Adiabatic Reactors Final Lab Group 1-A

transcript

Kinetics of An Adiabatic Reaction

Group 1-A

Keith Tan JunJie, Wang Jiaxi, Pranav Chokhani

Date of Experiment: 5th Oct 2015

Date of Report Submission: 13th Oct 2015

Member Contribution

Keith Tan JunJie Summary (5), Results and Calculations (7)

Wang Jiaxi Introduction and Objectives (4), Experimental details and Procedures (3), Error Analysis (5)

Pranav Chokhani Theory (3), Discussion and Conclusion (5), Notation/References (3)

Table of Contents

1) Summary.........................................................................................................3

2) Introduction and Objectives..........................................................................42.1 Introduction.....................................................................................................42.2 Objectives.......................................................................................................5

3) Theory..............................................................................................................6

4) Experimental details and procedures...........................................................9

5) Results and Calculations..............................................................................115.1) Determining Reaction Stoichiometry..........................................................115.2) Reaction Enthalpy ∆H.................................................................................135.3) Arrhenius Parameters: Pre exponential factor A’ and activation energy E.15

6) Error analysis...............................................................................................196.1) Error of ∆ H ..................................................................................................206.2) Error of E.....................................................................................................216.3) Errors of A’.................................................................................................22

7) Discussion and Conclusion..........................................................................23

8) References.....................................................................................................26

9) Nomenclature................................................................................................27

1) Summary

The aim of the experiment was to determine and compare with literature data

I. Overall Reaction StoichiometryII. Reaction Enthalpy ∆H

III. Arrhenius Parameters: Pre-exponential factor A’ and Activation Energy E

For an adiabatic exothermic liquid-based reaction between 1M Hydrogen Peroxide and 1M Sodium Thiosulphate in an adiabatic reactor while varying 6 volumes of the reagents to alter mixing ratios and observing the temperature rise during the reactions using a PC datalogger software.

Main findings of the experiment were generated by examining the mixing ratio with the greatest rise in temperature:

Experiment Overall Reaction Stoichiometry: Na2S2O3+H2O2→ Na2S2O4+H20

vA/vBAve ΔH(J/mol)

Ave A’(cm3/s.mol)

Ave E(J/mol)

Calculated Experimental

Values1 -160,857.6 7.288×1038 215,340

Literature Values [1] 1.96 -596,600 7×1014 76,500Table 1.1: Comparison of Calculated Experimental and Literature Values

Experimental and literature results differ due to main sources of error of incorrect assumptions that there were no heat loss from the reactor and that reactants were perfectly mixed. It can be seen that the results vary largely from literature values also due to high percentage errors in calculation of parameters shown below.

Parameters Percentage ErrorΔH ±0.69%E ±6.94%A’ ±582.86%

Table 1.2: Parameter Percentage Errors

Experimental trends observed are that the reaction between H2O2 and Na2S2O3 generates the greatest rise in temperature with the stoichiometry ratio of vA/vB=1.00. The experiment indicates that the stoichiometry ratio of 1.00 is the natural reaction between the reagents and hence creates the largest exothermic reaction when both reactants act as limiting reagents.

2) Introduction and Objectives

2.1 Introduction

In chemical engineering, chemical reactors are designed to contain different chemical reactions. Most common reactors include batch reactors, continuous stirred-tank reactor and plug flow reactor. Batch reactor is used for small-scale operation, for testing new processes, and for the processes that are difficult to convert to continuous operation. It has the advantage of high conversion rate can be reached by leaving the reactant in the reactor for long period of time, but also has the disadvantage of high labour cost per batch, the products vaiability from batch to batch and the difficulty of large-scale production. The comparison between different types of reactor is given in the below table. Baffles are used for most reactors which are flow-directing panels designed to ensure a better mixing of the reactants. A baffled reactor has higher efficiency than a non-baffled one. [3] In this experiment, magnetic stirrer is used to minimise the risk of contamination.

BR CSTR PFRProduction Rate Small High High

Capital Cost Small High HighLabour cost High Small Small

Scale of production Small Large LargeReactant conversion Small Small HighTemperature control Easy Easy Difficult

Table 2.1 Comparison between different reactors

The activation energy relates to the Arrhenius Equation correlates chemical reaction rate constants with temperature. It indicates the sensitivity of the reaction rate to temperature. From the Arrhenius Equation, the activation energy can be expressed as the equation below: [2]

k=A eEαRT

Where A is the frequency factor for the reaction, R is the universal gas constant, T is the temperature, k is the reaction rate coefficient and E is the activation energy.

An adiabatic reactions is one that occurs without transfer of heat or matter between a system and its surroundings, energy is transferred only as work (i.e. ∆Q=0). Adiabatic reactors are well-insulated as they are usually made of most plastics and polymers. Adiabatic reactors

ensure that the energy is well-trapped into the reactor and therefore in this experiment the temperature rise can be measured easily in order to achieve the objectives given below:

2.2 Objectives

The objectives of this experiment are to determine, and compare with literature data, the following parameters for an adiabatic exothermic liquid-based reaction by observing the temperature rise during reaction:

i) Overall reaction stoichiometry It is to use relationships between reactants and/or products in a chemical reaction to determine desired quantitative data.

ii) Reaction enthalpy ∆H Enthalpy change is the name given to the amount of heat evolved or absorbed in a reaction carried out at constant pressure.

iii) Arrhenius parameters: Pre-exponential factor A’ and activation energy E A’ is a term which includes factors like the frequency of collisions and their orientation. It varies slightly with temperature, although not much. It is often taken as constant across small temperature ranges. Activation energy E is the minimum energy needed for the reaction to occur. To fit this into the equation, it has to be expressed in joules per mole.[2]

3) Theory

The two reactants used in this experiment are:

I. Hydrogen Peroxide – H2O2 (Reactant A)II. Sodium Thiosulphate – Na2S2O3 (Reactant B)

Hydrogen Peroxide in its purest form is a colorless liquid and is marginally more viscous than water. It is a corrosive irritant to skin, eyes and mucous membranes and also is a very powerful oxidizer and bleaching agent. H2O2 containers are usually covered to avoid the evaporation of water from it, concentrating of the solution thus increasing the fire hazard of the remainder.

Sodium Thiosulphate is an inorganic compound, which also forms a colorless solution. Solid Na2S2O3 is a crystalline substance that dissolves readily in water. In this experiment both the reactant solutions where used at 1M.

The reaction between Hydrogen Peroxide (reactant A) and Sodium Thiosulphate (reactant B) is an exothermic one and it can take the following possible routes:

The assumptions made during the experiment are as follows: -

1. Negligible heat loses2. No changes in the volumetric heat capacity with system composition3.

Taking these assumptions it can be said that the rate of temperature rise during the reaction is proportional to the rate of reaction and the rate of reaction is in turn proportional to the rate of change in concentration of each reactant species. Since reaction stops with complete consumption of any one reactant, the maximum heat generation, per mole of reactants supplied, occurs when there is no excess of any reactant. Thus the overall stoichiometry may be determined by finding the mixing ratio of reactants, which gives the maximum temperature rise (Tf – T0) at constant initial molarity (1M) and constant volume (taken as 120 cm3 in this experiment).

From the temperature time data gathered by the computer during the experiment it is also possible to estimate the Arrhenius parameters: Pre-exponential factor A’ and activation energy E for the mixing ratio that gives the maximum temperature rise.

The reaction taking place in the experiment can be simply put as:

The kinetics of all species involved in the reaction can be related to the species independent reaction rate r given as:

For an adiabatic reaction, the rate of temperature change is given by the energy balance:

Now eliminating r, integrating and applying initial boundary conditions in EQ 3:

For the case where A is the limiting reagent, all of the CA gets used up at the time Tf when the reaction is over. Therefore:

From EQ 4 and EQ 6:

Assuming the reaction is irreversible and first order with respect to each reactant and using

the Arrhenius equation the kinetic rate expression becomes:

Where T is in Kelvin.

With A as the limiting reactant, substitution of EQ 8 and EQ 9 into EQ 4 gives:

Where:

All the equations mentioned above have been obtained from the UCL lab book for the module CENG3008 p.11 and 12.

4) Experimental details and procedures

The experiment is being conducted using the magnetic stirrer and a PC with data logger software as the diagram shown below. The change in reactor temperature is recorded as a function of time by a Data Logger on the PC. The study is conducted between Hydrogen Peroxide (1M H2O2) and Sodium Thiosulphate (1M Na2S2O3).

Figure 4.1 Experimental apparatus

Equipment:

1. Hydrogen Peroxide (1M H2O2) 2. Sodium Thiosulphate (1M Na2S2O3)3. Well-insulated reactor4. Magnetic stirrer5. Digital temperature monitor6. PC with data logger7. 2 conical flasks (250ml)8. 2 beakers (250ml)9. 2 disposable pipettes10. 2 measuring cylinders11. Filter funnel12. Temperature probe

Procedure:

1. Pour some of the reactant solutions from the containers into conical flasks. Prepare the reactant volumes by pipetting them from the conical flasks into beakers. The mixing ratio for each run is given below:

Run Mixing ratio H2O2, cm3 Na2S2O3, cm3

1 0.5 40 802 1 60 603 1.33 68.5 51.54 1.67 75 455 2 80 406 4 96 24

Table 4.2 Experimental mixtures of reactants for each run

2. Pour the reactant solution with the largest volume in the reactor and set the stirrer in motion.

3. Place the cover with the thermocouple onto the reactor, turn on the stirrer and gradually turn to setting 3, leave for about 3 minutes to ensure even movement of the stirrer.

4. At t = 0, start logging the temperature data on the PC and after a few seconds, pour the reactant solution with the smallest volume through a funnel into the reactor.

5. When the reaction stops, the temperature becomes constant, reaching its final value Tf. Stop data logging on the PC.

6. On completion of each experiment, the reactor and the flask should be rinsed with distilled water, and be allowed to cool down.

7. Repeat steps 1-6 for all mixing ratios considered. 8. Copy the data from the PC onto a USB stick to take away.

5) Results and Calculations

5.1) Determining Reaction Stoichiometry

Total Reacti

on Volume

Reactant A

H2O2 (cm3)

Reactant B

NA2S2O3

Initial Temperat

ureT0(°C)

Final Temperatu

reTf(°C)

Temperature Change

[Tf-T0](°C)

Initial

Timet0 (s)

Final Timetf (s)

Time Taken[tf-t0]

1 0.50 120 40 80 21.5 40.1 18.6 0.0 215 2152 1.00 120 60 60 24.3 43.5 19.2 0.0 137 1373 1.33 120 68.5 51.5 24.0 40.5 16.5 0.0 116 1164 1.67 120 75 45 23.8 39.4 15.6 0.0 104 1045 2.00 120 80 40 24.3 37.6 13.3 0.0 97 976 4.00 120 96 24 23.3 31.8 8.5 0.0 102 102

Table 5.1: Experiment Results

Table 1 indicates the specific volumes of

Reactant A: Hydrogen Peroxide 1M (H2O2) Reactant B: Sodium Thiosulphate 1M (Na2S2O3)

used in the experiment runs 1-6 to produce the following overall stoichiometry ratios of all possible reactions between both reactants A and B.

0 50 100 150 20020

Graph 5.1: Experiment Reactor Tempera-ture (°C) Change Against Time (s) for vary-ing mixing ratios of H2O2 and Na2S2O3

Run 1 : 0.5 Run 2: 1.0Run 3 : 1.33Run 4: 1.67Run 5 : 2.0Run 6 : 4.0

Time (s)

re (°

Graph 5.1: Raw Data Analysis of Experiment Results Runs 1-6 in Graphical Format

20 30 40 50 60 70 80 900

18.619.216.5

Graph 5.2: Temperature Change (°C) against Volume of Na2S203 (cm3)

Volume of Reactant B Na2S2O3 (cm3)

0](°C

Graph 5.2: Data Analysis of Experiment Results of Temperature Change against Volume of Reactant B

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.000

18.6(°C) 19.2(°C) 16.5(°C)

15.6(°C) 13.3(°C)

8.5(°C)

Graph 5.3: Temperature Change [Tf-T0](°C) against Mixing Ratio

Mixing Ratio

0](°C

Graph 5.3: Data Analysis of Experiment Results of Temperature Change against Mixing Ratios

Based on the experimental results from Table 1 and the raw data analysis in Graphs 1, 2 and 3, it can be seen that run 2 has the greatest temperature change and hence greatest rise in Temperature.

As reaction terminates with complete consumption of either reactant, maximum heat generation, per mole of reactants provided, takes place when there is no excess of reactants.

Thus the overall stoichiometry can be investigated by finding the mixing ratio of reactants that provides the greatest temperature increase at constant initial volume and molarity.

Overall Stoichiometric ratio =Vtotal−VB

From Graph 3, where the lines of best fit intercept, VB=60cm3

Hence Overall stoichiometric ratio = 120 cm3−60 cm3

60 cm3=1.00

Hence, the overall reaction stoichiometry vA/vB is 1.00 as seen in run 2 with a greatest Temperature Change [Tf-T0](°C) of 19.2°C.

The reaction between

Reactant A: Hydrogen Peroxide 1M (H2O2) Reactant B: Sodium Thiosulphate 1M (Na2S2O3)

in the experiment would therefore be,

Experiment ReactionStoichiometry

vA/vBLiterature Reaction

Enthalpy∆H (J/mol Na2S2O3)

Na2S2O3+H2O2→ Na2S2O4+H20 1.00 -173 300Table 5.4: Literature Data of Experiment Reaction of Stoichiometry Ratio 1.00[1]

5.2) Reaction Enthalpy ∆H

For the case where A is the limiting reactant,

CAo=(CpVA∆H )( Tf -To ) EQ 6

CAo refers to initial concentration of limiting reactant in mol/cm3

Cp refers to specific heat capacity of the limiting reactant in J

cm3 K vA refers to the reaction stoichiometry of the limiting reactant where a negative vA

indicates an exothermic reaction while a positive vA indicates an endothermic reaction. For the purpose of this experiment, the stoichiometry ratios are –ve as the reaction is exothermic.

(Tf-To) Refers the change in temperature in the experiment in Kelvin. ∆H refers to the specific enthalpy of the reaction with respect to each mol of limiting

reactant in J

mol ReactantA

Rearranging the Equation,

∆HA=(CpVACAo

)(Tf-To)

Sample Calculation for Run 2:

Where equal volumes of 60cm3 of Reactant A Hydrogen Peroxide 1M (H2O2) and Reactant B Sodium Thiosulphate 1M (Na2S2O3) react to produce a temperature rise of 19.2°C

1. C Ao=Reactant A Concentration∗R eactant A VolumeTotal Volume

¿1 M∗60 cm3120 cm 3

= 11000

molcm 3

∗60 cm 3

120 cm3=0.0005 mol

2. C Bo=Reactant B Concentration∗Reactant B VolumeTotalVolume

¿1 M∗60cm3120 cm 3

= 11000

molcm 3

∗60 cm 3

120 cm3=0.0005 mol

3. For the case of the specific heat capacity, as the initial concentration of reactants are extremely small, with bulk of the solution mainly in water, we make the assumption

that the specific heat capacity of reactants will be 4.187 J

gK [3] which is equivalent to

4.187 J

cm3 K as the density of water is 1g/cm3.

4. Note, for (Tf-To), ∆1°C = ∆1K.5. Note, for all equations, vA and vB are -1 as the reaction is exothermic and the chosen

overall reaction stoichiometry is 1 for each reactant based on the equation below:

Experiment ReactionStoichiometry

vA/vBLiterature Reaction

Enthalpy∆H (J/mol Na2S2O3)

Na2S2O3+H2O2→ Na2S2O4+H20 1.00 -173 300Table 5.5: Literature Data of Experiment Reaction of Stoichiometry Ratio 1.00[1]

6. Enthalpy per mole of reactant A

∆HA=(CpVACAo ) (Tf -To )

∆HA=4.187 J

cm 3K∗−1

0.0005 molcm3

∗19.2 K=−160,780.8 JmolH 2O2

7. Enthalpy per mole of reactant B

∆HB=(CpVBCBo ) (Tf -To )

∆HB=4.187 J

cm3 K∗−1

0.0005 molcm3

∗19.2 K=−160,780.8 JmolNa2S2o3

8. In the case of Run 2, as both reactants are limiting reactants, the Enthalpy of both A and B can be calculated in the same manner. However, for other runs, we can only find the enthalpy of the limiting reactant based on the equation and then convert the other enthalpy of the excess reactant from the enthalpy of the limiting reactant in the following fashion.

In Run 1, as the limiting reactant is H2O2, we will be able to calculate ∆HA .

∆HA=4.187 J

cm3 K∗−1

molcm3

∗40cm 3

120 cm3

∗18.6 K=−233,634.6 JmolH 2O 2

And from ∆HA we will be able to calculate ∆HB via stoichiometry.

∆HB = ∆HA * vB / vA =−233,634.6 JmolH 2O 2

* 1/1 = −233,634.6 JmolNa2S2o3

For runs 3-6, reactant B is the limiting reagent hence calculate ∆HA from ∆HB

Run CAo(mol/cm3)

CBo(mol/cm3)

Temperature Change

[Tf-T0](K)

∆HA(J/molH2O2)

∆HB(J/molNa2S2O3)

1 0.000333 0.000667 18.6 -233634.6 -233634.62 0.000500 0.000500 19.2 -160780.8 -160780.83 0.000571 0.000429 16.5 -161052.8 -161052.84 0.000625 0.000375 15.6 -174262.4 -174262.45 0.000667 0.000333 13.3 -167141.1 -167141.16 0.000800 0.000200 8.5 -178032.5 -178032.5

Ave reaction Enthalpy ∆HB (J/molNa2S2O3) -179182.1

Table 5.6: ∆HB Enthalpy of Na2S2O3 for Runs 1-6

5.3) Arrhenius Parameters: Pre exponential factor A’ and activation energy E

Assuming the reaction is irreversible and first order with respect to each reactant, the kinetic expression is with A as the limiting reactant

r=kCACB=CACB A ' exp (−ERT

) EQ 8

With the overall equation being

1(Tf −T ) [µ (Tf −¿ )−(T−¿ )]

=γ e−E /RT EQ 9

Let dTdt

1(Tf −T ) [µ (Tf −¿ )−(T−¿ )]

z=γ e−E /RT

ln (Zy )=(−E

R )∗( 1T )

lnz=(−ER )∗( 1

T )+ ln y

Which is similar to y=m∗x+C

Hence plot lnz vs 1/T to find the Pre exponential factor A’ and activation energy E.

Where,

µ = CBovA/CAovB EQ 10

γ= -A’vAvB Cp / ∆H EQ 11

Sample Calculation for Run 2,

1. µ = 0.005 mol

cm 3∗1

0.005 molcm 3

∗1=1.00

2.dTdt

=T i+1−Tit i+1−ti which refers to the temperature change per unit time.

For Run 2 where at t=38s

Run 2vA/vB = 1.0

Time (s) Temp (deg C)38 29.039 29.4

Table 5.7: Data Logger Raw Data from Run 2

= (29.4−29.0 ) K(39−38 ) s

=0.4 Ks

3. At t=38s (Tf −T ¿=43.5 (°C )−29.0 (°C )=14.5 (° C )=14.5 K

4. (T−¿ )=29.0 (°C )−24.3 (°C )=4.7 (°C )=4.7 K

5. Hence, Solve for z,

z= dTdt

1(Tf −T ) [ µ (Tf −¿ )−(T−¿) ]

=0.4 Ks [ 1

14.5 K∗[1.00∗(19.2 K )−(4.7 K ) ] ]z=1.902∗10−3 1

6. lnz=ln (1.902∗10−3 )=−6.264 1Ks

7. Plot lnz 1

Ks vs (1/T)K−1

0.0031 0.00315 0.0032 0.00325 0.0033 0.00335 0.0034 0.00345

f(x) = − 28515.6046506373 x + 88.2705575827255

f(x) = − 20344.8991158034 x + 60.7037632115431f(x) = − 19872.7039948635 x + 59.0756444612916

f(x) = − 21158.7348034055 x + 63.3588014871819

f(x) = − 25900.9243524667 x + 78.9288392363579

f(x) = − 15312.0705706748 x + 43.1754004935059

Graph 5.4: Graph of lnz(1/Ks) against 1/T(1/K)

Run 1Linear (Run 1)Linear (Run 1)Run 2Linear (Run 2)Linear (Run 2)Run 3Linear (Run 3)Run 4Linear (Run 4)Run 5Linear (Run 5)Linear (Run 5)Run 6Linear (Run 6)

1/T (K -1)

Graph 5.4: Runs 1-6 plot of ln z (1/Ks) against 1/T (K^-1)

8. From plot, comparing the linear plot to the equation lnz=(−ER )∗( 1

T )+lny

(−ER )=−25901

lny=78.929 1Ks

9. Hence, y=e78.929=1.898∗1034 1Ks

As γ= -A’vAvB Cp / ∆H where in run 2, ∆H = -160857.6(J/molNa2S2O3),Rearrange for A’,

A'= y∗−∆ HvAvBCp

=1.898∗1034 1

Ks∗160857.6 J

1∗1∗4.189 Jcm 3 K

A'=7.288∗1038 cm3mol∗s

10. Hence (−ER )=−25901 K

Where R = 8.314 J

molK[4]

Rearrange for E, E=25901 K∗8.314 JmolK

=215340 Jmol

Run µ A' cm3

mol∗s E J

1 23.14267E+2

3 127304

2 17.29055E+3

8215340.

3 1.331.26276E+3

2175915.

4 1.661.88571E+3

0165224.

5 29.21266E+3

0169148.

6 49.20444E+4

2 237082

Average1.53419E+4

2181669.

2Table 5.9 of Arrhenius Parameters: Pre exponential factor A’ and Activation energy E

Calculation from runs 1-6

From Runs 3-6, the limiting reactant is Na2S2O3 while in run 1, the limiting reactant is H2O2 and in run 2, both reagents were limiting. The calculation for µ defers in which reactant is limiting.

The Graphs of the runs are included in the appendix.

Hence, the Average Pre exponential factor A’ and activation energy E from runs 1-6 are as follows:

A’ = 1.53419E+42 cm3

mol∗s

E = 181669.2 J

6) Error analysis

If y=f(xi) is a function of N independent variables and ωxi is the uncertainty of the ith variable

Then the resulting combination is being calculated using the formula below:

ω y=√∑i=1

( ∂ y∂ x i

ωxi¿)2

Variable Uncertainty(ωxi)Temperature ωT=±0.05℃

Volume ωv=± 0.5 mlTable 6.1 variables and uncertainties

Dependent variables and partial derivatives are given in the table below,

Dependent variable Partial derivatives

ΔH=c p ν A(T f −T 0)(V A +V B)

CA V A

∂ ΔH∂ T f

=c p ν A (V A+V B )

C A V A

∂ ΔH∂T 0

=−c p ν A (V A+V B )

C A V A

∂ ΔH∂ V A

=−c p ν A V B (T f −T 0 )

C A V A2

∂ ΔH∂ V B

=−c p ν A (T f −T 0 )

CA V A

E=−mR ∂ ΔE∂ m

A'= e ln y ∆ H−ν A νB c p

∂ A '

∂ ln ϒ= e ln γ ∆ H

−ν A ν B c p

∂ A '∂ ΔH

= e ln γ

−ν A νB c p

Table 6.2 dependent variables and partial derivatives

6.1) Error of C A 0∧CB 0

Common sense method is used to calculate the errors of concentration for reactant A&B

Sample calculation is carried out below for Run 2:

CB 0 , nominal=0.0005 c m3

CB 0 , max=1

1000× 60+0.5

120−0.5=0.000506 cm3

mol=1.2 %

CB 0 , min=1

1000× 60−0.5

120+0.5=0.000494 cm3

mol=−1.2 %

average percentageerror=1.2 %+1.2 %2

=1.2 %

Run % % Average1 0. 000333 0. 000338912 0. 000327801 1. 775415583 1. 56131235 1. 6683642 0. 0005 0. 000506276 0. 000493776 1. 255230126 1. 244813278 1. 2500223 0. 000571 0. 000577406 0. 000564315 1. 121866504 1. 170691296 1. 1462794 0. 000625 0. 000631799 0. 000618257 1. 087866109 1. 078838174 1. 0833525 0. 000667 0. 00067364 0. 000659751 0. 995527341 1. 086800998 1. 0411646 0. 0008 0. 000807531 0. 000792531 0. 941422594 0. 933609959 0. 937516

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Table 6.3 Errors for C A

Run % % Average1 0. 000667 0. 00067364 0. 000659751 0. 995527341 1. 086800998 1. 0411642 0. 0005 0. 000506276 0. 000493776 1. 255230126 1. 244813278 1. 2500223 0. 000429 0. 000435146 0. 000423237 1. 432737416 1. 343469808 1. 3881044 0. 000375 0. 000380753 0. 000369295 1. 534170153 1. 521438451 1. 5278045 0. 000333 0. 000338912 0. 000327801 1. 775415583 1. 56131235 1. 6683646 0. 0002 0. 000205021 0. 000195021 2. 510460251 2. 489626556 2. 500043

( యሻሻ ( యሻሻ ( యሻሻ

Table 6.4 Errors for CB

6.2) Error of ∆ H

Enthalpy change is calculated from the equation given below,

ΔH=c p ν A(T f −T 0)

When mixing ratio is smaller than 1, hydrogen peroxide is the limiting reactant, and when it is larger than 1 then sodium thiosulphate is the limiting reactant.

Given that C A0=C A ×

V A+V B :

ΔH=c p ν A(T f −T 0)(V A +V B)

CA V A

ωΔH=√( ∂ ΔH∂T f

× ωT f )2

+( ∂ ΔH∂ T0

× ωT 0)2

+( ∂ ΔH∂V A

× ωV A)2

+( ∂ ΔH∂V B

×ωV B)2

The sample calculation is carried out for Run 2, when

νA=1, νB=1, C p=4.189 J /c m3 K , T f −T0=19.2 K , V A+V B=120 c m3

∂ ΔH∂ V A

=−4.189 ×1 ×1 ×19.20.001× 602 =−1340.48 J

molc m3

∂ ΔH∂ V B

=−4.189 ×1×19.20.001 ×60

=−1340.48 Jmol c m3

∂ ΔH∂ T f

=4.189 ×1×1200.001 ×60

=8378 Jmol K

∂ ΔH∂T 0

=−4.189 ×1 ×1200.001 ×60

=−8378 Jmol K

√( c p ν A (V A+V B )C A V A

×ωT f )2

+(−cp ν A (V A+V B )C A V A

× ωT0)2

+(−c p ν A V B (T f −T 0 )C A V A

2 × ωV A)2

+(−c p ν A (T f −T 0 )CA V A

× ωV B)2

¿√ (8378 ×0.05 )2+(−8378 × 0.05 )2+ (−1340.48× 0.5 )2+(−1340.48 ×0.5 )2

=± 1117.76 Jmol

≡±0.69%

The combination errors for all runs are given in the table below:

Run Mi xi ng rat i o1 0. 5 - 233746 - 3895. 77 - 3895. 77 25134 - 25134 3278. 27725 1. 402494352 1 - 160858 - 1340. 48 - 1340. 48 8378 - 8378 1117. 76462 0. 694878343 1. 33 - 161053 - 3034. 45 - 4036. 117 29353. 58 - 29353. 6 3268. 43967 2. 02942124 1. 67 - 174262 - 2613. 94 - 4356. 56 33512 - 33512 3473. 95162 1. 99351765 2 - 167141 - 1392. 84 - 2785. 685 25134 - 25134 2362. 96478 1. 413754486 4 - 178033 - 370. 901 - 1483. 604 20945 - 20945 1666. 77154 0. 93621756

Average 2528. 02825 1. 41171392

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Table 6.5 errors of enthalpy change

The average percentage error for all six runs is 1.41% from the table above.

In order to calculate the errors of E and A’, standard errors of the fitting line have to be obtained, the formula for standard error is given as

For our convenience, and also for higher accuracy, ‘LINEST’ Function in Excel is used in our calculation.

6.3) Error of E

E can be calculated from the gradient of the fitting line, therefore , we use the equation E=-mR

Sample calculation for Run 2, when E= 215340.9J

mol , ωm=1798.17

ωE=√( ∂ ΔE∂ m

× ωm)2

=−8.314 ×1798.17=± 14949.99 Jmol

≡± 6.94 %

Results for all other runs are given in the table below

Run se(sl ope)se(y- i nt ) sl ope(1/ K) l ny(1/ Ks) %1 793. 1687 2. 602121 - 15312. 07 43. 1754 6594. 405 5. 182 1798. 171 5. 829543 - 25900. 92 78. 92884 14949. 99 6. 943 973. 8809 3. 18055 - 21158. 73 63. 3588 8096. 846 4. 604 1323. 519 4. 323426 - 19872. 7 59. 07564 11003. 74 6. 665 1289. 433 4. 228342 - 20344. 9 60. 70376 10720. 34 6. 346 2200. 447 7. 311136 - 28515. 6 88. 27056 18294. 52 7. 72

Average 11609. 97 6. 24

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Table 6.6: Errors of E

The average percentage error for all six runs is 6.24% from the table above

6.4) Errors of A’

Pre-exponential factor A ‘ is calculated from the equation

A'= e ln y ∆ H−ν A νB c p

In order to obtain the combination error for this dependent variable, we need the derivatives with respect to the two independent variables in this formula, which are lny and ∆ H

ωA '=√( ∂ A '∂lny

× ωlny)2

+( ∂ A '∂ ΔH

×ωΔH )2

For Run 2, the sample calculation is given below

∂ A'

∂lny= e ln y ∆ H

−ν A νB c p= e78.93×−160858

−1× 1× 4.189=7.29 ×1038 cm3

mol. s

∂ A '∂ ΔH

= eln γ

−ν A νB c p= e78.93

−1× 1× 4.189=4.53× 1033 cm3

ω A '=√( 7.29× 1038×5.83 )2+ (4.53 ×1033 ×1117.76 )2

¿± 4.25 ×1039 cm3 smol

≡ ±582.86 %

Run %1 1. 57196E+23 3278. 2772 6. 72509E+17 4. 09044E+23 130. 162 7. 28938E+38 1117. 7646 4. 53157E+33 4. 24938E+39 582. 863 1. 05209E+31 3268. 4397 6. 5326E+25 3. 34624E+31 26. 504 1. 25669E+29 3473. 9516 7. 21149E+23 5. 43321E+29 28. 815 1. 15131E+30 2362. 9648 6. 88825E+24 4. 86813E+30 52. 846 2. 30009E+42 1666. 7715 1. 29195E+37 1. 68163E+43 182. 70

Average 2. 80342E+42 167. 31

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Table 6.7: Errors of A’

The average percentage error for all six runs is 167.31% from the table above

7) Discussion and Conclusion

The aims of the experiment included calculating:

Overall Reaction Stoichiometry Reaction enthalpy ΔH Arrhenius Parameters: Pre exponential factor A’ and Activation Energy E

For a liquid based adiabatic exothermic reaction between Sodium Thiosulphate and Hydrogen Peroxide.

Based on our calculations obtained from the raw data of the experiment, we can say that the highest temperature rise occurs when the Overall Reaction Stoichiometry is 1. This can clearly be seen in Graph 5.1 of the report. The theoretical reason behind this maximum rise in

temperature to 43.5°C in run 2 is that in this case both the reactants are in equimolar quantities and are completely consumed by the end of the reaction leading to a release of maximum heat. Talking about the trends of various mixing ratios in Graph 5.1 we see that the temperature for all runs start increasing as soon as H2O2 is added in the adiabatic reactor and as the reaction proceeds the curves starts becoming stable after reaching a maximum value. In run 2 and run 5 the temperature decreases after reaching a maximum value but by a very minor amount, which can be accounted as an experimental error due to loss of heat to the surroundings. Once the maximum temperature has been attained the temperature then remains constant as seen from the curves. This occurs when the reaction has been completed where either one or both of the limiting reagents have been completely consumed and hence there is no more heat released.

Talking about Graph 5.2 of the report which shows the temperature change in the reactor against the volume of Na2S2O3 in the mixture we can see that the temperature change increases as the volume of Na2S2O3 increases and reaches a maximum value of 19.2°C when the volume of Na2S2O3 is 60cm3. But then decreases as the volume of Na2S2O3 is further increased. This is because at low volumes of Na2S2O3 it acts as the limiting reactant and the reaction finishes when Na2S2O3 is completely consumed therefore releasing less heat. However as the volume of Na2S2O3 increases the reaction continues for a longer duration thus releasing more heat leading to increase in temperature. But after a certain quantity (60 cm3 in this case) the volume of Na2S2O3 exceeds that of H2O2 (to maintain total volume of 120 cm3) and in that case H2O2 acts a limiting reactant causing the reaction to finish as it is completely consumed giving off lower heat that than the previous result. Graph 5.3 of the report shows that the lowest temperature change occurs when the mixing ratio is 4. This result is expected because at this mixing ratio volume of sodium thiosulphate in the mixture is very low (24 cm3) causing the reaction to end very soon with the complete consumption of Na2S2O3 thus releasing the least amount of heat.

Average values of all runs calculated in this report have been summarised in the following table:

Parameter Average Value of all RunsOverall Reaction Enthalpy (ΔH) -179,182.1 J/molPre-exponential Factor (A’) 1.53×1042

Activation Energy (E) 181669.2 J/molTable 7.1: Average Values of all runs

Table 7.2 compares our calculated values for run 2 with the literature values:

vA/vB ΔH(J/mol)

A’ (cm3/s.mol)

E(J/mol)

Calculated Values

1 -160,857.6 7.288×1038 215,340

Literature Values [1]

1.96 -596,600 7×1014 76,500

Table 7.2: Comparison of Calculated and Literature Values

From the Table above we can see that our calculated values are quite different from the literatures values but lie in the same range. This can be explained by considering the errors that might have occurred while performing the experiment. Some of the potential sources of experimental errors in this experiment have been mentioned below: -

The small hole on the top of the adiabatic reactor might cause some of the heat to release to the surroundings thus varying the temperature rise

There might be unreacted liquid droplets on the walls of the adiabatic reactor Parallax error while measuring liquid quantity in the measuring cylinder Some liquid might be left on the funnel while transferring it into the reactor Error could due to different pouring rates of H2O2

The magnetic stirrer inside the adiabatic reactor might generate some heat leading to incorrect temperature measurements

Not all liquid might have transferred from the measuring cylinder to the reactor and could have been left as droplets on the walls of the measuring cylinder

The equipment used in the experiment could have trace impurities from other mixtures which would have not been removed completely even after washing

Some errors could have been introduced into our calculations due to the uncertainty of measuring devices i.e. thermocouple and measuring cylinder. These errors have been accounted for in the Error Analysis of the report using combination of errors technique and the following percentage errors have been obtained for our calculated values of run 2:

Parameters Percentage ErrorΔH ±0.69%E ±6.94%A’ ±582.86%

Table 7.2: Parameter Percentage Errors

From the table above we can see that the percentage error in Reaction Enthalpy calculation is almost negligible (<1%) and thus does not affect our final result much. However errors in calculation of activation energy and pre exponential factor are significantly high compared to reaction enthalpy. This is because in our calculations, we have assumed Graph 5.4 as a linear graph for ease of calculation of E and A’. Also this large percentage error in the calculation of pre exponential factor justifies the large difference amongst the literature and our calculated A’ values.

The other reason for the difference in our calculated and literature values are the assumptions made during the experiment. We have assumed that there are no heat losses during the experiment but this is almost never true as some heat is always lost to the environment due to radiation. In this experiment we also might have lost some heat through the hole on the top on the adiabatic reactor. The second assumption made was that all the components of the reaction were perfectly mixed. However in many instances some of the reactant might have stuck on the wall of the reactor and would have been left unreacted. Hence these assumptions could have played a major role in the deviation of our calculated values from the literature values.

Various improvements could be made to the experiment to get better and more accurate results. Some of them are mentioned below:

Use of a more advanced adiabatic reactor that better insulates the heat evolved during the exothermic reaction to give more accurate and precise temperature rises.

Use of a larger stirrer to ensure uniform mixing while avoiding generation of additional heat.

Use of an automatic mechanism for addition of H2O2 rather than manual addition to ensure uniformity while performing the experiment with different mixing ratios.

To summarize the findings of this experiment we can say that in the reaction between H2O2 and Na2S2O3 the maximum rise in temperature occurs when both the reactants act as limiting agents. Our calculated values though not very similar to the literature values lie in the same range. Error analysis shows that there is negligible error in enthalpy calculation but a relatively larger error in activation energy and pre exponential factor calculation due to the assumption made in calculations.

8) References

[1] Cohen, W.C., and Spencer, J.L.,Chem Eng Prog., 58, 1962, 40.

[2] Smith, J. and Smith, J. Solutions manual to accompany Chemical engineering kinetics,

third edition. New York: McGraw-Hill. p.156, 1981.

[3] Coulson, J., Richardson, J., Backhurst, J., Harker, J. and Coulson, J. Coulson &

Richardson's chemical engineering. Oxford: Butterworth-Heinemann vol.1, p.7, 1996.

[4] Coulson, J., Richardson, J., Backhurst, J., Harker, J. and Coulson, J. Coulson &

Richardson's chemical engineering. Oxford: Butterworth-Heinemann vol.1, p.179,

[5] H.S. Fogler Prentice-Hall, Elements of Chemical Reaction Engineering, 4th Ed., p.335 2006

9) Nomenclature

A’ Pre-exponential factor (cm3/s.mol)C Concentration (mol/cm3)cP Solution mean heat capacity (J/cm3K)E Activation energy (J/mol)

ΔH Reaction enthalpy (J/mol)k Reaction rate constant (cm3/s.mol)r Species-independent reaction rate (mol/cm3s)R Gas constant (J/molK)t Time (s)T Temperature (K)γ Constant defined by equation (11) (1/Ks)μ Normalized mixing ratio defined by equation (10)v Stoichiometric coefficient (reactants –ve, products +ve)

SubscriptsA,B Denotes components A,B

f Denotes final value0 Denotes initial value

Table 9.1: Nomenclature used in Report

Adiabatic Reactors Final Lab Group 1-A

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