Kinetics

AbstractThis study investigated the chemical reaction between hydrogen peroxide (H2O2) and sodium

thiosulphate (Na2S2O3) in an adiabatic batch reactor. To complete this, an understanding of the reaction

kinetics of a system is essential to understand reactor design. The aim was to determine the

stoichiometry, enthalpy of reaction and Arrhenius parameters of the reaction system and to identify the

reaction that takes place and compare the findings to a previous study by Cohen and Spencer.

The experiment was conducted by reacting various ratios of hydrogen peroxide and sodium thiosulphate

in a 200mL adiabatic reactor vessel. The temperature of the reacting mixture was recorded every 5

seconds to determine a temperature time profile for each run.

The stoichiometric ratio was determined to be 1.697 ± 0.0548 which was relatively less than Cohen and

Spencer’s value of 1.97. This value determined the dominating reaction in the simultaneous system to

be the following.

3Na2S2O3 + 5H2O2 → Na2S4O6 +2Na2SO4 + 5H2O

The enthalpy of reaction was calculated to be 445.09 kJmol-1 ± 38.85 kJmol-1 which also

corresponded to the above reaction. This value was 22.3% lower than Cohen and Spencer’s

value but their previous experiment found the dominating reaction to be the following.

2Na2S2O3 + 4H2O2 →Na2S3O6 + Na2SO4 +4H2O

The Arrhenius parameter were derived with an activation energy, E, of 112.39 kJmol -1 and a pre-

exponential constant, A, of 5.79×1011 Lmol-1s-1.

Several errors were found to exist through out the experiment. Some of these errors could have

been minimized by having more accurate measuring cylinders, a more accurate thermo-probe

and by using a better insulated reaction vessel.

i

The calculated rate constant, k, is not an accurate answer as the errors increase exponentially as the

concentrations of reactants decrease. A better experiment could be used to determine a more sufficient

rate constant.

This method does how ever provide an understanding of the reaction kinetics of a system.

ii

Contents

Abstract........................................................................................................................................................ i

Contents..................................................................................................................................................... iii

List of Tables................................................................................................................................................v

List of Figures..............................................................................................................................................vi

1 Introduction.........................................................................................................................................1

1.0 Aim..............................................................................................................................................1

1.1 Significance..................................................................................................................................1

1.2 Theory..........................................................................................................................................1

1.3 Stoichiometric Ratio....................................................................................................................2

1.4 Enthalpy of reaction.....................................................................................................................4

1.5 Arrhenius Parameters..................................................................................................................5

1.6 Previous Work.............................................................................................................................8

2 Experimental.....................................................................................................................................11

2.0 Equipment.................................................................................................................................11

2.0.1 Stirring table and magnetic stirrer:....................................................................................12

2.0.2 Thermo-probe:...................................................................................................................12

2.0.3 Reaction Vessel:.................................................................................................................12

2.1 Materials....................................................................................................................................13

2.2 Safety.........................................................................................................................................13

3 Experimental Procedure....................................................................................................................15

4 Results...............................................................................................................................................17

4.0 Stoichiometry............................................................................................................................17

4.1 Enthalpy of Reaction..................................................................................................................18

4.2 Arrhenius Parameters................................................................................................................19

5 Discussion..........................................................................................................................................22

5.0 Experimental Results.................................................................................................................22

5.0.1 Experimental Constants.....................................................................................................22

5.0.2 Stoichiometry.....................................................................................................................22

5.0.3 Enthalpy of Reaction..........................................................................................................24

5.0.4 Arrhenius parameters........................................................................................................26

5.1 Sources of error.........................................................................................................................27

iii

5.1.1 Error of Incomplete Mixing................................................................................................28

5.1.2 Error of Measuring Instruments.........................................................................................29

5.1.3 Error of Non Adiabatic Reactor..........................................................................................29

5.1.4 Error of Assumptions.........................................................................................................30

6 Conclusions........................................................................................................................................31

7 Nomenclature....................................................................................................................................32

8 References.........................................................................................................................................33

9 Bibliography.......................................................................................................................................33

A. Appendix : Data Recordings...............................................................................................................34

B. Appendix : Derived Data...................................................................................................................44

C Appendix : Sample Calculations........................................................................................................69

D. Appendix: Error Calculations.............................................................................................................74

E. Appendix: Previous Study..................................................................................................................77

G. Appendix: MSDS for Hydrogen Peroxide...........................................................................................79

H. Appendix: MSDS for Sodium Thiosulphate........................................................................................94

iv

List of TablesTable 1.1: Possible reactions between H2O2 and Na2S2O3........................................................................2Table 1.2: Theoretical results and relative error found in study by Cohen and Spencer...........................10Table 2.1: Practical equipment, specifications and quantities...................................................................11Table 4.1: Stoichiometric ratios.................................................................................................................18Table 4.2: Results for enthalpy of reaction................................................................................................19Table 4.: Results for Arrhenius Parameters...............................................................................................21

Table A 1:Recorded data for Run 1………………………………………………………………………………………………………..34 Table A 2:Recorded data for Run 2............................................................................................................34Table A 3:Recorded data for Run 3............................................................................................................35Table A 4:Recorded data for Run 4............................................................................................................36Table A 5: Recorded data for Run 5...........................................................................................................37Table A 6: Recorded data for Run 6...........................................................................................................38Table A 7: Recorded data for Run 7...........................................................................................................39Table A 8: Recorded data for Run 8...........................................................................................................40Table A 9: Recorded data for Run 9...........................................................................................................41Table A 10: Recorded data for Run 10.......................................................................................................42Table A 11: Recorded data for Run 11.......................................................................................................43

Table B 1:Experimental Constants.............................................................................................................44Table B 2: Parameters for each experimental Run....................................................................................45Table B 3:Calculations of enthalpy for each run with average Enthalpy....................................................46

Table B 4 I : Experimental parameters for all of Run 1..............................................................................47Table B 4 II: Experimental parameters for all of run 2...............................................................................48Table B 4 III: Experimental parameters for all of Run 3.............................................................................50Table B 4 IV: Experimental parameters for all of Run 4.............................................................................52Table B 4 V: Experimental parameters for all of Run 5..............................................................................54Table B 4 VI: Experimental parameters for all of Run 6.............................................................................56Table B 4 VII: Experimental parameters for all of Run 7............................................................................58Table B 4 VIII:Experimental parameters for all of Run 8............................................................................60Table B 4 IX: Experiment parameters for all of Run 9................................................................................62Table B 4 X: Experimental parameters for all of Run 10............................................................................64Table B 4 XI: Experimental parameters for all of Run 11...........................................................................66

Table D 1: Error Constants for experiment................................................................................................74Table D 2: Absolute Errors for each Run....................................................................................................75Table D 3: Relative Errors for each Run.....................................................................................................75Table D 4: Analytical Errors for each Run..................................................................................................76

v

List of FiguresFigure 1.1: Example of the plot created with change in temperature versus concentration ratio..............3Figure 1.2: Experimental Activation energy determination by Cohen and Spencer in 1962........................9Figure 2.1: Equipment used during the practical.......................................................................................11Figure 4.1: Plot of Total Temperature Difference against the Initial Concentration Ratio. Trend-line for runs 1-11 shown by y.................................................................................................................................17Figure 4.2: Trend line through data plots for runs 1 to 11 for Total Temperature Difference against the Limiting Concentration..............................................................................................................................18Figure 4.3: Plot of ln(k) against 1/T for runs 1 to 11..................................................................................20Figure 4.4: ln(k) against 1/T for Runs 8 and 9 only....................................................................................20Figure 4.5: ln(k) against 1/T with truncated data and a linear line of best fit............................................21

Figure B 1: Temperature Vs Initial Concentration Ratio to find Stoichiometric Ratio................................44Figure B 2: Plot of Temperature Change vs Clim for all runs.....................................................................45

Figure B 3 I: Temperature Vs Time for Run 1 with trend line....................................................................49Figure B 3 II: Temperature Vs Time for Run 2 with trend line....................................................................49Figure B 3 III: Temperature Vs Time for Run 3 with trend line...................................................................51Figure B 3 IV: Temperature Vs Time for Run 4 with trend line..................................................................53Figure B 3 V: Temperature Vs Time for Run 5 with trend line...................................................................55Figure B 3 VI: Temperature Vs Time for Run 6 with trend line..................................................................57Figure B 3 VII: Temperature Vs Time for Run 7 with trend line.................................................................59Figure B 3 VIII: Temperature Vs Time for Run 8 with trend line................................................................61Figure B 3 IX: Temperature Vs Time for Run 9 with trend line..................................................................63Figure B 3 X: Temperature Vs Time for Run 10 with trend line.................................................................65Figure B 3 XI: Temperature Vs Time for Run11 with trend line.................................................................67

Figure C 1: : A graph of T vs. t for all data points in Run 5 with fitted trend line fitted..............................71Figure C 2: Graph of all data point from all runs for ln(k) versus 1/T.........................................................73

vi

1 Introduction

1.0 Aim

The aim of this report is to study the kinetics of the reaction between sodium thiosulphate and

hydrogen peroxide under adiabatic batch conditions. Multiple reactions can occur between the

chemicals, so the stoichiometric ratio and the dominating reaction should be determined. The

enthalpy of the reaction and Arrhenius parameters were also investigated. The results are

compared with a previous study by Cohen and Spencer in 1962 so the accuracy of the results

could be determined.

1.1 Significance

Kinetics is the study of chemical reaction rates and mechanisms. (Fogler, 2006) Chemical

engineers require a vast knowledge of kinetics and reactor design so that a process or system

can be designed with distinct specifications. The kinetics of a reaction can be used to determine

the rate of reaction, enthalpy of reaction, stoichiometric proportions, Arrhenius parameters

etc. With the calculated data a suitable reactor can be designed to undertake the reaction, a

design that is economically viable and operates under safe and suitable conditions. Reaction

kinetics is important in many industries like oil recovery and pharmacokinetics. The majority of

artificial commercial products are made through industrial processes, process which require

production costs to be as low as possible and the process to be as efficient as possible. Reaction

kinetics describe the characteristics of a chemical reaction during the reaction.

1.2 Theory

The hydrogen peroxide and sodium thiosulphate used in this process can undergo several

feasible reactions to form different products. Each reaction has a different stoichiometric ratio

and different enthalpy of reaction. Hydrogen peroxide is a strong oxidisng agent and reacts with

sodium thiosulphate which is a strong reducing agent. The sulphur has multiple oxidization

1

states which allows it to form several bonds with over elements. Table 1.1 shows the multiple

reactions which can occur simultaneously in a reaction vessel along with their stoichiometric

ratio and enthalpy of reaction.

Table 1.1: Possible reactions between H2O2 and Na2S2O3

Reaction

Number

Reaction B٧/A٧ -ΔHR

(kJmol-1)

1 2Na2S2O3 + H2O2 → Na2S4O6 + 2NaOH 0.50 163.2

2 Na2S2O3 + H2O2 →Na2S2O4 + H2O 1.00 173.2

3 3Na2S2O3 + 4H2O2 → 2Na2S3O6 + 2NaOH +3H2O 1.33 512

4 3Na2S2O3 + 5H2O2 → Na2S4O6 +2Na2SO4 + 5H2O 1.67 432.2

5 2Na2S2O3 + 4H2O2 →Na2S3O6 + Na2SO4 +4H2O 2.00 596.2

1.3 Stoichiometric Ratio

As the enthalpies for each reaction are negative it has been identified that the reactions are

exothermic. Assuming the vessel used in the reaction is adiabatic, all heat produced is absorbed

by the mixture. This means a maximum temperature will occur in each reaction and the

temperature rise may be determined.

Temperature Rise (°K) = Tf-To

The graph of temperature rise verses initial concentration of reactants for each run a distinct

maximum will occur. This maximum occurs at the point representing the stoichiometric ratio

and equals the initial concentration ratio.

2

o

o

b

a

of TT

B

A

When reactants are mixed in stoichiometric ratio there is no reagent in excess, therefore

meaning both reagents completely react. For constant volume reactors, the maximum number

of moles of each reactant that fit into the reactant will react, thus the maximum heat will be

produced. The peak in the graph is distinct as no reagents are left throughout the reaction

which can absorb heat.

Equation 1, 2 and Figure 1.1 demonstrate how the concentration of ao, bo and the

stoichiometric ratio can be found respectively.

ao=astock∗V A .o

V total (1)

bo=bstock∗V B .o

V total (2)

Figure 1.1: Example of the plot created with change in temperature versus concentration ratio

3

1.4 Enthalpy of reaction

Usually one reactant limits the extent of reaction and as a result, the number of moles per litre

which react won’t equal the initial concentration of the reactant. Therefore the limiting

concentration of each reaction must be calculated otherwise the calculated enthalpy of

reaction will be higher than the actual enthalpy of reaction. The limiting concentration is

calculated through Equation 3 and is the smallest value between initial concentration of sodium

thiosulphate and the initial concentration of hydrogen peroxide divided by its stoichiometric

ratio. For this experiment, it is best to keep the sodium thiosulphate as the limiting reagent.

This is so possible side reactions of the sodium thiosulphate is mitigated (Cohen and Spencer,

1962) and thus the enthalpy of reaction is measured per mole of sodium thiosulphate.

c lim=MIN (bo ,ao .υB

υA

)(3)

By applying the steady state balance to the system, the temperature change can be directly

related to enthalpy of the reaction as seen in Equation 4.

(T f−T o )=−ΔHR .c lim

ρ .Cp (4)

By rearranging Equation 4 the enthalpy of the reaction can be calculated directly from Equation

5 or from a plot of temperature rise against the limiting concentration. Passing a line through

the origin of the plot of temperature rise against limiting concentration will have a slope of –

ΔHR/ρ.Cp as shown in Equation 6 and then the enthalpy can be calculated. In the practical both

methods are applied to find the enthalpy. The analytical enthalpy uses the arithmetic average

of all runs whilst the graphical enthalpy is derived from a line of best fit.

ΔH R=−(T f−T o )

c lim. ρ .C p

(5)

4

(T f−T o )=−ΔH R

ρ .Cp

.c lim(6)

The heat capacity, Cp , and density, ρ, of each stock solution is different to water, and thus every

solution mix will have varying densities and heat capacities. As the concentration of each of the

stock solutions is low, 1mol/L, the effect of the molecules in solution is insignificant thus the

two parameters can be assumed equal to water. The two parameters would need to be

calculated separately if higher concentrations of the chemicals were used.

1.5 Arrhenius Parameters

The reaction which takes place between the sodium thiosulphate and hydrogen peroxide is first

order and the rate law is described by Equation 7. As sodium thiosulphate is the limiting

reagent, the rate of reaction can be given as the negative change in concentration of sodium

thiosulphate with time.

r=−db

dt=k .a .b

(7)

As the system is adiabatic, it is assumed that shaft work is negligible and the enthalpy remains

constant with time. From the energy balance, the temperature and the rate of reaction may be

related by Equation 8.

dHdT

=ρ .C p .V .dTdt

+ΔH R .V .r=0(8)

5

The change in temperature with time has to be found using a plot of the data points. If a graph

is produced with temperature versus time, a line of best fit can be modeled to the plot. To get

the most accurate results possible, a quartic polynomial is fitted to the curve and the equation

can be lifted from the curve. The coefficients of the polynomial must be set so they have 12

significant figures otherwise there will be a significant round off error, see Section 5.1. This

equation can be derived such that a cubic is found representing the dT/dt at any point along the

graph. Each data point can then be substituted in for time to find the rate along the curve. This

is more accurate then the midpoint theorem and the curve generally has a good fit to the data

points.

Equation 8 can be rearranged and combined with Equations 9 and 10 to get the following

derivation.

k= 1a .b

. r (9)

r=ρ .C p .dTdt.

1−ΔH R (10)

If we combine Equation 8 now with Equation 10.

r= c limT f−T o

.dTdt (11)

Then Equation 12 for the rate constant, k, is produced when 11 is combined with 9.

6

k= 1a .b

.c l

im

T f−T o

.dTdt (12)

Equation 10 can be divided by Equation 9, and then integrated to obtain Equation 13.

ΔH R(b−bo )=ρ .Cp .(T−To ) (13)

If the enthalpy of reaction is substituted in from Equation 6, then Equation 14 can be developed

which is used to find the concentration of the sodium thiosulphate, b.

b=bo−c lim(T−T o )(T f−T o ) (14)

The concentration of hydrogen peroxide is found by conducting a mole balance for the system.

The equation used to calculate the value, a, is 15.

(a−ao )=νA

νB

.( b−bo )

Thus,

a=ao+ν A

νB

.(b−bo )(15)

7

The rate of reaction will vary with a change in temperature, and therefore must be considered.

The rate constant can be found which allows for the variable reaction rate. The rate constant

can be described using the Arrhenius Equation.

Arrhenius Equation, k=Ae(− E

RT)

Where,

K = rate constant (L/mol.s of H2O2)

A = Pre-exponential rate factor (L/mol.s of H2O2)

E = Activation Energy (J/mol)

R = Gas Constant (J/mol.K)

If we take the natural log of both sides, the Arrhenius equation becomes 16

ln (k )=ln ( A )− ER.1T (16)

If ln(k) is plotted against 1/T then the slope will be –E/R and the intercept will be ln(A)

This allows the calculation and A and E such that the accuracy and validation of the experiment

can be analysed.

1.6 Previous Work

In December of 1962, Cohen and Spencer released a paper titled “Determination of chemical

kinetics by calorimetry” and is found in Appendix E. The study was to determine the reaction

rate constants and activation energies of a system with multiple possible reactions. The

reactants used in the study were sodium thiosulphate and hydrogen peroxide. This experiment

8

was run closely to Cohen and Spencer’s and most of the same methods were used in finding the

results.

There are some key differences between the two methods and they are as follow-

- Cohen and Spencer assumed the calorimeter was non adiabatic

- The midpoint temperature was used to find the change in temperature with time, dT/dt.

- The natural log of the slope of the midpoint temperatures was plotted against the

reciprocal temperature to produce the activation energy seen in Figure 1.2

- Equation 16 was used to determine the reaction rate constant.

dTdt

=k (−ΔH ).(C p )syse−

ERT

a .b(16)

Figure 1.2: Experimental Activation energy determination by Cohen and Spencer in 1962

9

The results from the study can be found in Table 1.2 The original results were given different

units, so have been converted for comparison with experimental results. No error was specified

for the pre-exponential rate constant and the enthalpy of reaction.

Table 1.2: Theoretical results and relative error found in study by Cohen and Spencer

A (L/(s.g-

mol)) E (kJ/mol) -ΔHR (kJ/mol) v1/v2

Theoretical 6.85E+11 76.48 573.198 1.96

Error N/A 1.255 0.03

10

2 Experimental

2.0 Equipment

Figure 2.3: Equipment used during the practical

Table 2.1: Practical equipment, specifications and quantities

Equipment QuantityDigital Thermoprobe 1Reaction Vessel 1Stirring table 1Magnetic Stirrer 1Beakers 2Measuring Cylinders 4Funnel 2Mercury Thermometer 1GlovesMaterialsSodium Thiosulphate 1MHydrogen Peroxide 1MDistilled Water

Stop Watch

11

2.0.1 Stirring table and magnetic stirrer:

The automated stirring table has a level top on which the reaction vessel can be placed. The

top of the stirring table contains a rotating magnet which can be turned on and adjusted by

rotating the dial on the front. A magnetic stirrer is then placed inside the reaction vessel such

that the two magnets interact, and the magnetic bead rotates. The action of this causes the

reaction solutions to be mixed, and if rotating at a constant speed, the reaction mixture can be

evenly mixed. Once the speed is set, it is held constant for the remainder of the practical.

2.0.2 Thermo-probe:

A digital thermo-probe is used to measure the temperature of reaction mixture throughout the

reaction and the atmospheric temperature. The thermo-probe should be calibrated against a

mercury thermometer in warm and cold water to calculate any error in the device. Ensure that

probe is not held during the experiment as it measures the highest temperature along its

length.

2.0.3 Reaction Vessel:

The reaction vessel has been built to promote an adiabatic reaction within the vessel. The

reactants are held in a Pyrex beaker, which is surrounded by thick insulating foam and then

held in thin plastic container. A lid is then placed over the top of the vessel which has a foam

plug which is fitted into the beaker. The lid must be screwed into place such that there is a tight

fit. A small hole is present in the top of the lid so that the thermo probe can be inserted into

the reaction vessel.

12

2.1 Materials

Hydrogen Peroxide 1M:

Stock solution of hydrogen peroxide, H2O2 , is supplied at a concentration of 1 mol/L. The MSDS

for hydrogen peroxide is found in Appendix G and should be read before use. Hydrogen

peroxide deteriorates in direct sunlight, so fresh solution should be used and also stored in an

opaque bottle.

Sodium Thiosulphate 1M:

Stock solution of sodium thiosulphate, Na2S2O3 , is supplied at a concentration of 1 mol/L. The

MSDS for sodium thiosulphate is found in Appendix H and should be read be use.

2.2 Safety

Due to the dangerous nature of the chemicals used in this practical, anyone using the chemicals

must wear protective rubber gloves, long sleeves, long pants and safety glasses.

Sodium thiosulphate at low concentrations (<2%) is a low risk chemical but should be handled

with care. The MSDS found in Appendix H should be read and understood before the chemical

is handled and use. Safety procedures need to be understood incase of contamination. Major

spills are required to be reported to the demonstrator. Thorough rinsing with water should

mitigate any harm in the event of contamination, although the precautions found in the MSDS

should be followed.

Hydrogen peroxide even at low concentrations (<8%) is seen as a high risk chemical. Before its

use, the MSDS in Appendix G must be read. It has a moderate toxicity and high level hazard

when it makes bodily contact. As with sodium thiosulphate thorough rinsing with water should

mitigate any harm if contact occurs with eyes or skin. If swallowed water must be taken

immediately and medical attention maybe required if pain arises. Hydrogen Peroxide is a bleach

so contact with clothed my have a bleaching effect.

13

As distilled water is being used around electronic devices all spills should be cleaned up

immediately and the measurement of all liquids should occur away from the electronic devices

to avoid the chance of electrocution.

The laboratory is a hazardous environment due to the apparatus and chemicals used in the

room. Care must be taken when undertaking experiment and moving around room to minimize

the risk to your self, group members and other groups undertaking experiments.

14

3 Experimental Procedure

The following is a brief description of how the experiment was conducted.

1. Material Safety Data Sheets for sodium thiosulphate and hydrogen peroxide (Appendix

H and G respectively) must be read by all participating personnel.

2. All experimental equipment was arranged neatly on the bench space provided for the

practical.

3. The thermo probe was joined to the thermocouple and calibrated. This was done by

testing the thermo probe in hot and cold water baths and compared with the

temperatures given on the mercury thermometer.

4. The error of each of the measuring instruments and vessels was determined and

recorded.

5. The air and initial temperature of the two reactants was found and recorded.

6. The total volume of the reactant mixture is held constant at 200mL. The first

experiment was named Run 1. In Run 1, 100mL of water, 80mL of sodium thiosulphate

was measured and recorded as VB, and 20mL of hydrogen peroxide was measured and

recorded as VA.

7. The stirring table was turned on, with the magnetic stirrer placed in the vessel.

8. Both reactants were added to the reaction vessel and the lid quickly put into place, the

thermoprobe was also inserted into the reaction mixture.

9. As the reactants enter the vessel the stop watch was started and the initial temperature

was recorded.

10. The temperature of the reaction mixture was recorded every five seconds onto the

recording sheets. This continued until the temperature of the reactants became

constant (at least 60 seconds without a temperature rise), and a final temperature could

be recorded.

11. All liquids were emptied carefully from the reactant vessel into a waste disposal bucket.

12. The apparatus was then rinsed well with distilled water and dried with paper towel.

15

13. Steps 6 to 12 were then repeated with the VA /VB ratio increasing by .25 up to 2.5,

including ratios of 1.33 and 1.67. All raw data results can be found in Appendix A.

Once finished, all equipment was washed thoroughly, dried and returned back to their

cupboard.

16

4 Results

A complete set of raw data, derived data and errors involved from the experiment can be found

in Appendices A, B and D respectively.

Throughout the entire experiment, the following were taken as constant:

astock = 1.00 molL-1

bstock = 1.00 molL-1

Vtotal = 0.20 L ± 0.003L

ρ = 1000 gL-1

Cp = 4.183925359 Jg-1K-1

4.0 Stoichiometry

The total temperature difference was plotted against the initial concentration ratio for all

reactions. A trend line was fitted to the data to provide a maximum. Figure 4.1 shows the plot

of the Temperature Difference against the Initial Concentration Ratio with the distinct maxima.

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

f(x) = − 6.6303941588233 x² + 22.5097361907103 x − 0.0646813336873242R² = 0.966876524292153

Temperature Difference Vs Initial Concetration Ratio

ao/bo

Tf-T

i (de

g K)

17

Figure 4.4: Plot of Total Temperature Difference against the Initial Concentration Ratio. Trend-line for runs 1-11 shown by y.

From Figure 4.1 the equation of the line of best fit was derived to give the maximum. The

maximum of the concentration ratio was equal to 1.697, therefore υA/υB=1.697±0.0548. Table

4.1 summarizes the stoichiometric ratio found.

Table 4.1: Stoichiometric ratios

υA/υB (Experimental) υA/υB (Theoretical)

1.697 ± 0.0548 1.97 ±0.03

4.1 Enthalpy of Reaction

Two methods where used to calculate the enthalpy of reaction, a graphical method and an

analytical method. Equation 6 in Section 1 was used to find the analytical enthalpy of reaction

for each run then the average of all runs was taken. The graphical enthalpy of reaction was

found using the slope of the line through the plot of Temperature Difference against Limiting

Concentration. The plot is shown in Figure 4.2 and results shown in Table 4.2.

0.0500 0.0700 0.0900 0.1100 0.1300 0.1500 0.1700 0.19000

2

4

6

8

10

12

14

16

18

20f(x) = 106.376979431859 xR² = 0.997663050574185

Tf-Ti (°K) Vs clim

c lim

Tf-T

i

18

Figure 4.5: Trend line through data plots for runs 1 to 11 for Total Temperature Difference against the

Limiting Concentration.

Table 4.2: Results for enthalpy of reaction

-∆HR (Analytical) (kJmol-1) -∆HR (Graphical) (kJmol-1) -∆HR (Theoretical) (kJmol-1)

428.959 ± 56.68 445.09 ± 38.856 573.2

4.2 Arrhenius Parameters

The Arrhenius parameter was found using the concentration of hydrogen peroxide and sodium

thiosulphate at time t was calculated using Equations 14 and 15 in Section 1. The change in

temperature with time, dT/dt, was calculated using a plot of temperature against time. These

values can be found in Appendix B.

The reaction rate constant, k, was found using Equation 16, for each time interval in every run.

The natural log of these values, ln(k), could then be taken. By plotting the natural log of the

reaction rate constant against the inverse temperature, the Arrhenius parameters could be

found from a linear regression. The graph was plotted with all runs together in Figure 4.3, so

interpretations could be made. The data was then taken around Runs 8 and 9 and plotted,

shown in Figure 4.4.

19

0.003 0.003 0.004

-6.0000

-5.0000

-4.0000

-3.0000

-2.0000

-1.0000

0.00001/T vs ln(k)

run1run 2run 3run 4run 5run 6run 7run 8run 9run 10run 11

1/Tln

(k)

Figure 4.6: Plot of ln(k) against 1/T for runs 1 to 11.

0.003 0.003 0.004

-5.0000

-4.5000

-4.0000

-3.5000

-3.0000

-2.5000

-2.0000

-1.5000

-1.0000

-0.5000

0.00001/T vs ln(K)

run 9run 8

1/T

ln(k

)

Figure 4.7: ln(k) against 1/T for Runs 8 and 9 only.

20

The data was then truncated at ln(k) = -2 so that the exponential data plot was kept linear such

that the trend line would have a minimum amount of error. Thus Figure 4.5 was developed

with a trend line through the truncated data.

0.00325 0.00330 0.00335 0.00340 0.00345 0.00350

-5.0000

-4.5000

-4.0000

-3.5000

-3.0000

-2.5000

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

f(x) = NaN x + NaNR² = 0 1/T vs ln(k)

Modified 'Run 8 & 9'

Linear (Modified 'Run 8 & 9')

Run 8 & 9

1/T

ln(k

)

Figure 4.8: ln(k) against 1/T with truncated data and a linear line of best fit.

From Figure 4.5 the equation for the line of best fit was found to be:

ln(k) = -12609(1/T) + 39.22 (R2=0.9766) (17)

As the slope of Equation 17 was equal to the –E/R and the intercept was equal to ln(A), the

Table 4.3 could be collated.

Table 4.3: Results for Arrhenius Parameters

Arrhenius Parameters Experimental Theoretical

A (L.mol-1.s-1) 5.79×1011 6.85×1011

E (kJ.mol-1) 112.39 76.48 ± 1.255

21

5 Discussion

The accuracy and relevance of the experimental results from Section 4 need to be discussed,

including any errors associated with there results.

5.0 Experimental Results

5.0.1 Experimental Constants

The experimental constants determined at the start of the practical were assumed to remain

constant throughout the practical, although these constants contain some error in the values. It

was assumed the stock solutions were made on the day of the practical, but as hydrogen

peroxide is prone to deteriorate in sun light the actual concentration of the stick solution of

hydrogen peroxide may indeed have been lower than the recorded value. As more stock

solution had to be made during the practical by the chemistry lab, the two different stock

solutions may not have identical concentrations causing variations in initial concentrations

As the solutions of hydrogen peroxide and sodium thiosulphate are very dilute it is

approximated they have the same density and heat capacity as water. The number of

molecules within the system changes with time causing the density to differ slightly from the

theoretical density value. If the solutions weren’t diluted the heat capacity would have varied

significantly and would have needed to be calculated for each experiment.

As the variation of theoretical constant to actual value is minimal it is assumed that the actual

value remains constant, causing a negligible error.

5.0.2 Stoichiometry

The plot of temperature difference against initial concentration ratio shown in Figure 4.1

produces a trend line with a distinct maximum value. The temperature difference increase as

the initial concentration ratio approaches the stoichiometric ratio. The maximum temperature

22

change occurs when initial concentration ratio equals the stoichiometric ratio. The temperature

difference decreases as the initial concentration ratio moves away from the stoichiometric

ratio.

The maximum temperature reached is determined from the trend line fitted to the plot. From

runs 1-11 it was determined the trend line fitted to the data was appropriate to give a distinct

maximum. If a more accurate value was required more experiments could have been done with

initial ratios between 1.5 and 2 with no water to better determine the maximum, although

temperature change would be twice as big as that of runs 1-11.

The stoichiometric ratio error was calculated and is in Appendix D. The error in the temperature

is ±0.5°K which is quiet small and is due to the thermo probes accuracy. The largest error is

from the measuring of initial concentration ratio which arises from the measuring cylinders.

Three separate volume measurements were made for each run and the largest initial

concentration ratio was ±0.0548. The error in the adiabatic system in explained in Section 5.1.2

and is un-measurable.

The hydrogen peroxide and sodium thiosulphate can form five different reactions with different

stoichiometric ratios and enthalpies, which can be found in Table 1.1. The products formed in

some of the reactions can also participate in secondary reactions which will increase the

complexity of the reaction mixture. These reactions occur simultaneously, affecting the

enthalpy of the reaction and the stoichiometric ratio of the experimental results. This won’t

correspond to a single reaction’s properties.

The stoichiometric ratio for the experiment was calculated at 1.697 ± 0.0549 (3.24%) with and

enthalpy of -484 kJ/mol. These calculations correspond closely to reaction four in Table 1.1,

meaning this reaction is most dominant in the experiment.

23

Cohen and Spencer (1962) found their stoichiometric ratio equal to 1.96 ± 0.03 (1.5%). This

corresponds very closely to reaction 5 only, with only an insignificant amount of the other

reactions taking place. The difference in the two results (13%) can be justified by experimental

errors. These errors can include mixing, non-adiabatic system or poor measuring. These cannot

be calculated exactly and could increase the errors enough meaning that Cohen and Spencer’s

results are a viable solution to the experiment.

5.0.3 Enthalpy of Reaction

The enthalpy of reaction is found from the limiting concentration of the reaction mixture. The

limiting concentration had to be determined, which was found to be the concentration of

sodium thiosulphate which would fully react with hydrogen peroxide. This is dependent on

which reactant is in excess for the run. If sodium thiosulphate is in excess then the limiting

concentration is equal to the concentration of hydrogen peroxide divided by the stoichiometric

ratio, shown below.

If the hydrogen peroxide is in excess for all runs with an initial concentration ratio greater than

the stoichiometric ratio, the limiting concentration is equal to the initial concentration of

sodium thiosulphate as shown below.

These two equations produce Equation 4 (Section 1) where the lowest value of the two is equal

to the limiting concentration and is dependent on the initial concentration ratio. The relative

error for the limiting concentration is 8.73% which is relevant to the practical. This could be

reduced by using more accurate measuring cylinders.

24

C lim=ao υB

υA

( sodium thiosulphate in excess )

C lim=bo (hydrogen peroxide in excess)

The steady state energy balance relates the enthalpy of the reaction to the temperature

change. It can be rearranged to directly produce values for the enthalpy of reaction for each

run. The average of each run can be taken to find an analytical enthalpy of reaction. The

analytical enthalpy of reaction, ΔHR, was 428 kJ/mol ± 56.68 kJ/mol (14%), corresponding to the

enthalpy of reaction for reaction four, which corresponds to the stoichiometric ratio found as

well.

The enthalpy of reaction can also be found from a plot of temperature change against the

limiting concentration for each run. This plot produces a linear regression between the data

points from each run. With a R2 value of .9785 means the regression is close to each point. The

slope of the linear regression is equal to:

Slope =

106 .38=−ΔH R

ρ .C p

.

From calculations the value of the enthalpy of reaction was found equal to 445.09 kJ/mol ±

38.756kJ/mol, (8.73%), and was named ΔHR, graphical. As the linear regression fits so well, it can be

concluded that the error is caused mostly by the uncertainty in the limiting concentration of the

plot. The reduced error in the graphical enthalpy value means it is the more appropriate value

to be used.

Cohen and Spencer derived an enthalpy value of 573.2kJ/mol using a similar, yet unspecific

technique. The value relates closely to that of the number 5 reaction in Table 1.1, confirming

the previous findings that the reaction dominated in the system. No value for error was given

in the study. The variation between this previous result and the graphical enthalpy found in the

experiment is 22.3%. The two answers are very different. Cohen and Spencer found that the

reaction closely followed reaction 5 whilst the experiments undertaken in the practical found

25

the reaction followed reaction 4. This could be due to different techniques or the use of non-

adiabatic systems.

5.0.4 Arrhenius parameters

The reaction has been assumed first order throughout the practical allowing Equation 7 to

describe the rate of reaction. A relationship between the reaction rate constant and the

temperature of the reaction needs to be found. This relationship is described by the Arrhenius

Equation, where parameter A and E must be known. The parameters are found from a plot of

the natural logarithm of the rate constant against inverse temperature. The slope and intercept

of a linear regression gives the values of E and A.

The concentrations of sodium thiosulphate, b, and hydrogen peroxide, a, at any time in the

mixture can be found using Equations 16 and 15 respectively.

To find the rate constant the change in temperature with time was required at any interval for

every run. This was found by plotting the temperature against time for each run in Microsoft

Exel and fitting a polynomial regression to the data. A quartic polynomial was used as it gave a

best fit to the data and made computations minimal. As the coefficients for the quartic were

very small for higher powers a high number of significant figures were required to increase the

accuracy. With a high number of significant figures the error from change in temperature with

time is minimal.

Using the plot of experimental data the Arrhenius parameters, A and E, can be found. This is

done by rearranging the Arrhenius Equation so that it equals Equation 16. Using the plot of ln(k)

against inverse temperature the Equation can be used, with the slope equaling –E/R and the

intercept of ln(k) equal to ln(A). The data of one run would have been sufficient but accuracy

would be increased with more runs so all data was plotted as seen in Figure (all lnkv1/T). At low

temperatures the data is too scattered due to the small limiting concentration, meaning the

26

amount of reactants teat react is small and temperature rise is also small. For this reason only

two runs were used.

The data didn’t fit a linear regression due to a large variance of data due to increasing

temperature, T. This is not experimental error but due to calculation methods. The rate

constant, k, is inversely proportional to the concentration of reactants during the experiment.

This explains why k increases exponentially as the concentration moves towards zero as the

reaction takes place. After analysing each run it can be seen that this begins to occur when ln(k)

is greater than minus two. This was solved by truncating the data at ln(k)>-2. Figure 4.4 shows

the use of runs eight and nine to be analysed, whilst Figure 4.5 shows the truncated results with

the regression line.

From Figure 4.5 an Activation Energy, E, was found to be 112.39 kJ/mol -1. The difference of

32.97% from Cohen and Spencer (76.48 kJmol-1 ± 1.255) suggests that this could be due to the

different reactions between the past result and this practical.

Deriving the intercept of the regression gave a pre-exponential rate factor, A, equal to

5.79×1011L.mol-1.s-1. This gave a 15.5% difference with the result attained by Cohen and Spencer

(6.85×1011 L/mol.s).

Considering all the errors in the variables, it is possible the data obtained is valid even though

the result shows reaction 4 is most relevant were previous work found reaction 5 was most

relevant.

5.1 Sources of error

Observations made during the experiment identified various problems with the equipment and

the practical set up. These problems lead to errors in results, some which could have been

27

avoided in set up. Calculation errors have been discussed in Section 5.0. All calculated errors

can be found in Appendix D.

Errors for the Arrhenius parameter were not found. Not all values needed to find the errors for

the Arrhenius parameters were not found for ever run. This is due to the calculations required

to find the error for ln(k) for each run. Error in k were large in the errors that were found and

was due to the inverse proportionality to concentration of reagents. This meant error bars for

the graph of ln (k) against 1/T would have been very large even when the linear regression had

an accurate fit.

5.1.1 Error of Incomplete Mixing

As the reactor vessel could not be seen through the foam insulation it was impossible to tell

whether complete mixing was occurring by the stirring table and magnetic stirrer. To test if

mixing occurred sufficiently the beaker was filled with 200mL of water and set in the insulation

without the lid. Several magnetic beads where tested at a range of stirring speeds to determine

the best bead at the best speed by visual inspection.

The error for incomplete mixing could not be calculated although conclusion could be made

from the observation of the derived data. As each experiment stopped when no temperature

change was recorded after sixty seconds, it was then assumed all limiting reactant was

consumed in the reaction. From observing the data for reactant concentrations for derived data

it was seen the limiting reactant was completely reacted in the reaction. It can be assumed this

is due to complete mixing.

The change in temperature with time plot can also be used to observe the consistency and

extent of mixing. As the plots of each run had no sudden change in trends, out lying points or

high scattering, it can be concluded that the mixing of the chemicals was adequate.

28

5.1.2 Error of Measuring Instruments

The digital thermo probe was found to read within .5°K with a mercury thermometer when

calibrating. As the thermo probe only read to the nearest whole °K a plus or minus .5°K error

was determined. If the thermo probe read to .1°K the error in the enthalpy of reaction , dT/dt

and the concentrations of sodium thiosulphate and hydrogen peroxide with time would have

been reduced.

The measuring cylinders supplied for the practical had a resolution of 2mL and were adequate

for this experiment. As several measuring cylinders were used in each run, the error in each

cylinder had a compounding effect causing small errors to become more significant. This was

more significant when small volumes were being used. Using a pipette would have made errors

insignificant in the measurements.

5.1.3 Error of Non Adiabatic Reactor

The system used for the reaction was assumed to be adiabatic due to the thick insulation,

meaning all heat from the reaction is kept within the reaction mixture. It was obvious the

reaction vessel was not adiabatic as heat was absorbed by the reaction vessel. Heat produced

by the reaction could easily escape to the surroundings through convection via the small hole in

the lid for the thermo probe and also due to the lid not being air tight.

It was also evident that heat was conducted by the reaction vessel as the vessel was warm to

touch following the disposal of reagents after each run. This resulted in the maximum

temperature not being as high as that for an adiabatic system. The error from the system

increased as the temperature change increased. The extent of this error could not be measured

directly meaning error bars could not be included.

The error from the non adiabatic system could be minimised by making the reaction vessel out

of something other than Pyrex, something that has a lower convection heat transfer coefficient.

29

The lid could be made air tight to seal the vessel to stop heat be released. A more suitable

vessel would be a bomb calorimeter as the industry uses that equipment for similar

experiments and it better replicates adiabatic conditions.

5.1.4 Error of Assumptions

It was assumed that density and heat capacity remained constant and was equal to water. How

ever this not true as the molecular compositions of the reagents changes these properties.

These differences are proportional to the concentration of each reactant. So as the

concentrations of the reactants are low the effect of the molecules is minimal and therefore

negligible, so the properties of water can be used. There is however an error present and an

experiment conducted at higher concentrations would need to have the individual properties

calculated and accounted in each run.

30

6 Conclusions

From the conducted experiment it was determined the stoichiometric coefficient was 1.697 ±

0.0548. Comparing this value to that found by Cohen and Spencer in a previous study it was

13.4% less. This ratio meant that the dominating reaction in the experiment was Reaction 4

compared to Reaction 5 found by Cohen and Spencer.

3Na2S2O3 + 5H2O2 → Na2S4O6 +2Na2SO4 + 5H2O Reaction 4

2Na2S2O3 + 4H2O2 →Na2S3O6 + Na2SO4 +4H2O Reaction 5

The enthalpy of the reaction was calculated for the experiment and derived as 445.09 kJmol -1 ±

38.85 kJmol-1, which when compared to Cohen and Spencer’s value was 22.3% less. This is most

likely due to the different reactions that were determined to dominate between the two

experiments.

The pre-exponential rate constant was than determined to be 5.79×1011 Lmol-1s-1 which

deviated by 15.5% from the previous study by Cohen and Spencer which may also be explained

by the different dominating reactions

The activation energy for the reaction was calculated to be 112.39 kJmol -1. This deviated by

nearly 33% from Cohen and Spencer’s results and maybe due to either the different reactions

determined to dominate or the non-adiabatic vessel used to conduct the experiment.

31

7 Nomenclature

Symbolsa Concentration of H2O2 mol.L-1

A Pre-exponential rate factor L.mol-1.s -1 of H2O2

b Concentration of Na2S2O3 mol.L-1

C Concentration of solution molL-1

Clim Limiting concentration mol.L-1 of Na2S2O3

Cp Heat capacity of solution J.g-1.K-1

Cp,sys Heat capacity of whole system J.g-1.K-1

E Activation Energy J. mol-1

H Enthalpy of solution J∆HR Enthalpy change of reaction kJ. mol-1 of Na2S2O3

∆HR,graphical Enthalpy of reaction using graphical method kJ. mol-1 of Na2S2O3

∆HR, analytical Enthalpy of reaction using analytical method kJ. mol-1 of Na2S2O3

k Rate constant L.mol-1.s-1 of H2O2

m Mass gMW Molecular Weight g.mol-1 r Reaction rate mol.L-1.s-1 of Na2S2O3

R Gas constant J.mo-l-1.K-1

t Time sT Temperature °KV Volume L

Greek Symbols∆ Change in٧ Stoichiometric Coefficientρ Density of the solution g.L-1

SubscriptsA Denotes H2O2

B Denotes Na2S2O3

water Denotes H20air Denotes airf Final conditiono Initial conditionstock Standard solution conditions

32

total Total

8 References

Chemwatch MSDS, chemwatch.adelaide.edu.au, Site accessed 2/08/2010

Fogler, S 2006, Elements in Chemical Reaction Engineeering, Fourth Edition, Pearson Prentice Hall Fourth Edition, US

Cohen, Spencer 1962, Determination of Chemical Kinetics by Calirometery, Chemical Engineering Progress, vol 58, no.12 (1962) pp 40-41

9 Bibliography

Holman, JP 2002, Heat Transfer, Ninth Edition, McGraw Hill Publishing, Ninth Edition

Smith, Van Ness 2005, Introduction to Chemical Engineering Thermodynamics, Pearson Prentice Hall Fourth Edition, US

Housecroft, Constable 2006, Chemistry, Third Edition, Pearson Prentice Hall Fourth Edition, US

33

A. Appendix : Data RecordingsAll data was recorded in interval of 5 seconds until a maximum temperature was recorded for at least 60 seconds. In some cases this is not shown. All volumes are measured in litres (L) and temperature in degrees Celsius (0C)Table A 1:Recorded data for Run 1 Table A 2:Recorded data for Run 2

Va/Vb= 0.25 Tao= 15 Va/Vb= 0.5 Tao= 15Va= 0.02 Tbo= 13 Va= 0.035 Tbo= 13Vb= 0.08 Tair= 14 Vb= 0.065 Tair= 14

Vwater= 0.1 Tf= 17

Vwater= 0.1 Tf= 25

Tf-Ti= 3 Tf-Ti= 11Time Temp Time Temp Time Temp Time Temp

5 14 2:35 16 5 14 2:35 2110 14 2:40 16 10 14 2:40 2115 14 2:45 16 15 14 2:45 2120 14 2:50 16 20 15 2:50 2125 14 2:55 16 25 15 2:55 2230 14 3:00 16 30 15 3:00 2235 14 3:05 16 35 15 3:05 2240 14 3:10 16 40 15 3:10 2245 14 3:15 16 45 16 3:15 2250 14 3:20 16 50 16 3:20 2255 15 3:25 16 55 16 3:25 23

1:00 15 3:30 16 1:00 17 3:30 231:05 15 3:35 17 1:05 17 3:35 231:10 15 3:40 17 1:10 17 3:40 231:15 15 3:45 17 1:15 17 3:45 231:20 15 3:50 17 1:20 18 3:50 231:25 15 3:55 17 1:25 18 3:55 231:30 15 4:00 17 1:30 18 4:00 231:35 15 4:05 17 1:35 18 4:05 241:40 15 4:10 17 1:40 19 4:10 241:45 15 4:15 17 1:45 19 4:15 241:50 15 4:20 17 1:50 19 4:20 241:55 15 4:25 17 1:55 19 4:25 242:00 15 4:30 17 2:00 19 4:30 242:05 15 2:05 20 4:35 242:10 16 2:10 20 4:40 242:15 16 2:15 20 4:45 242:20 16 2:20 20 4:50 242:25 16 2:25 20 4:55 24

34

2:30 16 2:30 21 5:00 24Table A 3:Recorded data for Run 3

Va/Vb= 0.75 Tao= 15Va= 0.04 Tbo= 13Vb= 0.06 Tair= 13

Vwater= 0.1 Tf= 28

Tf-Ti= 14Time Temp Time Temp Time Temp

5 14 2:35 22 5:05 2710 14 2:40 22 5:10 2715 14 2:45 22 5:15 2720 15 2:50 23 5:20 2725 15 2:55 23 5:25 2730 15 3:00 23 5:30 2735 16 3:05 23 5:35 2740 16 3:10 24 5:40 2745 16 3:15 24 5:45 2750 16 3:20 24 5:50 2755 17 3:25 24 5:55 27

1:00 17 3:30 24 6:00 271:05 17 3:35 24 6:05 271:10 18 3:40 25 6:10 281:15 18 3:45 25 6:15 281:20 18 3:50 25 6:20 281:25 18 3:55 25 6:25 281:30 19 4:00 25 6:30 281:35 19 4:05 25 6:35 281:40 19 4:10 25 6:40 281:45 19 4:15 26 6:45 281:50 20 4:20 26 6:50 281:55 20 4:25 26 6:55 282:00 20 4:30 26 7:00 282:05 20 4:35 26 7:05 282:10 21 4:40 26 7:10 282:15 21 4:45 26 7:15 282:20 21 4:50 26 7:20 282:25 21 4:55 272:30 22 5:00 27

35

Table A 4:Recorded data for Run 4

Va/Vb= 1 Tao= 15Va= 0.05 Tbo= 14Vb= 0.05 Tair= 15

Vwater= 0.1 Tf= 31


5 14 2:35 24 5:05 3010 14 2:40 24 5:10 2915 15 2:45 24 5:15 3020 15 2:50 24 5:20 3025 16 2:55 25 5:25 3030 16 3:00 25 5:30 3035 16 3:05 25 5:35 3040 16 3:10 25 5:40 3045 17 3:15 26 5:45 3050 17 3:20 26 5:50 3055 18 3:25 26 5:55 30

1:00 18 3:30 26 6:00 301:05 18 3:35 26 6:05 311:10 18 3:40 27 6:10 311:15 19 3:45 27 6:15 311:20 19 3:50 27 6:20 311:25 19 3:55 27 6:25 311:30 20 4:00 27 6:30 311:35 20 4:05 28 6:35 311:40 20 4:10 28 6:40 311:45 21 4:15 28 6:45 311:50 21 4:20 28 6:50 311:55 21 4:25 28 6:55 312:00 22 4:30 28 7:00 312:05 22 4:35 29 7:05 312:10 22 4:40 29 7:10 312:15 22 4:45 29 7:15 312:20 23 4:50 29 7:20 312:25 23 4:55 29 7:25 312:30 23 5:00 29 7:30 31

36

Table A 5: Recorded data for Run 5


Vwater= 0.1 Tf= 31


5 14 2:35 23 5:05 2910 14 2:40 24 5:10 2915 15 2:45 24 5:15 2920 15 2:50 24 5:20 2925 15 2:55 24 5:25 2930 16 3:00 24 5:30 2935 16 3:05 25 5:35 2940 16 3:10 25 5:40 3045 17 3:15 25 5:45 3050 17 3:20 25 5:50 3055 17 3:25 26 5:55 30

1:00 18 3:30 26 6:00 301:05 18 3:35 26 6:05 301:10 18 3:40 26 6:10 301:15 19 3:45 26 6:15 301:20 19 3:50 27 6:20 301:25 19 3:55 27 6:25 301:30 19 4:00 27 6:30 301:35 20 4:05 27 6:35 311:40 20 4:10 27 6:40 311:45 20 4:15 27 6:45 311:50 21 4:20 28 6:50 311:55 21 4:25 28 6:55 312:00 21 4:30 28 7:00 312:05 21 4:35 28 7:05 312:10 22 4:40 28 7:10 312:15 22 4:45 28 7:15 312:20 22 4:50 28 7:20 312:25 23 4:55 29 7:25 31

37

2:30 23 5:00 29 7:30 31



Vwater= 0.1 Tf= 32Tf-Ti= 18

Time Temp Time Temp Time Temp5 14 2:35 23 5:05 30

10 14 2:40 24 5:10 3015 14 2:45 24 5:15 3020 15 2:50 24 5:20 3025 15 2:55 24 5:25 3030 15 3:00 25 5:30 3035 16 3:05 25 5:35 3040 16 3:10 25 5:40 3045 16 3:15 25 5:45 3150 16 3:20 26 5:50 3155 17 3:25 26 5:55 31

1:00 18 3:30 26 6:00 311:05 18 3:35 27 6:05 311:10 18 3:40 27 6:10 311:15 18 3:45 27 6:15 311:20 19 3:50 27 6:20 311:25 19 3:55 27 6:25 311:30 19 4:00 28 6:30 321:35 20 4:05 28 6:35 321:40 20 4:10 28 6:40 321:45 20 4:15 28 6:45 321:50 20 4:20 28 6:50 321:55 21 4:25 28 6:55 322:00 21 4:30 29 7:00 322:05 22 4:35 29 7:05 322:10 22 4:40 29 7:10 322:15 22 4:45 29 7:15 322:20 22 4:50 29 7:20 32

38

2:25 23 4:55 29 7:25 322:30 23 5:00 30 7:30 32



Vwater= 0.1 Tf= 33


5 14 2:35 24 5:05 3010 15 2:40 25 5:10 3115 15 2:45 25 5:15 3120 16 2:50 25 5:20 3125 16 2:55 25 5:25 3130 16 3:00 26 5:30 3135 17 3:05 26 5:35 3140 17 3:10 26 5:40 3145 17 3:15 26 5:45 3150 18 3:20 27 5:50 3255 18 3:25 27 5:55 32

1:00 18 3:30 27 6:00 321:05 18 3:35 27 6:05 321:10 19 3:40 28 6:10 321:15 19 3:45 28 6:15 321:20 20 3:50 28 6:20 321:25 20 3:55 28 6:25 321:30 20 4:00 28 6:30 321:35 21 4:05 28 6:35 321:40 21 4:10 29 6:40 321:45 21 4:15 29 6:45 321:50 22 4:20 29 6:50 321:55 22 4:25 29 6:55 332:00 22 4:30 29 7:00 332:05 23 4:35 30 7:05 332:10 23 4:40 30 7:10 33

39

2:15 23 4:45 30 7:15 332:20 23 4:50 30 7:20 332:25 24 4:55 30 7:25 332:30 24 5:00 30 7:30 33



Vwater= 0.1 Tf= 32


5 14 2:35 24 5:05 3010 15 2:40 24 5:10 3015 15 2:45 24 5:15 3020 15 2:50 24 5:20 3025 16 2:55 25 5:25 3030 16 3:00 25 5:30 3035 16 3:05 25 5:35 3040 17 3:10 25 5:40 3045 17 3:15 26 5:45 3050 17 3:20 26 5:50 3155 18 3:25 26 5:55 31

1:00 18 3:30 26 6:00 311:05 18 3:35 26 6:05 311:10 19 3:40 27 6:10 311:15 19 3:45 27 6:15 311:20 19 3:50 27 6:20 311:25 19 3:55 27 6:25 311:30 20 4:00 28 6:30 311:35 20 4:05 28 6:35 311:40 20 4:10 28 6:40 321:45 21 4:15 28 6:45 321:50 21 4:20 28 6:50 321:55 21 4:25 28 6:55 322:00 22 4:30 29 7:00 32

40

2:05 22 4:35 29 7:05 322:10 22 4:40 29 7:10 322:15 22 4:45 29 7:15 322:20 23 4:50 29 7:20 322:25 23 4:55 29 7:25 322:30 23 5:00 29 7:30 32


Va/Vb= 2 Tao= 16Va= 0.067 Tbo= 13Vb= 0.033 Tair= 14

Vwater= 0.1 Tf= 33Tf-Ti= 18

Time Temp Time Temp Time Temp5 15 2:35 24 5:05 30

10 15 2:40 24 5:10 3015 15 2:45 25 5:15 3120 15 2:50 25 5:20 3125 16 2:55 25 5:25 3130 16 3:00 25 5:30 3135 16 3:05 26 5:35 3140 17 3:10 26 5:40 3145 17 3:15 26 5:45 3150 17 3:20 26 5:50 3155 18 3:25 27 5:55 31

1:00 18 3:30 27 6:00 311:05 19 3:35 27 6:05 311:10 19 3:40 27 6:10 321:15 19 3:45 27 6:15 321:20 19 3:50 28 6:20 321:25 20 3:55 28 6:25 321:30 20 4:00 28 6:30 321:35 20 4:05 28 6:35 321:40 21 4:10 28 6:40 321:45 21 4:15 29 6:45 321:50 21 4:20 29 6:50 321:55 22 4:25 29 6:55 32

41

2:00 22 4:30 29 7:00 322:05 22 4:35 29 7:05 332:10 23 4:40 29 7:10 332:15 23 4:45 30 7:15 332:20 23 4:50 30 7:20 332:25 23 4:55 30 7:25 332:30 24 5:00 30 7:30 33



Vwater= 0.1 Tf= 31


5 15 2:35 23 5:05 2910 15 2:40 24 5:10 3015 15 2:45 24 5:15 3020 16 2:50 24 5:20 3025 16 2:55 24 5:25 3030 16 3:00 25 5:30 3035 17 3:05 25 5:35 3040 17 3:10 25 5:40 3045 17 3:15 26 5:45 3050 18 3:20 26 5:50 3055 18 3:25 26 5:55 30

1:00 18 3:30 26 6:00 301:05 19 3:35 26 6:05 301:10 19 3:40 27 6:10 311:15 19 3:45 27 6:15 311:20 19 3:50 27 6:20 311:25 20 3:55 27 6:25 311:30 20 4:00 27 6:30 311:35 20 4:05 28 6:35 311:40 21 4:10 28 6:40 311:45 21 4:15 28 6:45 31

42

1:50 21 4:20 28 6:50 311:55 21 4:25 28 6:55 312:00 22 4:30 28 7:00 312:05 22 4:35 28 7:05 312:10 22 4:40 28 7:10 312:15 23 4:45 29 7:15 312:20 23 4:50 29 7:20 312:25 23 4:55 29 7:25 312:30 23 5:00 29 7:30 31



Vwater= 0.1 Tf= 30


5 15 2:35 24 5:05 2910 15 2:40 24 5:10 2915 15 2:45 24 5:15 2920 16 2:50 24 5:20 2925 16 2:55 25 5:25 2930 16 3:00 25 5:30 2935 17 3:05 25 5:35 2940 17 3:10 26 5:40 2945 17 3:15 26 5:45 2950 18 3:20 26 5:50 2955 18 3:25 26 5:55 30

1:00 19 3:30 26 6:00 301:05 19 3:35 26 6:05 301:10 19 3:40 27 6:10 301:15 19 3:45 27 6:15 301:20 20 3:50 27 6:20 301:25 20 3:55 27 6:25 301:30 20 4:00 27 6:30 301:35 20 4:05 27 6:35 30

43

1:40 21 4:10 28 6:40 301:45 21 4:15 28 6:45 301:50 21 4:20 28 6:50 301:55 22 4:25 28 6:55 302:00 22 4:30 28 7:00 302:05 22 4:35 28 7:05 302:10 22 4:40 28 7:10 302:15 23 4:45 28 7:15 302:20 23 4:50 28 7:20 302:25 23 4:55 28 7:25 302:30 24 5:00 29 7:30 30

44

B. Appendix : Derived Data

Constants

Table B 1:Experimental Constants

astock = 1 mol/Lbstock = 1 mol/LVtotal = 0.2 L٧a/٧b = 1.697 ρ = 1000 g/LCp= 4.184 J/(g.K)

Stoichiometry

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

20

f(x) = − 6.6303941588233 x² + 22.5097361907103 x − 0.0646813336873242R² = 0.966876524292153

Temperature Difference Vs Initial Concetration Ratio

ao/bo

Tf-T

i (de

g K)

Figure B 1: Temperature Vs Initial Concentration Ratio to find Stoichiometric Ratio

45

Enthalpy of ReactionTable B 2: Parameters for each experimental Run

run VA (L) VB (L) ao (mol/L) bo (mol/L) ao/boclim (mol/L) Tf-Ti (°K)

1 0.02 0.08 0.1 0.4 0.25 0.0589 32 0.035 0.065 0.175 0.325 0.54 0.1031 113 0.04 0.06 0.2 0.3 0.67 0.1179 144 0.05 0.05 0.25 0.25 1.00 0.1473 175 0.055 0.045 0.275 0.225 1.22 0.1621 176 0.06 0.04 0.3 0.2 1.50 0.1768 187 0.062 0.038 0.31 0.19 1.63 0.1827 198 0.064 0.036 0.32 0.18 1.78 0.1800 189 0.067 0.033 0.335 0.165 2.03 0.1650 18

10 0.07 0.03 0.35 0.15 2.33 0.1500 1611 0.072 0.028 0.36 0.14 2.57 0.1400 15

Graphical Enthalpy

0.0500 0.0700 0.0900 0.1100 0.1300 0.1500 0.1700 0.19000

2

4

6

8

10

12

14

16

18

20f(x) = 105.582094177363 xR² = 0.993796543750969

Tf-Ti (°K) Vs clim

c lim

Tf-T

i

Figure B 2: Plot of Temperature Change vs Clim for all runs

Slope of line of best fit=

−ΔH R

ρ .C p =106.38If rearranged, graphical enthalpy, ∆HR,graphical= -(106.38)(4.184)(1000)

= -445093.92 J/mol ∆HR,graphical = -445.1 kJ/mol

46

Analytical EnthalpyTable B 3:Calculations of enthalpy for each run with average Enthalpy.

Run clim Tf-to -ΔHR (J/mol)

-ΔHR (kJ/mol)

10.0589275

19 3 213007.44 213.00744

20.1031231

59 11446301.30

29446.30130

29

30.1178550

38 14 497017.36 497.01736

40.1473187

98 17482816.86

4482.81686

4

50.1620506

78 17438924.42

18438.92442

18

60.1767825

57 18 426014.88 426.01488

70.1826753

09 19435176.49

03435.17649

038 0.18 18 418400 418.4

9 0.165 18456436.36

36456.43636

36

10 0.15 16446293.33

33446.29333

33

11 0.14 15448285.71

43448.28571

43

Average=428.06128

82

Arithmetic average taken for all experimental runs to find analytical enthalpy.Therefore, -∆HR,analytical = 428.06 kJ/mol

47

Table B 4 I : Experimental parameters for all of Run 1

t (s) T (°K) a (mol/L) b (mol/l) dT/dt

k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.1000 0.400 0.0101 0.0050 0.003 -5.306110 287 0.1000 0.400 0.0106 0.0052 0.003 -5.255920 287 0.1000 0.400 0.0111 0.0055 0.003 -5.210630 287 0.1000 0.400 0.0116 0.0057 0.003 -5.170140 287 0.1000 0.400 0.0120 0.0059 0.003 -5.134250 288 0.0667 0.380 0.0124 0.0096 0.003 -4.647060 288 0.0667 0.380 0.0127 0.0099 0.003 -4.620170 288 0.0667 0.380 0.0130 0.0101 0.003 -4.597680 288 0.0667 0.380 0.0132 0.0103 0.003 -4.579690 288 0.0667 0.380 0.0134 0.0104 0.003 -4.5662

100 288 0.0667 0.380 0.0135 0.0105 0.003 -4.5574110 288 0.0667 0.380 0.0136 0.0105 0.003 -4.5534120 289 0.0333 0.361 0.0136 0.0222 0.003 -3.8084130 289 0.0333 0.361 0.0135 0.0220 0.003 -3.8150140 289 0.0333 0.361 0.0133 0.0218 0.003 -3.8274150 289 0.0333 0.361 0.0131 0.0214 0.003 -3.8461160 289 0.0333 0.361 0.0127 0.0208 0.003 -3.8719170 289 0.0333 0.361 0.0123 0.0201 0.003 -3.9056180 289 0.0333 0.361 0.0118 0.0193 0.003 -3.9484190 289 0.0333 0.361 0.0112 0.0183 0.003 -4.0018200 289 0.0333 0.361 0.0105 0.0171 0.003 -4.0678210 290 0.0000 0.341 0.0097 0.0000 0.003220 290 0.0000 0.341 0.0087 0.0000 0.003230 290 0.0000 0.341 0.0077 0.0000 0.003240 290 0.0000 0.341 0.0065 0.0000 0.003250 290 0.0000 0.341 0.0052 0.0000 0.003260 290 0.0000 0.341 0.0038 0.0000 0.003

48

270 290 0.0000 0.341 0.0023 0.0000 0.003280 290 0.0000 0.341 0.0006 0.0000 0.003290 290 0.0000 0.341 -0.0012 0.0000 0.003300 290 0.0000 0.341 -0.0032 0.0000 0.003

Table B 4 II: Experimental parameters for all of run 2


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.1750 0.325 0.0360 0.00593 0.003 -5.127010 287 0.1750 0.325 0.0393 0.00647 0.003 -5.040320 288 0.1591 0.316 0.0420 0.00783 0.003 -4.849430 288 0.1591 0.316 0.0441 0.00823 0.003 -4.799440 288 0.1591 0.316 0.0457 0.00854 0.003 -4.762950 289 0.1432 0.306 0.0469 0.01003 0.003 -4.602360 290 0.1273 0.297 0.0476 0.01182 0.003 -4.438270 290 0.1273 0.297 0.0479 0.01189 0.003 -4.431980 291 0.1114 0.288 0.0478 0.01401 0.003 -4.268090 291 0.1114 0.288 0.0474 0.01388 0.003 -4.2772

100 292 0.0955 0.278 0.0467 0.01647 0.003 -4.1060110 292 0.0955 0.278 0.0456 0.01610 0.003 -4.1287120 292 0.0955 0.278 0.0443 0.01564 0.003 -4.1578130 293 0.0795 0.269 0.0428 0.01875 0.003 -3.9765140 293 0.0795 0.269 0.0410 0.01799 0.003 -4.0179150 294 0.0636 0.259 0.0391 0.02222 0.003 -3.8066160 294 0.0636 0.259 0.0371 0.02107 0.003 -3.8600170 294 0.0636 0.259 0.0350 0.01985 0.003 -3.9193180 295 0.0477 0.250 0.0327 0.02573 0.003 -3.6601190 295 0.0477 0.250 0.0305 0.02396 0.003 -3.7313200 295 0.0477 0.250 0.0282 0.02219 0.003 -3.8083210 296 0.0318 0.241 0.0260 0.03184 0.003 -3.4472220 296 0.0318 0.241 0.0238 0.02916 0.003 -3.5350230 296 0.0318 0.241 0.0217 0.02658 0.003 -3.6274240 296 0.0318 0.241 0.0197 0.02415 0.003 -3.7235250 297 0.0159 0.231 0.0179 0.04557 0.003 -3.0886260 297 0.0159 0.231 0.0162 0.04133 0.003 -3.1862

49

270 297 0.0159 0.231 0.0148 0.03762 0.003 -3.2803280 297 0.0159 0.231 0.0135 0.03452 0.003 -3.3662290 297 0.0159 0.231 0.0126 0.03211 0.003 -3.4385300 297 0.0159 0.231 0.0120 0.03048 0.003 -3.4908310 297 0.0159 0.231 0.0117 0.02969 0.003 -3.5170320 298 0.0000 0.222 0.0117 0.00000 0.003330 298 0.0000 0.222 0.0122 0.00000 0.003340 298 0.0000 0.222 0.0130 0.00000 0.003350 298 0.0000 0.222 0.0144 0.00000 0.003360 298 0.0000 0.222 0.0162 0.00000 0.003

0 50 100 150 200 250 300 350285.5

286

286.5

287

287.5

288

288.5

289

289.5

290

290.5

f(x) = − 1.6930565E-10 x⁴ − 0.0000000403927933 x³ + 0.0000266508495 x² + 0.01028685176 x + 287

Run 1 dT/dt

Time (s)

Tem

pe

ratu

re (

de

g K

)

Figure B 3 I: Temperature Vs Time for Run 1 with trend line

0 50 100 150 200 250 300 350 400280

285

290

295

300

f(x) = 1.31189195E-09 x⁴ − 0.00000100443837 x³ + 0.00017791129 x² + 0.036001433058 x + 287R² = 0.998491108344519

Run 2 dT/dt

time (s)

Te

mp

eratu

re

(d

eg

K)

Figure B 3 II: Temperature Vs Time for Run 2 with trend line

50

Table B 4 III: Experimental parameters for all of Run 3


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.2000 0.300 0.0552 0.0090 0.00348 -4.705910 287 0.2000 0.300 0.0560 0.0092 0.00348 -4.691720 288 0.1857 0.292 0.0566 0.0103 0.00347 -4.579530 288 0.1857 0.292 0.0569 0.0103 0.00347 -4.574040 289 0.1714 0.283 0.0570 0.0115 0.00346 -4.463150 289 0.1714 0.283 0.0568 0.0115 0.00346 -4.465260 290 0.1571 0.275 0.0565 0.0129 0.00345 -4.353770 291 0.1429 0.266 0.0560 0.0145 0.00344 -4.236380 291 0.1429 0.266 0.0553 0.0143 0.00344 -4.248790 292 0.1286 0.258 0.0545 0.0161 0.00342 -4.1267

100 292 0.1286 0.258 0.0535 0.0158 0.00342 -4.1453110 293 0.1143 0.249 0.0523 0.0180 0.00341 -4.0161120 293 0.1143 0.249 0.0510 0.0176 0.00341 -4.0409130 294 0.1000 0.241 0.0496 0.0202 0.00340 -3.9008140 294 0.1000 0.241 0.0481 0.0196 0.00340 -3.9317150 295 0.0857 0.233 0.0465 0.0229 0.00339 -3.7760160 295 0.0857 0.233 0.0448 0.0221 0.00339 -3.8131170 296 0.0714 0.224 0.0431 0.0264 0.00338 -3.6342180 296 0.0714 0.224 0.0412 0.0253 0.00338 -3.6777190 297 0.0571 0.216 0.0393 0.0313 0.00337 -3.4631200 297 0.0571 0.216 0.0374 0.0298 0.00337 -3.5134210 297 0.0571 0.216 0.0355 0.0282 0.00337 -3.5671220 298 0.0429 0.207 0.0335 0.0370 0.00336 -3.2970230 298 0.0429 0.207 0.0315 0.0348 0.00336 -3.3581240 298 0.0429 0.207 0.0295 0.0326 0.00336 -3.4231250 298 0.0429 0.207 0.0275 0.0304 0.00336 -3.4920260 299 0.0286 0.199 0.0256 0.0442 0.00334 -3.1181270 299 0.0286 0.199 0.0237 0.0410 0.00334 -3.1953

51

280 299 0.0286 0.199 0.0219 0.0378 0.00334 -3.2766290 299 0.0286 0.199 0.0201 0.0347 0.00334 -3.3622300 300 0.0143 0.191 0.0183 0.0662 0.00333 -2.7156310 300 0.0143 0.191 0.0167 0.0603 0.00333 -2.8092320 300 0.0143 0.191 0.0152 0.0547 0.00333 -2.9063330 300 0.0143 0.191 0.0137 0.0495 0.00333 -3.0061340 300 0.0143 0.191 0.0124 0.0447 0.00333 -3.1076350 300 0.0143 0.191 0.0112 0.0404 0.00333 -3.2091360 300 0.0143 0.191 0.0101 0.0366 0.00333 -3.3082370 301 0.0000 0.182 0.0092 0.0000 0.00332380 301 0.0000 0.182 0.0085 0.0000 0.00332390 301 0.0000 0.182 0.0079 0.0000 0.00332400 301 0.0000 0.182 0.0075 0.0000 0.00332410 301 0.0000 0.182 0.0073 0.0000 0.00332420 301 0.0000 0.182 0.0074 0.0000 0.00332430 301 0.0000 0.182 0.0076 0.0000 0.00332440 301 0.0000 0.182 0.0080 0.0000 0.00332450 301 0.0000 0.182 0.0087 0.0000 0.00332

0 50 100 150 200 250 300 350 400 450 500280

285

290

295

300

305

f(x) = 4.6972905E-10 x⁴ − 0.000000426256318 x³ + 0.000045717325973 x² + 0.055238918593 x + 286.657261795R² = 0.996124575441447

Run 3 dT/dt

time (s)

Tem

pe

ratu

re (

de

gK)

Figure B 3 III: Temperature Vs Time for Run 3 with trend line.

52

Table B 4 IV: Experimental parameters for all of Run 4


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.2500 0.250 0.0710 0.0098 0.003 -4.620410 287 0.2500 0.250 0.0706 0.0098 0.003 -4.626720 288 0.2361 0.242 0.0700 0.0106 0.003 -4.544330 289 0.2222 0.234 0.0693 0.0116 0.003 -4.459040 289 0.2222 0.234 0.0686 0.0114 0.003 -4.470550 290 0.2083 0.225 0.0677 0.0125 0.003 -4.383460 291 0.1944 0.217 0.0667 0.0137 0.003 -4.292270 291 0.1944 0.217 0.0656 0.0135 0.003 -4.308780 292 0.1806 0.209 0.0644 0.0148 0.003 -4.214490 293 0.1667 0.201 0.0631 0.0163 0.003 -4.1142

100 293 0.1667 0.201 0.0618 0.0160 0.003 -4.1358110 294 0.1528 0.193 0.0604 0.0178 0.003 -4.0305120 295 0.1389 0.185 0.0589 0.0199 0.003 -3.9168130 295 0.1389 0.185 0.0573 0.0194 0.003 -3.9437140 296 0.1250 0.176 0.0557 0.0219 0.003 -3.8216150 296 0.1250 0.176 0.0540 0.0212 0.003 -3.8522160 297 0.1111 0.168 0.0523 0.0242 0.003 -3.7194170 297 0.1111 0.168 0.0505 0.0234 0.003 -3.7539180 298 0.0972 0.160 0.0487 0.0271 0.003 -3.6071190 298 0.0972 0.160 0.0468 0.0261 0.003 -3.6459200 299 0.0833 0.152 0.0450 0.0308 0.003 -3.4804210 299 0.0833 0.152 0.0430 0.0295 0.003 -3.5239220 300 0.0694 0.144 0.0411 0.0357 0.003 -3.3321230 300 0.0694 0.144 0.0391 0.0340 0.003 -3.3808240 300 0.0694 0.144 0.0372 0.0323 0.003 -3.4323250 301 0.0556 0.135 0.0352 0.0406 0.003 -3.2050260 301 0.0556 0.135 0.0332 0.0383 0.003 -3.2628

53

270 301 0.0556 0.135 0.0313 0.0360 0.003 -3.3241280 302 0.0417 0.127 0.0293 0.0479 0.003 -3.0391290 302 0.0417 0.127 0.0273 0.0447 0.003 -3.1083300 302 0.0417 0.127 0.0254 0.0415 0.003 -3.1819310 302 0.0417 0.127 0.0235 0.0384 0.003 -3.2605320 303 0.0278 0.119 0.0216 0.0565 0.003 -2.8727330 303 0.0278 0.119 0.0197 0.0517 0.003 -2.9630340 303 0.0278 0.119 0.0179 0.0469 0.003 -3.0602350 303 0.0278 0.119 0.0161 0.0422 0.003 -3.1654360 303 0.0278 0.119 0.0144 0.0376 0.003 -3.2798370 304 0.0139 0.111 0.0127 0.0713 0.003 -2.6407380 304 0.0139 0.111 0.0110 0.0621 0.003 -2.7788390 304 0.0139 0.111 0.0095 0.0532 0.003 -2.9329400 304 0.0139 0.111 0.0079 0.0447 0.003 -3.1069410 304 0.0139 0.111 0.0065 0.0366 0.003 -3.3069420 304 0.0139 0.111 0.0051 0.0289 0.003 -3.5425430 304 0.0139 0.111 0.0039 0.0217 0.003 -3.8306440 304 0.0139 0.111 0.0027 0.0149 0.003 -4.2047450 304 0.0139 0.111 0.0015 0.0087 0.003 -4.7494

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 2.0244333E-10 x⁴ − 0.000000207103753 x³ − 0.000019229846 x² + 0.07103171305 x + 286.611378353R² = 0.99751970373902

Run 4 dT/dt

time (s)

Tem

pe

ratu

re (

de

gK)

Figure B 3 IV: Temperature Vs Time for Run 4 with trend line.

54

Table B 4 V: Experimental parameters for all of Run 5


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.2750 0.225 0.0634 0.0098 0.003 -4.628010 287 0.2750 0.225 0.0640 0.0099 0.003 -4.619720 288 0.2588 0.215 0.0643 0.0110 0.003 -4.510930 289 0.2426 0.206 0.0644 0.0123 0.003 -4.399540 289 0.2426 0.206 0.0643 0.0123 0.003 -4.401050 290 0.2265 0.196 0.0640 0.0137 0.003 -4.289160 291 0.2103 0.187 0.0635 0.0154 0.003 -4.172670 291 0.2103 0.187 0.0629 0.0153 0.003 -4.182780 292 0.1941 0.177 0.0621 0.0172 0.003 -4.063190 292 0.1941 0.177 0.0612 0.0169 0.003 -4.0785

100 293 0.1779 0.168 0.0601 0.0192 0.003 -3.9542110 294 0.1618 0.158 0.0588 0.0219 0.003 -3.8208120 294 0.1618 0.158 0.0575 0.0214 0.003 -3.8437130 295 0.1456 0.149 0.0561 0.0247 0.003 -3.7017140 295 0.1456 0.149 0.0545 0.0240 0.003 -3.7295150 296 0.1294 0.139 0.0529 0.0280 0.003 -3.5758160 297 0.1132 0.130 0.0512 0.0332 0.003 -3.4041170 297 0.1132 0.130 0.0494 0.0321 0.003 -3.4394180 297 0.1132 0.130 0.0476 0.0309 0.003 -3.4771190 298 0.0971 0.120 0.0457 0.0374 0.003 -3.2869200 298 0.0971 0.120 0.0438 0.0358 0.003 -3.3297210 299 0.0809 0.111 0.0419 0.0446 0.003 -3.1100220 299 0.0809 0.111 0.0399 0.0425 0.003 -3.1579230 300 0.0647 0.101 0.0379 0.0553 0.003 -2.8950240 300 0.0647 0.101 0.0360 0.0524 0.003 -2.9480250 300 0.0647 0.101 0.0340 0.0496 0.003 -3.0035

55

260 301 0.0485 0.092 0.0321 0.0689 0.003 -2.6748270 301 0.0485 0.092 0.0302 0.0649 0.003 -2.7352280 301 0.0485 0.092 0.0284 0.0609 0.003 -2.7980290 301 0.0485 0.092 0.0266 0.0571 0.003 -2.8628300 302 0.0324 0.082 0.0249 0.0895 0.003 -2.4140310 302 0.0324 0.082 0.0233 0.0836 0.003 -2.4822320 302 0.0324 0.082 0.0217 0.0780 0.003 -2.5513330 302 0.0324 0.082 0.0202 0.0727 0.003 -2.6209340 303 0.0162 0.072 0.0189 0.1536 0.003 -1.8732350 303 0.0162 0.072 0.0177 0.1436 0.003 -1.9407360 303 0.0162 0.072 0.0166 0.1346 0.003 -2.0054370 303 0.0162 0.072 0.0156 0.1267 0.003 -2.0657380 303 0.0162 0.072 0.0148 0.1201 0.003 -2.1197390 303 0.0162 0.072 0.0141 0.1147 0.003 -2.1657400 304 0.0000 0.063 0.0136 0.0000 0.003410 304 0.0000 0.063 0.0133 0.0000 0.003420 304 0.0000 0.063 0.0132 0.0000 0.003430 304 0.0000 0.063 0.0132 0.0000 0.003440 304 0.0000 0.063 0.0135 0.0000 0.003450 304 0.0000 0.063 0.0140 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 4.265978E-10 x⁴ − 0.0000003855484071 x³ + 0.0000323987611 x² + 0.063442830998 x + 286.746633408R² = 0.997077423002322

Run 5 dT/dt

time (s)

Tem

pera

ture

(deg

K)

Figure B 3 V: Temperature Vs Time for Run 5 with trend line.

56

Table B 4 VI: Experimental parameters for all of Run 6


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.3000 0.200 0.0568 0.0093 0.003 -4.677110 287 0.3000 0.200 0.0587 0.0096 0.003 -4.644720 288 0.2833 0.190 0.0603 0.0110 0.003 -4.510830 288 0.2833 0.190 0.0616 0.0112 0.003 -4.489840 289 0.2667 0.180 0.0626 0.0128 0.003 -4.360150 290 0.2500 0.171 0.0633 0.0146 0.003 -4.228060 291 0.2333 0.161 0.0638 0.0167 0.003 -4.092370 291 0.2333 0.161 0.0640 0.0168 0.003 -4.088780 292 0.2167 0.151 0.0640 0.0192 0.003 -3.951790 292 0.2167 0.151 0.0638 0.0192 0.003 -3.9553

100 293 0.2000 0.141 0.0633 0.0220 0.003 -3.8148110 293 0.2000 0.141 0.0627 0.0218 0.003 -3.8249120 294 0.1833 0.131 0.0619 0.0253 0.003 -3.6789130 295 0.1667 0.121 0.0609 0.0295 0.003 -3.5220140 295 0.1667 0.121 0.0597 0.0290 0.003 -3.5411150 296 0.1500 0.112 0.0584 0.0343 0.003 -3.3735160 297 0.1333 0.102 0.0570 0.0412 0.003 -3.1886170 297 0.1333 0.102 0.0554 0.0401 0.003 -3.2165180 298 0.1167 0.092 0.0537 0.0492 0.003 -3.0123190 298 0.1167 0.092 0.0519 0.0475 0.003 -3.0461200 299 0.1000 0.082 0.0501 0.0599 0.003 -2.8157210 299 0.1000 0.082 0.0481 0.0575 0.003 -2.8554220 300 0.0833 0.072 0.0461 0.0751 0.003 -2.5886230 300 0.0833 0.072 0.0440 0.0717 0.003 -2.6346240 301 0.0667 0.063 0.0419 0.0988 0.003 -2.3147250 301 0.0667 0.063 0.0398 0.0937 0.003 -2.3672

57

260 301 0.0667 0.063 0.0376 0.0887 0.003 -2.4231270 302 0.0500 0.053 0.0354 0.1322 0.003 -2.0238280 302 0.0500 0.053 0.0333 0.1241 0.003 -2.0868290 302 0.0500 0.053 0.0311 0.1161 0.003 -2.1534300 303 0.0333 0.043 0.0290 0.1995 0.003 -1.6120310 303 0.0333 0.043 0.0269 0.1852 0.003 -1.6862320 303 0.0333 0.043 0.0249 0.1713 0.003 -1.7642330 303 0.0333 0.043 0.0230 0.1579 0.003 -1.8459340 304 0.0167 0.033 0.0211 0.3761 0.003 -0.9779350 304 0.0167 0.033 0.0193 0.3442 0.003 -1.0666360 304 0.0167 0.033 0.0176 0.3140 0.003 -1.1583370 304 0.0167 0.033 0.0160 0.2859 0.003 -1.2521380 304 0.0167 0.033 0.0146 0.2600 0.003 -1.3470390 305 0.0000 0.023 0.0133 0.0000 0.003400 305 0.0000 0.023 0.0121 0.0000 0.003410 305 0.0000 0.023 0.0111 0.0000 0.003420 305 0.0000 0.023 0.0103 0.0000 0.003430 305 0.0000 0.023 0.0096 0.0000 0.003440 305 0.0000 0.023 0.0092 0.0000 0.003450 305 0.0000 0.023 0.0089 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 4.974355E-10 x⁴ − 0.000000527567232 x³ + 0.00010155932 x² + 0.056849978265 x + 286.716710718R² = 0.997470009007813

Run 6 dT/dt

time (s)

tem

pe

ratu

re (

de

gK)

Figure B 3 VI: Temperature Vs Time for Run 6 with trend line.

58

Table B 4 VII: Experimental parameters for all of Run 7


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.3100 0.190 0.0294 0.00480 0.003 -5.339610 288 0.2937 0.180 0.0292 0.00530 0.003 -5.240020 289 0.2774 0.171 0.0290 0.00589 0.003 -5.134530 289 0.2774 0.171 0.0290 0.00589 0.003 -5.134540 290 0.2611 0.161 0.0288 0.00659 0.003 -5.022350 291 0.2447 0.152 0.0286 0.00743 0.003 -4.902760 291 0.2447 0.152 0.0286 0.00743 0.003 -4.902770 292 0.2284 0.142 0.0285 0.00844 0.003 -4.774680 293 0.2121 0.132 0.0283 0.00969 0.003 -4.636990 293 0.2121 0.132 0.0283 0.00969 0.003 -4.6369

100 294 0.1958 0.123 0.0281 0.01124 0.003 -4.4879110 295 0.1795 0.113 0.0279 0.01322 0.003 -4.3258120 295 0.1795 0.113 0.0279 0.01322 0.003 -4.3258130 296 0.1632 0.103 0.0277 0.01579 0.003 -4.1482140 296 0.1632 0.103 0.0277 0.01579 0.003 -4.1482150 297 0.1468 0.094 0.0275 0.01922 0.003 -3.9519160 298 0.1305 0.084 0.0274 0.02393 0.003 -3.7326170 298 0.1305 0.084 0.0274 0.02393 0.003 -3.7326180 299 0.1142 0.075 0.0272 0.03067 0.003 -3.4845190 299 0.1142 0.075 0.0272 0.03067 0.003 -3.4845200 300 0.0979 0.065 0.0270 0.04080 0.003 -3.1990210 300 0.0979 0.065 0.0270 0.04080 0.003 -3.1990220 301 0.0816 0.055 0.0268 0.05708 0.003 -2.8633230 301 0.0816 0.055 0.0268 0.05708 0.003 -2.8633240 301 0.0816 0.055 0.0268 0.05708 0.003 -2.8633250 302 0.0653 0.046 0.0267 0.08577 0.003 -2.4561

59

260 302 0.0653 0.046 0.0267 0.08577 0.003 -2.4561270 302 0.0653 0.046 0.0267 0.08577 0.003 -2.4561280 303 0.0489 0.036 0.0265 0.14379 0.003 -1.9394290 303 0.0489 0.036 0.0265 0.14379 0.003 -1.9394300 303 0.0489 0.036 0.0265 0.14379 0.003 -1.9394310 304 0.0326 0.027 0.0263 0.29183 0.003 -1.2316320 304 0.0326 0.027 0.0263 0.29183 0.003 -1.2316330 304 0.0326 0.027 0.0263 0.29183 0.003 -1.2316340 304 0.0326 0.027 0.0263 0.29183 0.003 -1.2316350 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956360 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956370 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956380 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956390 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956400 305 0.0163 0.017 0.0261 0.90882 0.003 -0.0956410 306 0.0000 0.007 0.0259 0.00000 0.003420 306 0.0000 0.007 0.0259 0.00000 0.003430 306 0.0000 0.007 0.0259 0.00000 0.003440 306 0.0000 0.007 0.0259 0.00000 0.003450 306 0.0000 0.007 0.0259 0.00000 0.003

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 4.0366431E-10 x⁴ − 0.000000362587756 x³ + 0.0000211547747 x² + 0.06930472673 x + 287.202606713R² = 0.99765610050637

Run 7 dT/dt

time (s)

tem

pe

ratu

re (

de

g K

)

Figure B 3 VII: Temperature Vs Time for Run 7 with trend line.

60

Table B 4 VIII:Experimental parameters for all of Run 8


k (L/(mol.s))

1/T (1/degC) ln(k)

0 287 0.3200 0.180 0.0643 0.0112 0.003 -4.495410 288 0.3030 0.170 0.0646 0.0125 0.003 -4.378620 288 0.3030 0.170 0.0648 0.0126 0.003 -4.376230 289 0.2861 0.160 0.0648 0.0141 0.003 -4.258240 290 0.2691 0.150 0.0646 0.0160 0.003 -4.135450 290 0.2691 0.150 0.0642 0.0159 0.003 -4.140660 291 0.2521 0.140 0.0637 0.0181 0.003 -4.014170 292 0.2352 0.130 0.0631 0.0206 0.003 -3.880280 292 0.2352 0.130 0.0624 0.0204 0.003 -3.892390 293 0.2182 0.120 0.0615 0.0235 0.003 -3.7517

100 293 0.2182 0.120 0.0605 0.0231 0.003 -3.7681110 294 0.2012 0.110 0.0594 0.0268 0.003 -3.6186120 295 0.1842 0.100 0.0581 0.0316 0.003 -3.4558130 295 0.1842 0.100 0.0568 0.0309 0.003 -3.4785140 296 0.1673 0.090 0.0555 0.0368 0.003 -3.3013150 296 0.1673 0.090 0.0540 0.0359 0.003 -3.3282160 297 0.1503 0.080 0.0524 0.0436 0.003 -3.1323170 297 0.1503 0.080 0.0508 0.0423 0.003 -3.1633180 298 0.1333 0.070 0.0492 0.0527 0.003 -2.9431190 298 0.1333 0.070 0.0475 0.0509 0.003 -2.9783200 299 0.1164 0.060 0.0457 0.0655 0.003 -2.7253210 299 0.1164 0.060 0.0440 0.0630 0.003 -2.7648220 300 0.0994 0.050 0.0422 0.0849 0.003 -2.4665230 300 0.0994 0.050 0.0404 0.0812 0.003 -2.5104240 301 0.0824 0.040 0.0386 0.1169 0.003 -2.1461250 301 0.0824 0.040 0.0367 0.1114 0.003 -2.1943

61

260 301 0.0824 0.040 0.0349 0.1060 0.003 -2.2448270 302 0.0655 0.030 0.0331 0.1688 0.003 -1.7792280 302 0.0655 0.030 0.0314 0.1598 0.003 -1.8340290 302 0.0655 0.030 0.0296 0.1509 0.003 -1.8910300 302 0.0655 0.030 0.0279 0.1423 0.003 -1.9499310 303 0.0485 0.020 0.0263 0.2711 0.003 -1.3052320 303 0.0485 0.020 0.0247 0.2547 0.003 -1.3678330 303 0.0485 0.020 0.0232 0.2389 0.003 -1.4318340 303 0.0485 0.020 0.0217 0.2238 0.003 -1.4969350 304 0.0315 0.010 0.0203 0.6449 0.003 -0.4387360 304 0.0315 0.010 0.0190 0.6038 0.003 -0.5045370 304 0.0315 0.010 0.0178 0.5657 0.003 -0.5697380 304 0.0315 0.010 0.0167 0.5308 0.003 -0.6333390 304 0.0315 0.010 0.0157 0.4995 0.003 -0.6942400 305 0.0145 0.000 0.0149 0.0000 0.003410 305 0.0145 0.000 0.0141 0.0000 0.003420 305 0.0145 0.000 0.0135 0.0000 0.003430 305 0.0145 0.000 0.0130 0.0000 0.003440 305 0.0145 0.000 0.0127 0.0000 0.003450 305 0.0145 0.000 0.0126 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 3.2560896E-10 x⁴ − 0.000000312209752 x³ + 0.0000212413573 x² + 0.06428392384 x + 287.075611207R² = 0.997474704803678

Run 8 dT/dt

time (s)

tem

pera

ture

(deg

K)

Figure B 3 VIII: Temperature Vs Time for Run 8 with trend line.

62

Table B 4 IX: Experiment parameters for all of Run 9


k (L/(mol.s))

1/T (1/degC) ln(k)

0 288 0.3350 0.165 0.0542 0.0090 0.003 -4.711910 288 0.3350 0.165 0.0568 0.0094 0.003 -4.665520 288 0.3350 0.165 0.0589 0.0098 0.003 -4.628330 289 0.3194 0.156 0.0607 0.0112 0.003 -4.494140 290 0.3039 0.147 0.0621 0.0128 0.003 -4.361050 290 0.3039 0.147 0.0631 0.0130 0.003 -4.344760 291 0.2883 0.138 0.0638 0.0147 0.003 -4.216870 292 0.2728 0.128 0.0641 0.0168 0.003 -4.086780 292 0.2728 0.128 0.0642 0.0168 0.003 -4.085890 293 0.2572 0.119 0.0640 0.0191 0.003 -3.9565

100 294 0.2417 0.110 0.0635 0.0219 0.003 -3.8218110 294 0.2417 0.110 0.0627 0.0216 0.003 -3.8335120 295 0.2261 0.101 0.0618 0.0248 0.003 -3.6955130 296 0.2106 0.092 0.0606 0.0288 0.003 -3.5481140 296 0.2106 0.092 0.0592 0.0281 0.003 -3.5709150 297 0.1950 0.083 0.0577 0.0329 0.003 -3.4151160 297 0.1950 0.083 0.0560 0.0319 0.003 -3.4449170 298 0.1794 0.073 0.0542 0.0377 0.003 -3.2771180 298 0.1794 0.073 0.0522 0.0364 0.003 -3.3136190 299 0.1639 0.064 0.0502 0.0438 0.003 -3.1293200 299 0.1639 0.064 0.0481 0.0419 0.003 -3.1724210 300 0.1483 0.055 0.0459 0.0516 0.003 -2.9649220 300 0.1483 0.055 0.0437 0.0491 0.003 -3.0144230 301 0.1328 0.046 0.0414 0.0624 0.003 -2.7740

63

240 301 0.1328 0.046 0.0392 0.0590 0.003 -2.8298250 301 0.1328 0.046 0.0370 0.0557 0.003 -2.8884260 302 0.1172 0.037 0.0348 0.0741 0.003 -2.6019270 302 0.1172 0.037 0.0326 0.0696 0.003 -2.6656280 302 0.1172 0.037 0.0305 0.0651 0.003 -2.7313290 303 0.1017 0.028 0.0286 0.0936 0.003 -2.3685300 303 0.1017 0.028 0.0267 0.0875 0.003 -2.4364310 303 0.1017 0.028 0.0249 0.0817 0.003 -2.5043320 304 0.0861 0.018 0.0233 0.1354 0.003 -1.9992330 304 0.0861 0.018 0.0219 0.1271 0.003 -2.0629340 304 0.0861 0.018 0.0206 0.1198 0.003 -2.1219350 304 0.0861 0.018 0.0196 0.1137 0.003 -2.1744360 304 0.0861 0.018 0.0187 0.1088 0.003 -2.2179370 305 0.0706 0.009 0.0181 0.2573 0.003 -1.3577380 305 0.0706 0.009 0.0178 0.2525 0.003 -1.3764390 305 0.0706 0.009 0.0178 0.2516 0.003 -1.3797400 305 0.0706 0.009 0.0180 0.2550 0.003 -1.3665410 305 0.0706 0.009 0.0185 0.2628 0.003 -1.3364420 305 0.0706 0.009 0.0194 0.2753 0.003 -1.2899430 306 0.0550 0.000 0.0207 0.0000 0.003440 306 0.0550 0.000 0.0223 0.0000 0.003450 306 0.0550 0.000 0.0243 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 7.7904011E-10 x⁴ − 0.000000723029621 x³ + 0.00013928113 x² + 0.05419520974 x + 287.448149861R² = 0.997291453135603

Run 9 dT/dt

T (°K)Polynomial (T (°K))

time (s)

tem

pera

ture

(deg

K)

Figure B 3 IX: Temperature Vs Time for Run 9 with trend line.

64

Table B 4 X: Experimental parameters for all of Run 10


k (L/(mol.s))

1/T (1/degC) ln(k)

0 288 0.3500 0.150 0.0602 0.0108 0.003 -4.532610 288 0.3500 0.150 0.0604 0.0108 0.003 -4.530020 289 0.3341 0.141 0.0604 0.0121 0.003 -4.418430 289 0.3341 0.141 0.0603 0.0120 0.003 -4.419840 290 0.3182 0.131 0.0601 0.0135 0.003 -4.305450 291 0.3023 0.122 0.0598 0.0152 0.003 -4.185360 291 0.3023 0.122 0.0594 0.0151 0.003 -4.192470 292 0.2864 0.113 0.0588 0.0171 0.003 -4.067380 292 0.2864 0.113 0.0582 0.0169 0.003 -4.078090 293 0.2705 0.103 0.0575 0.0193 0.003 -3.9465

100 294 0.2545 0.094 0.0567 0.0223 0.003 -3.8049110 294 0.2545 0.094 0.0558 0.0219 0.003 -3.8211120 295 0.2386 0.084 0.0548 0.0255 0.003 -3.6692130 295 0.2386 0.084 0.0537 0.0250 0.003 -3.6891140 296 0.2227 0.075 0.0525 0.0295 0.003 -3.5241150 296 0.2227 0.075 0.0513 0.0288 0.003 -3.5479160 297 0.2068 0.066 0.0500 0.0345 0.003 -3.3659170 297 0.2068 0.066 0.0486 0.0336 0.003 -3.3937180 298 0.1909 0.056 0.0472 0.0412 0.003 -3.1894190 298 0.1909 0.056 0.0457 0.0399 0.003 -3.2215200 299 0.1750 0.047 0.0442 0.0505 0.003 -2.9866210 299 0.1750 0.047 0.0426 0.0486 0.003 -3.0235220 300 0.1591 0.038 0.0409 0.0643 0.003 -2.7445

65

230 300 0.1591 0.038 0.0392 0.0616 0.003 -2.7867240 300 0.1591 0.038 0.0375 0.0589 0.003 -2.8318250 301 0.1432 0.028 0.0357 0.0832 0.003 -2.4871260 301 0.1432 0.028 0.0339 0.0790 0.003 -2.5388270 301 0.1432 0.028 0.0321 0.0747 0.003 -2.5942280 301 0.1432 0.028 0.0302 0.0704 0.003 -2.6537290 302 0.1273 0.019 0.0284 0.1114 0.003 -2.1945300 302 0.1273 0.019 0.0265 0.1040 0.003 -2.2636310 303 0.1114 0.009 0.0246 0.2205 0.003 -1.5117320 303 0.1114 0.009 0.0226 0.2033 0.003 -1.5930330 303 0.1114 0.009 0.0207 0.1860 0.003 -1.6818340 303 0.1114 0.009 0.0188 0.1688 0.003 -1.7793350 303 0.1114 0.009 0.0169 0.1515 0.003 -1.8873360 303 0.1114 0.009 0.0149 0.1342 0.003 -2.0081370 304 0.0955 0.000 0.0130 0.0000 0.003380 304 0.0955 0.000 0.0111 0.0000 0.003390 304 0.0955 0.000 0.0093 0.0000 0.003400 304 0.0955 0.000 0.0074 0.0000 0.003410 304 0.0955 0.000 0.0056 0.0000 0.003420 304 0.0955 0.000 0.0038 0.0000 0.003430 304 0.0955 0.000 0.0020 0.0000 0.003440 304 0.0955 0.000 0.0002 0.0000 0.003450 304 0.0955 0.000 -0.0015 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500280

285

290

295

300

305

310

f(x) = 1.5768228E-10 x⁴ − 0.000000212573254 x³ + 0.0000109637497 x² + 0.06021739581 x + 287.64279437R² = 0.997037680793761

Run 10 dT/dt

time (s)

tem

pera

ture

(deg

K)

Figure B 3 X: Temperature Vs Time for Run 10 with trend line

66

Table B 4 XI: Experimental parameters for all of Run 11


k (L/(mol.s))

1/T (1/degC) ln(k)

0 288 0.360 0.1400 0.063 0.0116 0.003 -4.453810 288 0.360 0.1400 0.063 0.0117 0.003 -4.447220 289 0.344 0.1307 0.063 0.0132 0.003 -4.330230 289 0.344 0.1307 0.063 0.0132 0.003 -4.330640 290 0.328 0.1213 0.063 0.0148 0.003 -4.213150 291 0.312 0.1120 0.063 0.0167 0.003 -4.090460 292 0.297 0.1027 0.062 0.0190 0.003 -3.961170 292 0.297 0.1027 0.061 0.0188 0.003 -3.973880 293 0.281 0.0933 0.060 0.0215 0.003 -3.839290 293 0.281 0.0933 0.059 0.0211 0.003 -3.8576

100 294 0.265 0.0840 0.058 0.0243 0.003 -3.7154110 294 0.265 0.0840 0.057 0.0238 0.003 -3.7394120 295 0.249 0.0747 0.055 0.0277 0.003 -3.5867130 295 0.249 0.0747 0.054 0.0269 0.003 -3.6164140 296 0.233 0.0653 0.052 0.0318 0.003 -3.4496150 297 0.217 0.0560 0.050 0.0384 0.003 -3.2606160 297 0.217 0.0560 0.048 0.0369 0.003 -3.2990170 297 0.217 0.0560 0.046 0.0354 0.003 -3.3404180 298 0.202 0.0467 0.044 0.0438 0.003 -3.1270190 299 0.186 0.0373 0.042 0.0567 0.003 -2.8699200 299 0.186 0.0373 0.040 0.0539 0.003 -2.9212

67

210 299 0.186 0.0373 0.038 0.0510 0.003 -2.9760220 300 0.170 0.0280 0.036 0.0701 0.003 -2.6577230 300 0.170 0.0280 0.034 0.0659 0.003 -2.7200240 300 0.170 0.0280 0.031 0.0616 0.003 -2.7865250 301 0.154 0.0187 0.029 0.0950 0.003 -2.3540260 301 0.154 0.0187 0.027 0.0881 0.003 -2.4293270 301 0.154 0.0187 0.025 0.0813 0.003 -2.5095280 301 0.154 0.0187 0.023 0.0747 0.003 -2.5948290 301 0.154 0.0187 0.021 0.0682 0.003 -2.6855300 302 0.138 0.0093 0.019 0.1380 0.003 -1.9803310 302 0.138 0.0093 0.017 0.1246 0.003 -2.0826320 302 0.138 0.0093 0.015 0.1118 0.003 -2.1912330 302 0.138 0.0093 0.014 0.0997 0.003 -2.3061340 302 0.138 0.0093 0.012 0.0883 0.003 -2.4272350 302 0.138 0.0093 0.011 0.0777 0.003 -2.5543360 303 0.122 0.0000 0.009 0.0000 0.003370 303 0.122 0.0000 0.008 0.0000 0.003380 303 0.122 0.0000 0.007 0.0000 0.003390 303 0.122 0.0000 0.006 0.0000 0.003400 303 0.122 0.0000 0.006 0.0000 0.003410 303 0.122 0.0000 0.005 0.0000 0.003420 303 0.122 0.0000 0.005 0.0000 0.003430 303 0.122 0.0000 0.005 0.0000 0.003440 303 0.122 0.0000 0.005 0.0000 0.003450 303 0.122 0.0000 0.005 0.0000 0.003

0 50 100 150 200 250 300 350 400 450 500280

285

290

295

300

305

f(x) = 4.3131255E-10 x⁴ − 0.000000393435432 x³ + 0.0000265635563 x² + 0.06282556511 x + 287.644872473R² = 0.995963378641071

Run 11 dT/dt

time (s)

tem

pera

ture

(deg

K)

68

Figure B 3 XI: Temperature Vs Time for Run11 with trend line.

Arrhenius Parameters

0.00325 0.00330 0.00335 0.00340 0.00345 0.00350

-5.0000

-4.5000

-4.0000

-3.5000

-3.0000

-2.5000

-2.0000

-1.5000

-1.0000

-0.5000

0.0000

f(x) = NaN x + NaNR² = 0 1/T vs ln(k)

Modified 'Run 8 & 9'

Linear (Modified 'Run 8 & 9')

Run 8 & 9

1/T

ln(k

)

Figure B 4: Plot of ln(k) Vs inverse temperature.

From Figure B.54the modified runs had a line best fit applied which gave Equation B.1

ln (k )=−12609( 1T )+39.22 (B.1)

From Equation B.1 the following was derived:

slope=−ER

=−12609

Therefore,

69

Activation Energy = E = 112369.626 J/mol= 112.37 kJ/mol

Intercept = ln(A) = 39.22Therefore, A = 5.79E+11 L/mol.s

70

C Appendix : Sample CalculationsThe following describes the calculation of experiment results using the information provided by Run 5. For the calculation of individual variables the time t=230 seconds and Temperature, T=300 deg K will be used.

Stoichiometery

Total Volume;Vtotal = Vwater + VA + VB = constant = .1 + .055 + .045 = .2L

Initial Concentration of a, ao:

Initial Concentration of b, bo:

Concentration Ratio, ao /bo:

Stoichiometric Ratio, ٧A/٧B:

The stoichiometric ratio is determined using the graph of the temperature difference, Tf-To, against the initial concentration ratio, ao /bo. The stoichiometric ratio is found at the maximum temperature increase is found at an initial concentration ratio of 1.697

Thus,

71

ao=astock∗V A

V total

=1 .0∗0.0550.20

=0 .275molL−1

bo=bstock∗V B

V total

=B1.0∗0 .0450 .02

=0 .225molL−1

ao

bo

=0.2750.225

=1 .22

νA

νB

=1 .697

Enthalpy of Reaction

Limiting Concentration, clim:

The limiting concentration is the minimum of the two values bo and (ao.٧B)/٧A. The excel function MIN( ) was used to determine the value using Equation C.1

Clim ¿=MIN (b0 , a0vB

vA)=MIN (.225 , .2751.697 )=MIN (.225 ,.1621 )=0.1621 ¿ (C.1)

Temperature Increase, Tf-To:

Tf-To = 304- 287 = 17°K

Enthalpy of Reaction, Δ H R:

Using a steady state energy balance, the enthalpy of reaction and temperature can be related.

(T f−T 0 )=−∆H R .Clim ¿

ρ .Cp

¿

This equation can be rearranged to give:

−∆ H R=(T ¿¿ f−T 0). ρCp

C lim ¿=17∗1000∗4.184

0.1621=438924 J /mol¿

¿

Therefore,

∆ H R=438.9kJ /mol

72

Arrhenius parameters:

Concentration of Na2S2O3, b:Using Equation 1.13 we can find b:

b=b0−Clim ¿

(T−T0 )

(T ¿¿ f−T0 )=.225−.1621(300−287)(304−287)

=.101mol/L¿¿

Concentration of H2O2, a:Using Equation 1.14 we can find a:

a=a0+v A

vB(b−b0 )=.275+ (1.697 ) (.101−.225 )=.0647mol /L

Change in temperature with change in time, dT/dt:

To find the value of the change in temperature with time at a particular point, a formula had to be fitted to the data points. The midpoint theorem could have been used although the accuracy of the method is low. To reduce the error in the calculation, the data points for the whole run were put on a graph of T vs t as seen in Figure C.1. A trend line was fitted to the data.

0 50 100 150 200 250 300 350 400 450 500275

280

285

290

295

300

305

310

f(x) = 4.265978E-10 x⁴ − 0.0000003855484071 x³ + 0.0000323987611 x² + 0.063442830998 x + 286.746633408R² = 0.997077423002322

Run 5 dT/dt

time (s)

Tem

pera

ture

(deg

K)

Figure C 1: : A graph of T vs. t for all data points in Run 5 with fitted trend line.: A graph of T vs. t for all data points in Run 5 with fitted trend line.

73

The equation of the line of best fit had to be given with twelve significant figures so that the curve was represented properly.

The equation was derived for Run five as,

y = 4.27*10-10 x4 – 3.85548*10-7 x3 + 3.2398761*10-5x2 + 0.063442830995x + 287.7466334

Which represents,

T(t) = 4.27*10-10 t4 – 3.85548*10-7 t3 + 3.2398761*10-5 t2 + 0.063442830995t + 287.7466334

Using this equation we can derive the equation to obtain:

dT/dt = 1.708*10-9t3 -1.15664*10-6t2 +6.47975*10-5t + 0.063442830995

Thus the value of t can be substituted in to obtain the instantaneous rate of temperature with respect with to time.

dT/dt =1.708*10-9(230)3 -1.15664*10-6(230)2 +6.47975*10-5(230)+ 0.063442830995

dT/dt = 0.03794103 °Ks-1

Arrhenius Rate Constant, k:

k=1

a .b.

C lim ¿

(T f−T0).dTdt

=

1.0647∗.101

∗.1621

17∗.03794103=0.0552977 Lmol−1 s−1 ¿

Inverse Temperature, 1/T:

1T

= 1300

=.003333K−1

Natural logarithm of k, ln(k):

74

ln (k )=ln (0.0552977 )=−2.8950

Arrhenius Parameters, E and A:

Using the Arrhenius Equation we can find the activation energy, E, and the pre exponential rate constant, A.

ln (k )=ln ( A )−ER1T

This equation demonstrates how a plot of ln(k) against 1/T will give a slope of -E/R and an intercept of ln(A).

If we plot all data points from all runs in the experiment we will get Figure C.2.

0.003 0.003 0.004

-6.0000

-5.0000

-4.0000

-3.0000

-2.0000

-1.0000

0.00001/T vs ln(k)

run1run 2run 3run 4run 5run 6run 7run 8run 9run 10run 11

1/T

ln (k)

Figure C 2: Graph of all data point from all runs for ln(k) versus 1/T

The resulting cloud of data follows a trend, yet its fit to a linear regression is poor.

75

76

D. Appendix: Error CalculationsThe following error calculations are based on Run 5 with all error calculations shown at the end of Appendix D.

ConstantsTable D 1: Error Constants for experiment

Stop Watch δt= ± 0.5 s 0.5

Thermo Probe δT=± 0.5 deg K 0.5

Measuring Cylinder δV= ± 0.001L 0.001δV (Total)= δVA + δVB + δVwater = 0.003

Stoichiometric Coefficient Ratio Error 0.0548163

3

Initial concentrations, δa & δb

δ a0=ao( δV A

V A

+ δVV )=.225( .001.045

+ .003.2 )=.006375mol . L−1

δb=bo( δV B

V B

+ δVV )=.275( .001.055

+ .003.2 )=.000425mol . L−1

δ ( a0b0 )=a0b0 (

δa0a0

+δb0b0 )= .225.275 ( .006375.225

+ .00425.25 )=.03064

Limiting Concentration, Clim

Clim ¿=MIN (b0 , a0vB

vA)=MIN (.225 , .2751.697 )=MIN (.225 ,.1621 )=0.1621mol L−1¿

δC lim ¿=C

lim ¿( δa0a0

+δ (

v A

vB

)

(vA

vB

) )=.1621 (.006375.225+ .0548161.697 )=.008991174mol L−1 ¿

¿

Temperature Riseδ (T f−T 0 )=δT f+δT 0=0.5+0.5=1

0 K

Enthalpy of Reaction, ∆HR

GraphicalThe graphical enthalpy was found from a plot of Temperature change vs the limiting concentration for all runs. A linear regression was fitted to the plot with a R2 value equal to .979 meaning the regression fits the data accurately. Therefore the absolute error for the graphical

77

enthalpy was taken as the maximum error for the limiting concentration. This equaled 38.856kJ/mol

Analyticalδ ∆ HR ,analytical=∆ H R, analytical¿ The error for every round was found then averaged to find the analytical arithmetic average error. Therefore ∆HR,analytical= 428.06 kJ/mol ± 56.66 kJ/mol

Table D 2: Absolute Errors for each Run.

run δVA (L) δVB (L)δao (mol/L)

δbo (mol/L) δ(ao/bo)

δclim (mol/L)

δ(Tf-Ti) (°K)

1 0.001 0.001 0.0055 0.0006 0.0141250.00514448

4 1

2 0.001 0.001 0.005875 0.0005250.01894674

60.00679306

6 1

3 0.001 0.001 0.006 0.00050.02111111

10.00734259

3 1

4 0.001 0.001 0.00625 0.00045 0.02680.00844164

7 1

5 0.001 0.001 0.006375 0.0004250.03064197

50.00899117

4 1

6 0.001 0.001 0.0065 0.0004 0.03550.00954070

1 1

7 0.001 0.001 0.00655 0.000390.03782271

50.00976051

2 1

8 0.001 0.001 0.0066 0.000380.04041975

30.00952684

2 1

9 0.001 0.001 0.006675 0.0003650.04494582

2 0.0086175 1

10 0.001 0.001 0.00675 0.000350.05044444

40.00773814

2 1

11 0.001 0.001 0.0068 0.000340.05481632

70.00716671

1 1

MAX= 0.001 0.001 0.0068 0.00060.05481632

70.00976051

2 1

Table D 3: Relative Errors for each Run.

runδVA/VA (%)

δVB/VB (%)

δao/ao (%)

δbo/bo (%)

δ(ao/bo)/(ao/bo) (%)

δclim/clim (%)

δTf-Ti/Tf-Ti (%)

78

1 5 1.25 5.5 0.15 5.658.730190

13133.33333

333

22.857142

8571.538461

5383.357142

8570.161538

462 3.5186813196.587332

9899.090909

091

3 2.51.666666

667 30.166666

667 3.1666666676.230190

1317.142857

143

4 2 2 2.5 0.18 2.685.730190

1315.882352

941

51.818181

8182.222222

2222.318181

8180.188888

889 2.5070707075.548371

955.882352

941

61.666666

667 2.52.166666

667 0.2 2.3666666675.396856

7985.555555

556

71.612903

2262.631578

9472.112903

2260.205263

158 2.3181663845.343093

3575.263157

895

8 1.56252.777777

778 2.06250.211111

111 2.2736111115.292690

1315.555555

556

91.492537

3133.030303

031.992537

3130.221212

121 2.2137494355.222727

4455.555555

556

101.428571

4293.333333

3331.928571

4290.233333

333 2.1619047625.158761

56 6.25

111.388888

8893.571428

5711.888888

8890.242857

143 2.1317460325.119079

026.666666

667

MAX= 53.571428

571 5.50.242857

143 5.658.730190

13133.33333

333

Table D 4: Analytical Errors for each Run.

Absolute error for analytical enthalpy Relative error

Run δclim δTf-to δ-ΔHR (J/mol)

δ -ΔHR (kJ/mol)

δ -ΔHR/-ΔHR (%)

1 0.00514448 189598.434

5 89.5984345 42.06352346

2 0.00679307 169972.198

7 69.9721987 15.67824208

3 0.00734259 166466.366

5 66.4663665 13.37304727

4 0.00844165 156067.316

3 56.0673163 11.612543075 0.00899117 1 50172.243 50.1722431 11.43072489

79

1

6 0.0095407 146658.906

3 46.6589063 10.952412357 0.00976051 1 46155.912 46.155912 10.606251258 0.00952684 1 45389.06 45.38906 10.848245699 0.0086175 1 49196.003 49.196003 10.778283

10 0.00773814 150916.542

3 50.9165423 11.40876156

11 0.00716671 152833.814

2 52.8338142 11.78574569Average= 56.6751634 14.59434367

80

E. Appendix: Previous Study

81

82

G. Appendix: MSDS for Hydrogen Peroxide

Hydrogen Peroxide Solution < 8%Chemwatch Material Safety Data SheetIssue Date: 13/ 02/2006Hazard Alert Code: High

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H. Appendix: MSDS for Sodium Thiosulphate

Sodium Thiosulphate Solution 2%Chemwatch Material Safety Data SheetIssue Date: 30/ 03/2006Hazard Alert Code: Nil

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Issue Date: 30-Mar-2006

Print Date: 12-May-2008

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