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

Contents1

1. Introduction ………………………………………………………………………………………….. 3

2. Objective ………………………………………………………………………………………………. 3

3. Theory ………………………………………………………………………. ……………………….. 3

4. Apparatus …………………………………………………………………………………………….. 6

5. Experimental Set-up …………………………………………………………………………………... 7

6. Procedure ……………………………………………………………………………………..…. 7

7. Observations and Calculations ………………………………………………………..…………. 8

8. Results ……………………………………………………………………………….………….. 16

9. Error Analysis ……………………………………………………………………….…………….. 17

10. Sources of Errors ………………..………………………………………………..……………….. 18

11. Questions and Answers …………………………………………………….…………………… 19

12. Nomenclature ……………………………………………………………….…………………. 21

13.Refrences ……………………………………………………………………………………………… 22

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

]][[1

1 bakdt

da

dt

dN

Vr ===

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.

k1 = rate constants.

INTEGRAL APPROACH:-

If the concentrations of the reactants are equal ([a] = [b]) and the reverse reaction is neglected

(k2 is very small).

21ak

dt

da −= or 21bk

dt

db −= …… (3)

Integrating the above equation, we get:

−

=obbk

t111

1

......... (4)

Where time (“t”) required to reduce the concentration of B (NaoH) from bo to b.

Thus, a plot of t vs. (1 / b) would yield a straight line from which k1 can be estimated.

DIFFERENTIAL APPROACH

Plotting log [-(d[b] / dt)] and log [b] would yield a straight line

bkdt

dblog2loglog 1 +=

−

…… (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 Ea can be evaluated from the rate constant at any

temperature (within the validity of the Arrhenius equation)

Thus a plot of log (k1) vs. (1/T) would yield a straight line, which enables evaluation of k10 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 bath. 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:

o Standardization of NaoH solution.o Neutralization of NaoH present in reaction mixture at different time

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

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o Temperature for the first reading is taken to be 400C and reaction is carried out at this temperature. User sets the set point at 400C

o After Set point is achieved, NaoH (1000ml) and ethyl acetate (1000 ml) were mixed in 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.

o Eight different samples were prepared for taking readings at different time intervals. Each 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.

Observation and Calculation

Standardization of NaOH

Gram Equivalent BalanceNumber of Equivalents in HCL= Number of Equivalents of NaOH by Titration+Number of Equivalents of NaOH in Reaction Mixture

RRNaOHNaOHHClHCl VNVNVN +=

NHCL VHCL = NT VT + NR VR

NHCL=0.0284N, VHCL =10 mlNT (Concentration of NaOH Titrate) =0.0338N,VT =Volume of Titrate NaOH usedVR = Volume Of Reaction mixture used= 5 mlNR= Concentration of NaOH in reaction mixture at a given time

NR= (NHCL VHCL - NT VT)/10NR = (.029*10 – 0.0338* VT)/5 =0.058-0.00676 VT

Concentration of NaOH: b= NR

Observations at bath temperature = 40°C

S.NO

Time(min)

ml of0.0338 N

NaOH

UnreactedNaOH (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:

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Fig: -2 Graph between 1/Conc. Of Rxn Mixture Vs Time at T=313K

By linear regression we gett= 0.016(1/b) -1.59511/k= 0.016k=62.5 (l/mol.min)

Differential approach:

Linear regression giveslog(-db/dt)=1.0949*log(b avg) -1.0581

10

k=0.088 l/mol.min

Observations at bath temperature = 30°C

S.NO

Time(min)

ml of0.0338 N

NaOHUsed

UnreactedNaOH (b)(mol / l)

1/b(l/mol )

b avg(mol/l)

(-db/dt)mol/l.min/(10000)

log(bavg)Log(-db/dt)

1 1 6.5 0.01406 71.1237 0.01315 2.9894 -1.8811 -3.5244

2 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

8 167.4

0.007976 125.37610.00975

62.1171 -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

Table 1. Tabulation of experimental data and Calculation of Different Variables for T=313K

Integral approach:

11

By linear regression we gett= 0.2554(1/b) -14.6821/k= 0.2554k=3.92 (l/mol.min)Differential approach:

12

Linear regression giveslog(-db/dt)= 1.0928*log(b avg) -1.4691k=0.339 l/mol.min

Observations at bath temperature = 21°C

S.NO

Time(min)

ml of0.0338 N

NaOHused

UnreactedNaOH (b)(mol / l)

1/b(l/mol )

b avg(mol/l)

(-db/dt)mol/l.min/(10000)

log(bavg)Log(-db/dt)

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 115.58020.00946

51.6281

-2.0238-3.7883

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

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 gett= 0.542(1/b) -39.6851/k= 0.542k=1.844 (l/mol.min)Differential approach:

Linear regression giveslog(-db/dt)= 1.0927*log(b avg) -1.5744k=0.0266 l/mol.min

Calculation of activation energy:

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Average reaction temperature(K)

k (l/mol/min)

1/T ln (K diff) ln (K int)

Diff Int.

3130.088

62.5 0.0032

-2.4304 4.135

3030.0339

3.92 0.0033

-3.3843 1.366

2940.0266

1.844

0.0034

-3.626 0.611

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 +16.581Slope = -Ea / R = -5978Ea= 49 KJ/mol.Intercept = ln A =16.581A= 1.589E7 lt/mol.min

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Integral Approach

ln k= -17620/T + 60.183Slope = -Ea / R = -17620Ea= 144.48 KJ/mol.Intercept = ln A =60.183A= 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 = 0.2mlLeast Count of measuring cylinder used = 0.2mlLeast Count of stop watch used = 0.1 sec

Error in determining rate constants Calculation done for reading at t = 11 min and Tbath= 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 30 o C

S.No

(-db/dt)/10000

mol/l.min

-2*log(b avg)

K (mol/l.min) (K - <K>)^2

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

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11 -3.8241 4.3210 3.1397 0.9807

Standard deviation can be calculated from following formula:

So S.D =0.455695 % confidence limit = 1.9599 * S.D = 0.8930So % 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 humanerrors 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 Answers19

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:

CH3COOC2H5 + NaOH CH3COONa + C2H5OH

Rate expression for the above rxn is

-rA = k1ab……………………… (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

-rA = K1*ao( 1 – XA)( bo – ao*XA ) This eqn in differential form can be written as

-da/dt = K1 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 very 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

k1 = rate constant for the forward and backward reaction respectively.

V = volume of the reaction mixture, ( m3 ).

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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 CH3COOC2H5, NaOH, CH3COONa and C2H5OH respectively.

T = time, (s).

bo = initial concentration of CH3COOC2H5 or NaOH , ( moles / liter ).

K10 = 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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