Batch Reactor
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Abstract In this experiment, the change of NaOH concentration and conductivity is observed. Using the “integral method” of analysis, the reaction is found to be a second order reaction. The experimental value of the activation energy is determined as well. According to authentic theoretical sources; the values of the rate constant & activation energy were relatively inaccurate, where for example the experimental reaction rate constant was found to be 0.229 L/mol.s at 25 ºC, where the theoretical value is equal to 0.111 L/mol.s at 25 ºC. At the end of the report, discussion about the calculation was written in addition to some recommendations.
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Contents Objective .................................................. ....................................................................................... 1 Introduction &Theory ................................................ ..................................................................... 1 Apparatus & Experimental Setup .............................................................................................. ..... 3 Apparatus .................................................. .............................................................................. 3 Procedure ................................................................................................................................ 4 Safety consideration:.................................................. ..................................................................... 4 Experimental Data .......................................................................................................................... 6 Calculations..................................................................................................................................... 7 Reaction Taking Place ............................................................................... ................................. 7 Concentration from Conductivity Measurements ............................................... ........................ 7 Steady State Concentration .................................................. ................................................... 7 Discussion ................................................ ..................................................................................... 13 Conclusion .................................................................................................................................... 13 Recommendations ............................................. ............................................................................ 14 References ................................................ ..................................................................................... 15
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List of Figures Figure 1: Chemical reactors apparatus flow diagram ................................................................ ..... 3 Figure 2: Concentration vs. Time at 25 ºC...................................................................... ................ 9 Figure 3: Concentration vs. Time at 30 ºC...................................................................... ................ 9 Figure 4: Concentration vs. Time at 35 ºC...................................................................... ................ 9 Figure 5: Concentration vs. Time at 25 ºC, 30 ºC and 35 ºC ................................................... ..... 10 Figure 6: 1/Concentration vs. Time at 25 ºC ................................................................................ 10 Figure 7: 1/Concentration vs. Time at 30 ºC ................................................................................ 11 Figure 8: 1/Concentration vs. Time at 35 ºC ................................................................................ 11 Figure 9: ln(K) vs. temperature..................................................................................................... 12
List of Tables Table 1: Experimental raw data collected....................................................................................... 6 Table 2: Initial and final conductivity at different temperatures. ................................... ................ 7 Table 3: Sodium hydroxide concentration at different temperatures and time interval. ................ 8
III
Objective The aim of this experiment is to determine the order, rate constant, frequency factor, and activation energy of the reaction between sodium hydroxide and ethyl acetate.
Introduction &Theory In a batch reactor the reactants and the catalyst are placed in a container, are well mixed, which is then closed to transport of matter and the reaction is allowed to proceed for a given time. Then the mixture of un-reacted material together with the products is withdrawn. This is an unsteady state operation where composition changes with time; however at any instant the composition throughout the reactor is uniform. A batch reactor can be used to find the reaction rate constant, activation energy and order of the reaction. The use of a batch reactor for the most part eliminates the effects due to fluid flow on the resulting reaction rates. Consequently, the data reflect the intrinsic kinetics for the reaction being investigated. A batch reactor can also be used to demonstrate the mechanism of a chemical reaction and the effects of the operative conditions, such as reaction temperature, concentration, and stirring rate on reaction rate in isothermal and adiabatic conditions. Isothermal condition requires a water chiller or cold tap water in case of exothermic reactions. The reaction chosen is the hydrolysis of ethyl acetate by sodium hydroxide (saponification); this reaction can be carried out under safe conditions of temperature and pressure, and it is well documented in the literature. CH 3 COOC 2 H 5 NaOH CH 3 COONa C 2 H 5 OH EtAc
NaOH
NaAc
EtOH
Ethyl acetate sodium hydroxide sodium acetate ethanol As the reaction proceeds, hydroxyl ions are consumed and acetate ions are produced. Both sodium hydroxide and sodium acetate contribute conductance to the reaction solution, whereas ethyl acetate and ethyl alcohol do not. Hydroxyl ion has a very much larger specific conductance than acetate ion. Hence, the alkaline hydrolysis of ethyl acetate may be monitored by following the change in the conductance of the reaction mixture with time. By 1
determination of the conductivity and hence concentration as a function of time, order of reaction and hence the rate constant is found. If the reaction is carried out at different temperatures, the activation energy can also be found. The following correlations allow calculating the concentration of NaOH, using the measured conductivity, and then the conversion. At infinite time (Assuming 100% conversion)
c NaAc c EtAc
if c inEtAc c inNaOH
c NaAc c inNaOH
if c inEtAc c inNaOH
in
c NaOH c NaOH c EtAc in
in
if c inEtAc c inNaOH , then
The following correlations allow calculating the conversion at t ime t:
c NaOH c NaOH t 0 t
c NaOH c NaOH 0
X A
0
Where
t
0
c NaOH t
:
Conductivity of reaction mixture at time t
o:
Conductivity of reaction mixture at time t=0 :
Conductivity of reaction mixture at time t= (Assuming 100% conversion)
The conductivity (Siemens/cm) is correlated with concentration of the species and the temperature by the following equations: c=0.070*[1 + 0.0284(T – 294)]Cco
for T 294for
NaOH =0.195*[1 + 0.0184(T – 294)]CAo
for T 294
NaOH 0
0 (Assumes c NaAc 0 )
2
NaOH NaAc
Apparatus & Experimental Setup Apparatus The reactor is provided of a base to be located on the service unit, and it is vacuum insulated on the walls and the bottom. Inside the reactor, a stainless steel coil provides the heat transfer surface for either heating or cooling the reactant chemicals. If heating is being carried out, the coil connectors are connected to the supply and return flexible tubing of the hot water circulator, which is incorporated in the service unit. If cooling is required, the flexible tubes can be connected with a chiller or tap water. A turbine agitator works to provide efficient mixing and heat transfer. The agitator is driven by an electric motor mounted on the head of the reactor, and the motor is driven by a variable speed unit in the service bench and is connected electrically to this by plug. The socket for the plug is on the switchboard of the service unit. The connections in the reactor head are to house the conductivity and temperature probes, which are supplied with the service unit. The larger of the two is for the conductivity probe. The smaller is unscrewed by hand, the temperature probes inserted and then retightened by hand.
Figure 1: Chemical reactors apparatus flow diagram
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Procedure Preparations of chemicals required for experiments (Reactants) have been done: o
2 liters of 0.05 M Ethyl Acetate This should be made by diluting concentrated (10 M, available in lab) ethyl acetate as follows:
Volume of concentrate = Molwt 0.1
1
88 .11 0.05
Density
0.90
4.9 ml/liter of solution.
Ethyl acetate solution required for 2 liters = 4.9 2 9.8 ml. Add 9.8 ml ethyl acetate in 1.5 liter of distilled water. Shake the mixture vigorously until the two liquids have mixed. Add further water to make up the final volume to 2 liter. o
0.05 M Sodium Hydroxide
Mass of NaOH required for 0.05 molar NaOH solution=0.05x40=2g/liter. For experiment 2 liter of 0.05 M NaOH 4gm is required. This may be prepared by adding 4 g of NaOH to 1.5 liter distilled water then making up the solution to 2 liter.
Fill the reactor with 0.5 liter of 0.05 M ethyl acetate.
Start the hot water circulator and wait till the desired temperature (25 C) is reached.
Pour the 0.05 M sodium hydroxide in the reactor (use the stopper on the lid).
0
Start the stirrer at 50% of the speed, and at the same time, start taking the data with a sampling time of 10 sec for 5 minutes.
Drain the reactor and repeat the experiment at 30°C and 35°C.
Safety consideration:
Dissolution of sodium hydroxide is highly exothermic and resulting heat may cause heat burn and ignite flammable. So, don’t dissolve large quantity (above 10 g) in small volume of water because solution will be highly concentrated and will liberate high amount of heat.
Ethyl acetate is very flammable. Make sure that there is no source of ignition near where you work. The vapor may be ignited by contact with a hot plate or hot water pipe. You must wear hand gloves and safety glasses while preparing ethyl acetate solution. 4
Prepare chemicals and operate the equipment in well-ventilated area.
Only used chemicals specified in the equipment’s manual and in the concentration instructed [1].
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Experimental Data The following data represents the conductivity at different time intervals for a batch o o o reactor at using three different reactor temperatures: 25 C, 30 C and 35 C. Table 1: Experimental raw data collected.
Temperature: 25°C Temperature: 30°C Temperature: 35°C Time Conductivity Time Conductivity Time Conductivity Λ Λ Λ t t t s mS/cm s mS/cm s mS/cm 10 4.35 10 4.58 10 4.4 20 4.3 20 4.45 20 4.23 30 4.2 30 4.34 30 4.12 40 4.18 40 4.25 40 4 50 4.11 50 4.15 50 3.9 60 4.05 60 4.07 60 3.81 70 3.98 70 4 70 3.71 80 3.91 80 3.91 80 3.63 90 3.86 90 3.82 90 3.56 100 3.81 100 3.76 100 3.48 110 3.76 110 3.7 110 3.42 120 3.71 120 3.63 120 3.35 140 3.58 140 3.5 140 3.23 160 3.51 160 3.41 160 3.14 180 3.44 180 3.33 180 3.05 200 3.38 200 3.25 200 2.98 220 3.31 220 3.17 220 2.91 240 3.25 240 3.11 240 2.85 260 3.2 260 3.06 260 2.8 280 3.15 280 3 280 2.75 300 3.11 300 2.95 300 2.7 320 3.06 320 2.91 320 2.66 340 3.02 340 2.86 340 2.62 360 2.98 360 2.83 360 2.59 380 2.94 380 2.79 380 2.56 400 2.91 400 2.75 400 2.53 420 2.87 420 2.72 420 2.5 440 2.84 440 2.69 440 2.47 460 2.81 460 2.66 460 2.5 480 2.78 480 2.63 480 2.42 500 2.75 500 2.6 500 2.4 520 2.73 520 2.58 520 2.38 540 2.7 540 2.56 540 2.36 560 2.68 560 2.53 560 2.34 580 2.66 580 2.51 580 2.32 600 2.64 600 2.49 600 2.31
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Calculations Reaction Taking Place Sodium hydroxide + Ethyl acetate Sodium acetate + Ethyl alcohol NaOH CH 3CooC 2 H 5 CH 3COONa C 2 H 5 OH
A+BC+D Concentration from Conductivity Measurements Sodium hydroxide (reactant) and sodium acetate (product) being ionic compounds contribute conductance to the reaction solution, whereas ethyl acetate and ethyl alcohol do not. The conductivity of a sodium hydroxide solution at a given concentration and temperature, however, is not the same as that of a sodium acetate solution at the same molarity and temperature, and a relationship has been established allowing conversion to be inferred from conductivity.
1. Determining the initial and final conductivity at the different temperatures:
0 0.195 1 0.0184 T 294 C A0
0.07 1 0.0184 T 294 C A0 The results can be represented in the following table: Table 2: Initial and final conductivity at different temperatures.
T = 25 °C T = 30 °C T = 35 °C Λ0
Λ0
Λ0
mS/cm 5.2338
mS/cm 5.6823
mS/cm 6.1308
Λ∞
Λ∞
Λ∞
mS/cm 1.9488
mS/cm 2.1973
mS/cm 2.4458
Steady State Concentration As the reaction proceeds sodium hydroxide concentration will be go down and sodium acetate will start forming. Progress of reaction can be monitored by measurement of conductivity contributed by unconsumed sodium hydroxide and formed sodium acetate after reaction. Since conductivity changes linearly with concentration, relation between concentration and conductivity can be derived as follows. C A C A0
0
7
------------ (10)
Where:
= Measured Conductivity (mSiemens/cm), at steady state
o
= Initial conductivity, i.e conductivity of pure NaOH
= Conductivity after 100% conversion, i.e conductivity of CH 3COONa 2. Calculating the concentration of sodium hydroxide using the concentration-conductivity relation at the three different temperatures: C A
C A0 C A
0
C A0 0
The results are summarized in the Table 3, for an initial concentration of 0.025 mol/L: Table 3: Sodium hydroxide concentration at different temperatures and time interval. Temperature : 25°C
Temperature : 30°C
Temperature: 35°C
Time Conductivity Concentration Time Conductivity Concentration Time Conductivity Concentration t s 10 20
mS/cm
CA mol/L
t s
4.35
0.018
10
4.3
0.018
20
Λ
mS/cm
CA mol/L
t s
mS/cm
CA mol/L
4.58
0.017
10
4.4
0.01326
4.45
0.016
20
4.23
0.01210 0.01136
Λ
Λ
30
4.2
0.017
30
4.34
0.015
30
4.12
40
4.18
0.017
40
4.25
0.015
40
4
0.01054
50
4.11
0.016
50
4.15
0.014
50
3.9
0.00987
60
4.05
0.016
60
4.07
0.013
60
3.81
0.00926
70
3.98
0.015
70
4
0.013
70
3.71
0.00858
80
3.91
0.015
80
3.91
0.012
80
3.63
0.00803
90
3.86
0.015
90
3.82
0.012
90
3.56
0.00756
100
3.81
0.014
100
3.76
0.011
100
3.48
0.00702
110
3.76
0.014
110
3.7
0.011
110
3.42
0.00661
120
3.71
0.013
120
3.63
0.010
120
3.35
0.00613
140
3.58
0.012
140
3.5
0.009
140
3.23
0.00532
160
3.51
0.012
160
3.41
0.009
160
3.14
0.00471
180
3.44
0.011
180
3.33
0.008
180
3.05
0.00410
200
3.38
0.011
200
3.25
0.008
200
2.98
0.00362
220
3.31
0.010
220
3.17
0.007
220
2.91
0.00315
240
3.25
0.010
240
3.11
0.007
240
2.85
0.00274
260
3.2
0.010
260
3.06
0.006
260
2.8
0.00240
280
3.15
0.009
280
3
0.006
280
2.75
0.00206
300
3.11
0.009
300
2.95
0.005
300
2.7
0.00172
320
3.06
0.008
320
2.91
0.005
320
2.66
0.00145
340
3.02
0.008
340
2.86
0.005
340
2.62
0.00118
360
2.98
0.008
360
2.83
0.005
360
2.59
0.00098
380
2.94
0.008
380
2.79
0.004
380
2.56
0.00077
400
2.91
0.007
400
2.75
0.004
400
2.53
0.00057
420
2.87
0.007
420
2.72
0.004
420
2.5
0.00037
440
2.84
0.007
440
2.69
0.004
440
2.47
0.00016
460
2.81
0.007
460
2.66
0.003
460
2.44
-0.00004
480
2.78
0.006
480
2.63
0.003
480
2.42
-0.00018
500
2.75
0.006
500
2.6
0.003
500
2.4
-0.00031
520
2.73
0.006
520
2.58
0.003
520
2.38
-0.00045
540
2.7
0.006
540
2.56
0.003
540
2.36
-0.00058
560
2.68
0.006
560
2.53
0.002
560
2.34
-0.00072
580
2.66
0.005
580
2.51
0.002
580
2.32
-0.00085
600
2.64
0.005
600
2.49
0.002
600
2.31
-0.00092
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3. Plotting the concentration versus the time: 0.020 0.018 ) L 0.016 / l o 0.014 m ( n 0.012 o i t 0.010 a r t 0.008 n e 0.006 c n o 0.004 C 0.002 0.000 0
100
200
300
400
500
600
700
400
500
600
700
500
600
700
Time(s)
Figure 2: Concentration vs. Time at 25 ºC
0.018 0.016
) L / 0.014 l o m0.012 ( n 0.010 o i t a 0.008 r t n 0.006 e c n 0.004 o C
0.002
0.000 0
100
200
300 Time(s)
Figure 3: Concentration vs. Time at 30 ºC
0.01400 0.01200
) L / 0.01000 l o m ( 0.00800 n o i t 0.00600 a r t n 0.00400 e c n 0.00200 o C
0.00000
-0.00200 0
100
200
300
400 Time(s)
Figure 4: Concentration vs. Time at 35 ºC
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Summing the three graphs in one: 0.020
0.015 ) L / l o m 0.010 ( n o i t a r t n e 0.005 c n o C
concentration at 25 C concentration at 30 C concentration at 35 C
0.000 0
100
200
-0.005
300
400
500
600
700
Time(s)
Figure 5: Concentration vs. Time at 2 5 ºC, 30 ºC and 35 ºC
4. Using the integral method to find the rate order of the reaction at different temperatures: 200.000 180.000
y = 0.229x + 47.971 R² = 0.9969
) L 160.000 / l o 140.000 m ( n 120.000 o i t a 100.000 r t n 80.000 e c n o 60.000 C / 40.000 1
20.000 0.000 0
100
200
300
400 Time(s)
Figure 6: 1/Concentration vs. Time at 25 ºC
10
500
600
700
600.000 y = 0.6415x + 20.632 R² = 0.9572
) 500.000 L / l o m400.000 ( n o i t a 300.000 r t n e c n 200.000 o C / 1 100.000
0.000 0
100
200
300
400
500
600
700
600
700
Time(s)
Figure 7: 1/Concentration vs. Time at 30 ºC
10,000.000 5,000.000 ) L 0.000 / l o m ( -5,000.000 n o i t a -10,000.000 r t n e c -15,000.000 n o C / -20,000.000 1
0
100
200
300
400
500
-25,000.000 -30,000.000
Time(s)
Figure 8: 1/Concentration vs. Time at 35 ºC
The plot of the inverse of the concentration versus time determines the rate of the reaction. o o The plot at a temperature of 25 C and 30 C shows a straight positive slope, which gives it the characteristics of the second order reaction as shown in the following equation: 1
Ca
= kt +
1
Cao
o
The third plot of 35 C, showed unreasonable results, thus it was neglected in the calculation. 5. The pre-exponential factor (E/R.T) can be determine by plotting Ln(k) versus 1/T, as shown in the following equation: 11
K (T ) A e
E / RT
Ln[ K (T )] Ln[ A]
E R T
k T 1/T ln k L/mol.s K 1/K 0.229 -1.474033275 298.15 0.003354016 0.6415 -0.443946095 303.15 0.003298697 By plotting Ln(K) vs. the temperature(T), the slop would represent(-E/RT) and the intercept gives the pre-exponential factor(A): 3.29E-03 0
3.30E-03
3.31E-03
3.32E-03
3.33E-03
3.34E-03
3.35E-03
3.36E-03
-0.2 -0.4 -0.6 ] K [ n -0.8 L
-1
y = -18621x + 60.98
-1.2 -1.4 -1.6
[1/T]
Figure 9: ln(K) vs. temperature
Slope(m) 18621
E R
18621 E 18621 R 18621 8.314 154814.994
Intercept (c) 60 .98 Ln[ A] A 3.0428 10
26
12
J mol
Discussion Through this experiment, the reaction between sodium hydroxide and ethyl acetate was analyzed in order to improve understanding and gain hands-on experience in reaction engineering in general and batch reactors in specific. Both ethyl acetate and ethyl alcohol are none conductive. On the other hand, sodium hydroxide and sodium acetate are conductive, sodium hydroxide is a stronger ionic compound than sodium acetate and as a result, it has higher conductivity. From these relations, the decrease in conductivity that occur as the reaction proceeds also indicate a decrease in sodium hydroxide concentration and an increment in sodium acetate concentration. Since sodium hydroxide is being consumed over time, its concentration decline with time as can be observed in Figure 2, Figure 3 and Figure 4. After that, Figure 5 was generated in such it combines the concentration vs. time for the three temperatures of study. Figure 6, clearly indicate that the reaction is accelerated with higher temperature; that is the reaction rate increases with increasing temperature, where higher conversion rates are achieved at equal time intervals. From Figure 6 and Figure 7, using the integral method we can conclude that the overall reaction rate is second order. Nevertheless, the experiment showed inaccurate results at 35 o C, as a result Figure 8 and its data were neglected in calculations. Furthermore, the calculated reaction rate constant and activation energy did not match for any of the used temperatures; this is mainly due to the lack of accuracy in reporting the conductivity probe measurements. In Figure 9, the natural logarithm of the reaction rate constant was drawn against the reciprocal of temperature. The obtained line clarify the inverse proportional relationship between ln(k) and (1/T), which confirm that increasing the reaction temperature results in an increase in the reaction rate constant. The error % that resulted at the end of the calculations was found to be relatively high. This is a result of human error factor and inaccurate temperature control.
Conclusion The following points were the main conclusions from this experiment:
Sodium hydroxide reacts with ethyl acetate to form sodium acetate and ethyl alcohol; as a result, the concentration of sodium hydroxide was reported to decrease with time.
Sodium hydroxide has higher conductivity that any present chemical in the system, hence to find the concentration change with time, conductivity was the measured parameter.
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It was noted that the concentration-time curve slope change with time, where the curve becomes less steep at the final stage, due to the decrease in reagents concentrations.
The reaction rate increases with increasing temperature, hence higher conversions are achieved for higher temperatures at equal time intervals.
The reaction rate was found to be second order, which confirms literature studies on the reaction.
ln k and 1/T are inversely proportional, since the reaction rate constant increases with increasing temperature.
Batch reactors are used to determine the rate law and activation energy, by measuring concentration as function of time. And then a procedure of calculations steps is followed to find, valuable reaction parameters.
High error percentage was reported when comparing literature reaction rate constant values with those obtained from the experiment. Sources of such error are: Human factor. Imprecise temperature control.
Recommendations In order to, obtain accurate results and save effort. We recommend to, link the conductivity probe with a PC computer that reads and save data continuously with higher accuracy and precision. Furthermore, to stay within a small temperature range, we recommend improving the reactor temperature control system, by replacing the ON/OFF controller with PI or PID controller.
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References [1] M.H. Arshad, Manual: Chemical Engineering Laboratory III Reaction Engineering and Process control Lab, in: Q. University, C.o. Engineering, D.o.C. Engineering (Eds.), Qatar University, Doha, 2012.
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