vs. (1/T) would yield a straight line, which enables evaluation of k 10 and E.
Apparatus 1) Reaction vessel (of 2 liters capacity). 2) Stirrer 3) Constant temperature bath. 4) Standard solutions of HCl and NaOH. 5) Phenolphthalein indicator. 6) Ethyl acetate (approximately 0.1N). 7) Sodium hydroxide (approximately 0.1N). 8) Stop watch/timer.
Experimental Setup
6
Figure 1 Schematic of the apparatus used in the experiment
The setup consisted of a constant temperature bath filled with water provided with a heater and a stirrer to maintain uniform temperature in the b ath. A reactor vessel was at the centre of the bath which was also provided with a stirrer so that concentration and temperature of the reacting mixture was uniform. Both the stirrers were connected to two variacs which could be used to change the stirrer speeds. Two thermocouples were placed in the bath and the reactor vessel which measured their temperatures. The temperature of the bath was controlled by a temperature controller which switched off the heater if the temperature crossed the set point.
PROCEDURE
•
Preparation of standard HCl solution: A 500 ml solution of 0.1 N HCl was prepared. This solution is further used for two purpose: Standardization of NaoH solution. o Neutralization of NaoH present in reaction mixture at different time o intervals.
•
Standardization of NaoH: To standardize it, NaoH is titrated with 10 ml of prepared HCl solution. Normality of NaoH is given as 0.338.
•
Sample Analysis
7
Temperature for the first reading is taken to be 40 0C and reaction is carried out at this temperature. User sets the set point at 40 0C After Set point is achieved, NaoH (1000ml) and ethyl acetate (1000 ml) were mixed in o reactor and the solution was stirred aptly and time was observed with the help of stop watch. To take the Sample of reaction mixture, stirrer was stopped and sample is taken out after which again stirrer is set in motion along with stopwatch. Eight different samples were prepared for taking readings at different time intervals. Each o conical flask contains 10 ml of 0.1 N HCl solution along with indicator and each sample is used to titrate with reaction mixture for one particular time interval so that amount of HCl unreacted can be calculated. From which amount of NaoH present in the Reaction mixture can be calculated. o All the steps which have been mentioned above, are repeated for different set points of 300C and 210C For every titration 1-2 drops of Phenolphthalein indicator is used. o
•
Observation and Calculation
Standardization of NaOH
Gram Equivalent Balance Number of Equivalents in HCL= Number of Equivalents of NaOH by Titration+ Number of Equivalents of NaOH in Reaction Mixture N HCl V HCl
= N NaOH V NaOH + N RV R
NHCL VHCL = NT VT + NR VR NHCL=0.0284N, VHCL =10 ml N T (Concentration of NaOH Titrate) =0.0338N, V T =Volume of Titrate NaOH used VR = Volume Of Reaction mixture used= 5 ml NR= Concentration of NaOH in reaction mixture at a given time NR= (NHCL VHCL - NT VT) /10 NR = (.029*10 – 0.0338* V T)/5 =0.058-0.00676 V T Concentration of NaOH: b= NR
Observations at bath temperature = 40°C
S.N O
Time (min)
ml of 0.0338 N NaOH
Unreacted NaOH (b) (mol / l)
1/b (l/mol )
b avg (mol/l)
(-db/dt) mol/l.min /(10000)
log(bavg)
Log(db/dt) 8
used 1
1
8.3
0.001892
528.541
0.002535
1.2600
-2.5960
-3.8996
2
2
8.3
0.001892
528.541
0.002409
1.1974
-2.6182
-3.9217
3
3
8.0
0.00392
255.102
0.002289
1.1378
-2.6404
-3.9439
4
4
8.3
0.001892
528.541
0.002175
1.0813
-2.6625
-3.9660
5
5
8.1
0.003244
308.261
0.002067
1.0275
-2.6847
-3.9882
6
6
8.3
0.001892
528.541
0.001964
0.9764
-2.7069
-4.0103
7
11
8.3
0.001892
528.541
0.00169
0.7566
-2.7721
-4.1212
8
16
8.5
0.000541
1848.428
0.00131
0.5863
-2.8827
-4.2319
9
21
8.7
0.000812
1231.527
0.00102
0.4543
-2.9913
-4.3426
10
26
8.7
0.000812
1231.527
0.000786
0.3521
-3.1045
-4.4533
11
31
8.4
0.000675
1481.851
0.000609
0.2728
-3.2153
-4.5641
Table 1. Tabulation of experimental data and Calculation of Different Variables for T=313K
Fig 1. Graph Between Conc. Of Rxn Mix. Vs Time at T=313K
b= .0026*exp (-0.051*t);
Integral approach: 9
Fig: -2 Graph between 1/Conc. Of Rxn Mixture Vs Time at T=313K By
linear regression we get t= 0.016(1/b) -1.5951 1/k= 0.016 k=62.5
(l/mol.min )
Differential approach :
Linear regression gives log(-db/dt)=1.0949*log(b avg) -1.0581 10
k=0.088 l/mol.min Observations at bath temperature = 30°C ml of 0.0338 N NaOH Used
Unreacted NaOH (b) (mol / l)
1/b (l/mol )
b avg (mol/l)
(-db/dt) mol/l.min /(10000)
log(bavg)
Log(db/dt)
6.5
0.01406
71.1237
0.01315
2.9894
-1.8811
-3.5244
2
6.6
0.013384
74.7160
0.01285
2.9214
-1.8911
-3.5344
3
3
6.9
0.011356
88.0599
0.01256
2.8550
-1.9010
-3.5444
4
4
7.0
0.01068
93.6329
0.01227
2.7901
-1.9112
-3.5544
5
5
7.1
0.010004
99.6015
0.01199
2.7266
-1.9212
-3.5644
6
6
6.8
0.012032
83.1117
0.01172
2.6646
-1.9311
-3.5743
7
11
6.1
0.016764
59.7376
0.01094
2.3752
-1.9609
-3.6243
8
16
0.007976
125.3761
0.00975 6
2.1171
-2.0107
-3.6743
9
21
7.5
0.0073
136.9863
0.00869
1.8871
-2.0609
-3.7242
10
26
7.7
0.005948
168.1237
0.00775
1.6821
-2.11069
-3.7741
11
31
7.4
0.007976
125.376
0.00691
1.4994
-2.1605
-3.8241
S.N O
Time (min)
1
1
2
7.4
Table 1. Tabulation of experimental data and Calculation of Different Variables for T=313K
Integral approach: 11
By
linear regression we get t= 0.2554(1/b) -14.682 1/k= 0.2554 k=3.92
(l/mol.min )
Differential approach:
12
Linear regression gives log(-db/dt)= 1.0928*log(b avg) -1.4691 k=0.339 l/mol.min Observations at bath temperature = 21°C
S.N O
Time (min)
ml of 0.0338 N NaOH used
1
1
6.4
0.014736
67.8610
0.01308
2.3336
-1.8834
-3.6319
2
2
6.7
0.012708
78.6905
0.01285
2.2919
-1.8910
-3.6398
3
3
6.8
0.012032
83.1117
0.01262
2.2510
-1.8989
-3.6476
4
4
6.8
0.012032
83.1117
0.01239
2.2109
-1.9069
-3.6554
5
5
6.9
0.011356
88.059
0.01217
2.1715
-1.9147
-3.6632
6
6
6.7
0.012708
78.6905
0.01196
2.1327
-1.9223
-3.6710
7
11
7.0
0.01068
93.6329
0.01133
1.9491
-1.9457
-3.7101
8
16
7.2
0.009328
107.2041
0.01036
1.7814
-1.9846
-3.7492
9
21
7.3
0.008652
115.5802
0.00946 5
1.6281
10
26
7.3
0.008652
115.5802
0.00865
1.4879
-2.0629
-3.8274
11
31
7.4
0.007976
125.3761
0.00790
1.3599
-2.1021
-3.8664
Unreacted NaOH (b) (mol / l)
1/b (l/mol )
b avg (mol/l)
(-db/dt) mol/l.min /(10000)
Log(db/dt)
log(bavg)
-2.0238
-3.7883
13
5 Table 3. Tabulation of experimental data and Calculation of Different Variables for T=294K
Integral approach:
14
Fig: - Graph between 1/Conc. Of Rxn Mixture vs. Time at T=294K By
linear regression we get t= 0.542(1/b) -39.685 1/k= 0.542 k=1.844
(l/mol.min )
Differential approach:
Linear regression gives log(-db/dt)= 1.0927*log(b avg) -1.5744 k=0.0266 l/mol.min
Calculation of activation energy:
Average reaction temperature( K)
k (l/mol/min)
1/T
ln (K diff)
ln (K int)
Diff
Int.
313
0.08 8
62.5
0.003 2
-2.4304
4.135
303
0.03 39
3.92
0.003 3
-3.3843
1.366
294
0.02 66
1.84 4
0.003 4
-3.626
0.611
15
Table 4. Tabulation of values of K by two different approaches for different temperatures
The values of ln K obtained from the rate equation using integral and differential analysis varies linearly with 1/T as per the Arrhenius Equation. The slope of the plot is equal to -E/R and hence will give the value of activation energy. Differential Approach
From linear regression we get ln k= -5978/T +16.581 Slope = -Ea / R = -5978 Ea= 49 KJ/mol. Intercept = ln A =16.581 A= 1.589E7 lt/mol.min 16
Integral Approach
ln k= -17620/T + 60.183 Slope = -Ea / R = -17620 Ea= 144.48 KJ/mol. Intercept = ln A =60.183 A= 1.37*E26 lt/mol.min
Result Rate Expression for saponification of Ethyl acetate Using Differential Approach r == 1.589E7 *exp (-49/(R*T)) b^2 mol/L.min Using Integral Approach r == 1.37E26 *exp (-144.48/(R*T)) b^2 mol/L.min
ERROR ANALYSIS Least Count of burette used = 0.2ml Least Count of measuring cylinder used = 0.2ml Least Count of stop watch used = 0.1 sec Error in determining rate constants Calculation done for reading at t = 11 min and T bath= 30oC: Differential Method
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-db/dt = k1.b^2 Δk1/k1 = Δ (-db/dt)/ (-db/dt) + 2Δb/b Δ (-db/dt)/ (-db/dt) = Δb/b Δk1/k1 = 3*Δb/b = 3* 0.00001/0.005364= 0.000186 % error = 0.02% Integral Method
t = 1/k1 [1/b – 1/b0] k1 = 1/t [1/b – 1/b0] Δk1/k1 = Δb/b + Δt/t = 0.0002+ 0.1/60 = 0.017 % error = 1.7 %
Standard Deviation Table : Standard Deviation for K at 30oC
S.No
(db/dt)/10000
-2*log(b avg)
K (mol/l.min)
(K - )^2
mol/l.min 1
-3.5244
3.7622
1.7290
0.1767
2
-3.5344
3.7822
1.7690
0.1447
3
-3.5444
3.8020
1.8096
.0.1155
4
-3.5544
3.8224
1.8535
0.0876
5
-3.5644
3.8424
1.8967
0.0639
6
-3.5743
3.8622
1.9404
0.0437
7
-3.6243
3.9218
1.9838
0.0274
8
-3.6743
4.0214
2.2238
0.0055
9
-3.7242
4.1218
2.4980
0.1215
10
-3.7741
4.2214
2.8009
0.4245 18
11
-3.8241
4.3210
3.1397
0.9807
Standard deviation can be calculated from following formula:
So S.D =0.4556 95 % confidence limit = 1.9599 * S.D = 0.8930 So % error calculated by this method is = 0.8930/2.1494 *100 =41 % This Error is quite high than what we calculated previously because there is possibility of human errors while doing titrations, counting time and measuring volumes.
Sources of Error
1) In preparing the 0.1 N HCL solutions regarding the quantity of HCL cannot be exact. 2) As this experiment involves a lot of titrations for a large number of times, error in observing the burette reading (reading of upper and lower meniscus) is a common one.
3) Stopwatch is used for measuring the time between two observations. It is a very frequently done so there is human error that may be the time at which reaction mixture is taken out is different from the time at which stopwatch is stopped. 4) One basic assumption of this whole experiment which introduces a large amount of error is the assumption of isothermal operations. All data and calculations are done keeping in mind the isothermal nature of reactor which is in anyway not true.
5) Observer has assumed that at every time the volume of reaction mixture is constant which is not true in any case as for every observation, he is taking out some amount of reaction mixture for calculating the extent of reaction. 6) The rate of stirrer motion is changed sometimes which also introduces some minor error in the data. 7) Keep a note of the equivalence point in the titration. Excess NaoH should not be used otherwise it give a dark pinkish color with severe errors in the reading.
Questions and Answers 19
Ques 1.
Set up the equations and show how you will
calcualte the constants if the concentrations a and b are not equal. The saponification reaction between ethyl acetate and sodium hydroxide is represented as: CH3COOC 2H5 + NaOH
CH3COONa + C2H5OH
Rate expression for the above rxn is -r A = k 1ab……………………… (1)
bo = Initial Concentration of Sodium Hydroxide(B) in the reaction mixture (mol/lit) ao = Initial Concentration of ethyl acetate (A ) in the reaction mixture (mol/lit) a = ao (1 – XA) b = bo (1- XB) XA = Conversion of Ethyl Acetate (A) XB = Conversion of Sodium Hydroxide (B) b = bo – bo*XB = bo – ao*XA Since bo*XB = ao*XA
-r A = K 1*ao( 1 – X A)( bo – ao*XA ) This eqn in differential form can be written as -da/dt = K 1 a*2(1 – XA)(M – XA) Where: M =bo/ao
Ques 2. Can you use this type of reactor for determining rate of reaction of a: (i) Heterogeneous reaction: We can use this type of reactor (batch) for determining rate of reaction of a heterogeneous reaction only if gas phase is not present. Additional equipment to measure the vapor pressure of the gas (if present) periodically is required. (ii) Rapid Reaction: A mechanized setup would be necessary for a rapid reaction because the reaction will cease quickly and to remove samples of the mixture (say at intervals of 10 seconds) manually during the reaction would not be feasible. (iii) Reaction yielding a number of products: We can use this for multi-product case because we can find out concentrations of various reactants at different times by just measuring the concentration of one of them.
20
(iv) Gas Phase reactions: We can use this method for gas-phase reactions by calculating vapor pressures and use them in calculating the concentration of different components of the mixture.
Additionally, the vessel is to be sealed to avoid leakage of gases. Also, pressure measuring equipment is required to determine the kinetics of a gas phase reaction. (v) In case you can use this type of reactor, mention additional equipment needed. Otherwise point out the difficulties which make it impractical to be used in a particular case.
The answers for this question have been provided in the above answer itself. To add a few points, (1) High operating cost for a gas phase reaction (2) A mechanized setup would not give a feel of the experiment to the observer.
(vi)Write down the drawbacks of this method of finding kinetics.
Drawbacks o this method for finding kinetics are: 1) The fluctuation of temperature was ver y much. This would affect the value of rate constant. 2) The reactor vessel was open to atmosphere due to which there were energy losses & also this will delay the time taken to attain a desired temperature. 3) The method of taking the reaction mixture out using pipette is tedious & time-consuming. 4) The method can not be extended to include heterogeneous and fast reactions.
(vii) Suggest improvements in the experimental setup if you come across any drawbacks and shortcomings.
1) The reaction mixture does not attain the temperature of the bath (the set value) immediately and this results in some error which is more significant for faster reactions(higher temperatures). The reactants must be heated separately to the set value before putting them in the batch reactor.
2) Another source of error is from drawing the 10ml samples from the reactor periodically. A dropper which sucks out exactly 10ml each time should be designed and implemented.
Nomenclature k 1
= rate constant for the forward and backward reaction respectively.
V
= volume of the reaction mixture, ( m 3 ).
21
N
= moles of ethyl acetate present in the reactor at time t, (moles).
r
= rate of reaction.
a, b, c and d
= concentrations of A,B,C and D respectively , ( moles / liter ) .
A, B, C and D = represents CH3COOC 2H5, NaOH, CH3COONa and C2H5OH respectively. T
= time, (s).
bo
= initial concentration of CH 3COOC 2H5 or NaOH , ( moles / liter ).
K 10
= pre-exponential factor or frequency factor.
Ea
= activation energy, J/mol or cal/mol.
R
= universal gas constant, J/mol or cal/mol.
T
= absolute temperature, k
bo
= Initial Concentration of Sodium Hydroxide(B) in the reaction mixture (mol/lit)
ao
= Initial Concentration of ethyl acetate (A ) in the reaction mixture (mol/lit)
XA
= Conversion of Ethyl Acetate (A)
XB
= Conversion of Sodium Hydroxide (B)
References
[1] Fogler H. Scott ; Elements of Chemical Reaction Engineering , printice hall of India private limited III Edition , New Delhi. [2] Levenspiel, O; Chemical Reaction Engineering, Wiley Eastern, 2nd Edition, New Delhi, 1999. [3] Smith J.M.; Chemical Engineering Kinetics, McGraw Hill Book Co.3rd Edition, New York, 1981.
[4] Unit operations lab manual.
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