kinetics of benzene diazonium

Physical Measurements Goux Spring 2016 Daniel Gonzalez

Kinetics of benzene Diazonium

Physical Measurements

Goux

Spring 2016

Daniel Gonzalez

Partner: Jenny J.

1


ABSTRACT:

The kinetics of the decomposition of benzenediazonium tetrafluoborate in a .2M HCl solution

was investigated at temperatures 0, 25, and 40˚ C using a UV-Vis spectrophotometer over the

course of approximately 100 minutes. It was determined that the rate law of decomposition

was first order with respect to the concentration of benzenediazonium tetrafluoborate with k

values of .000507, 5.3x10-6, and .00108 (s-1) obtained at the respective temperatures of 0, 25,

and 40˚ C. Epsilon, the molar extinction coefficient, was calculated to be 1939.24± 150.84 cm

mol- L and the activation energy was calculated to Ea=187.22 ± 69.1 kJ/mol. All values calculated

are significantly different than literature values obtained by Canning[6], Weisman[7] and Chas[5],

suggesting that delay in recording absorbance while transferring samples at 0o C does in fact

result in non-negligible error in calculations and affects processing of all kinetic data relevant to

this experiment.

INTRODUCTION:

Chemical kinetics is the study and discussion of chemical reactions with respect to reaction

rates, effects of different variables, re-arrangement of atoms, formation of intermediates ect[1].

Kinetics is effected specifically and nearly in all cases, by changes of temperature, and changing

concentration. When taking into consideration the theory that reactions can proceed by

effective collisions between two molecules, intuitively, by changing the amount of molecules to

collide, (concentration) or by speeding up the molecules so they collide more frequently (raising

the temperature), one can increase the reaction rate. For species in which only the

concentration of one molecule determines the rate law, the reaction can be said to be

2


unimolecular; such is the case with many decomposition reactions. When considering the

decomposition of benzene diazonium the following reaction is occurring:

C6H5N2+ +H2O C6H5OH + N2(g) + H+ (1)

Figure 1.

Aryl Diazonium salts are notoriously reactive and decompose rapidly at room temperature. Some salts decompose rapidly enough to become highly explosive compounds. For these reasons the kinetics of Benzenediazomiumfluorborate (C6H5N2BF4 ), a much less reactive Aryl diazonium salt was investigated.

Figure 2.

If one can follow the course of the reaction at a given temperature, and utilize a spectroscopic

method for determining changing concentration of either the product or the reactant, one can

determine the overall rate order (n+m), and the rate constant (k) such that:

3


−ddt

¿C6H5N2+) = k (C6H5N2

+)n(H2O)m (2)

In this case, the change in the concentration of C6H5N2+ is negative as it will decrease as it

decomposes, and the rate at which it decomposes is equal to the concentration of C6H5N2+ to

some power n multiplied by the rate constant k.

Assuming the reaction is carried out in an aqueous environment, the concentration of water is

significantly (many orders of magnitude) greater than the concentration of any other reagent.

With this being the case, any change in the concentration of water as the reaction proceeds is

considered negligible and can thus be ignored. The ability to ignore a reagent in extreme excess

is known as flooding. In addition to flooding due to water, the concertation of H+ can also be

considered negligible as well. (This is one reason the reaction is carried out in an acidic solution)

With the previously mentioned considerations equation 2 can be re-written as follows:

−ddt

¿C) = k (C)n (3)

Where C= [C6H5N2+]

If Equation 3 is integrated:

∫−ddt

(C)=∫ k (C )n

C = Co e-kt (n=1) (4)

and

C1-n -Co1-n =(n-1)kt (n≠1) (5)

Where in equations 4 and 5 Co is the concentration at time =0

With these equations in mind, it is possible to determine the order of the reaction (n) by plotting C1-n at hypothetical n values and determining which of these plots vs time will result in the most linear graph. If the reaction is first order a plot of the Log(C) vs t, should result in a linear plot with slope= -k/ 2.303 .

4


K=A e-Ea/RT (6)

By rearranging the Arrhenius equation, equation 6 can be obtained such that A is a constant and plots of log(K) vs 1/T can be graphed to yield a linear relationship with the slope equal to

the following:

Slope = -Ea/2.303(R) (7)

Which can be rearranged to solve for the Activation Energy in kJ as follows:

Ea= -(Slpoe)(2.303)(R) R=8.314x10-3 kJmol-1

(8)

For this particular decomposition, it is convenient to monitor the absorbance of the aryldiazonium salt, which should result in decreasing absorbance values and will be directly proportional to the decreasing concentration of aryldiazonium salt.

From Beer Lambert’s Law:

A=logI oI= cεd2.302

(9)

Figure 3 [2].

Such that A is absorbance, Io is the intensity of light shined through the sample, I is the measured intensity of light that has passed through the sample, c is the concentration in

Moles/Liter, ε is the molar extinction coefficient with units cm-1Lmol-1, and d is the cuvette path length in cm.

Using this relationship, absorbance values can be used in place of concentration values and converted to concentration units by dividing by εd. However, with d being equal to 1 cm in this situation, d can essentially be ignored for calculation purposes. ε can be determined from a comparison of two known concentration of any solution given that the solutions obey Beer’s law at a low concentration.

5


By monitoring absorbance values with respect to time at different temperatures, the data ca be plotted such that A1-n vs t will yield a linear plot at different values of n, with the following producing linear plots:

½ Order: A1/2 vs t

1st order: log(A) vs t

3/2 Order: A-1/2 vs t

2nd Order: A-1 vs t

Using regression analysis, the best fit plot can be evaluated and from that plot, the order of the decomposition (n) can be determined.

Upon determination of the order of the reaction using the relationship

slope= -k/ 2.303

the rate constant k can be solved for, at each temperature.

A plot of lnK vs 1/T will then result in a slope that can be used to calculate the activation energy of the decomposition.

METHODS:

All methods were performed at the University f Texas at Dallas’ Berkner Hall in the teaching laboratory under the guidance of Dr. Warren Goux while following the general protocal outlined by Shoemaker[8].

Three solutions of benzendiazonium fluoborate were prepared in solutions of .2M HCl using a 100ml volumetric flask and analytical balance 4.

Tale 1. Preparation of Solutions

Solution Temperature C˚ Mass benzendiazonium

fluoborate

MolarityMol/liter

1 0 17.3 mg 9.015x10-4

2 25 15.0 mg 7.817x10-4

3 40 18.4 mg 10.265x10-4

Three groups of two carried out the experiment at 3 different temperatures. The solutions were

made at the same time and immediately placed in their respective heat/water/ or ice bath to

6


ensure the correct reaction temperature. As soon as a sample was drawn from any of the

solutions, it was immediately placed on ice to slow the reaction, allowing time for the UV vis

measurement to be taken. After the initial addition of the benzendiazonium fluoborate to the

acid, an initial sample was taken from each solution to be used to generate a concentration

curve and calculate ε using Beer’s law. This curve is only possible if known concentrations are

plotted against measured absorbance values, which is why these sample were taken from each

solution before allowed to equilibrate in their respective temperatures. Each group maintained

their own solution’s temperature and took samples at different but consistent time intervals.

For 0˚ C, a sample was taken after 20minutes (equilibrium temp), and then at 15minute

intervals subsequently until the last point was 120min.

For 25˚ C a sample was taken after 20 minutes (equilibrium temp), and then at 15 minute


For 40˚ C a sample was taken after 20 minutes (equilibrium temp), and then at 10 minute


As each sample was drawn it was immediately placed in ice and taken by one group member to

be analyzed in the UV-vis Spectrophotometer with a 1X1 cm glass cuvette. The UV-vis

spectrophotometer was calibrated with a blank of .2M HCL before any spectra were recorded.

The absorbance value at λ=305 was recorded for each sample and used to produce graphs to

determine reaction order as well as generate a curve to calculate ε, the molar extinction

coefficient.

7


RESULTS:

Table 2. 0˚ C Absorbance Vs Time

0C Order: 0.5 1 2 1.5t(min) t(s) A A.5 log A C-1 A-.5

0 0 1.738 1.318 0.553 1115.788 0.75920 1200 1.531 1.237 0.426 1266.649 0.80820 1200 1.53 1.237 0.426 1267.477 0.80870 4200 1.521 1.233 0.419 1274.977 0.81195 5700 1.518 1.232 0.417 1277.497 0.812

120 7200 1.508 1.228 0.411 1285.968 0.814


25C Order: 0.5 1 2 1.5t(min) t(s) A A^.5 log A C^-1 A^-.5

20 1200 1.400 1.183 0.336 1385.171 0.84535 2100 1.312 1.145 0.272 1477.516 0.87350 3000 1.280 1.131 0.247 1515.031 0.88465 3900 1.226 1.107 0.204 1581.761 0.90380 4800 1.239 1.113 0.214 1565.165 0.89895 5700 1.223 1.105 0.201 1585.642 0.904

110 6600 1.231 1.109 0.208 1575.337 0.901


40C Order: 0.5 1 2 1.5t (min) t(s) A A^.5 log A C^-1 A^-.5

20 1200 1.496 1.223 0.403 1296.283 0.81830 1800 1.24 1.114 0.215 1563.903 0.89840 2400 1.123 1.060 0.116 1726.839 0.944

8


50 3000 0.937 0.968 -0.065 2069.627 1.03360 3600 0.889 0.943 -0.118 2181.372 1.06170 4200 0.452 0.672 -0.794 4290.354 1.48780 4800 0.456 0.675 -0.785 4252.719 1.48190 5400 0.456 0.675 -0.785 4252.719 1.481

100 6000 0.606

Table 5. Calculation of ε in a 1cmx 1cm cuvette

ε= Adc

M mol/Liter A ε L mol-1 cm-1 Average ε9.02E-04 1.738 1927.89 1939.241.03E-03 1.842 2095.44 SD7.82E-04 1.638 1794.40 150.84

Chart 1.

0 1000 2000 3000 4000 5000 6000 7000 800012551260126512701275128012851290

f(x) = 0.00289516572258555 x + 1263.23436405912R² = 0.946380925498413

A-1 vs t at 0C

time (s)

A-1

Chart 2.

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0 1000 2000 3000 4000 5000 6000 7000 80001.222

1.224

1.226

1.228

1.23

1.232

1.234

1.236

1.238f(x) = − 1.39835418372782E-06 x + 1.2389719494637R² = 0.947867367939351

A.5 vs t at 0C

time (s)

A.5

Chart 3.

0 1000 2000 3000 4000 5000 6000 7000 80000.4

0.405

0.41

0.415

0.42

0.425

0.43

f(x) = − 2.26869919801124E-06 x + 0.428582723141077R² = 0.947374697737649

LN(A) vs t at 0C

Time (s)

Ln(A

)

Chart 4.

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0 1000 2000 3000 4000 5000 6000 7000 80000.8050.8060.8070.8080.809

0.810.8110.8120.8130.8140.815

f(x) = 9.20192064346182E-07 x + 0.807105544442784R² = 0.946879213819351

A-.5 vs t at 0C

Time (s)

A--.5

Chart 5.

1000 1500 2000 2500 3000 3500 4000 45001250

1300

1350

1400

1450

1500

1550

1600

f(x) = 0.0696984727832567 x + 1312.13906843458R² = 0.974385315327026

A-1 vs t at 25 C

Time (s)

A-1

Chart 6.

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1000 1500 2000 2500 3000 3500 4000 45001.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

f(x) = − 2.69082683489233E-05 x + 1.21048597756742R² = 0.966970468872442

A.5 vs t at 25 C

Time (s)

A.5

Chart 7.

1000 1500 2000 2500 3000 3500 4000 45000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

f(x) = − 4.70244260970772E-05 x + 0.384668003435147R² = 0.969667426874091

Ln(A) vs t at 25 C

TIme (s)

Ln(A

)

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Chart 8.

1000 1500 2000 2500 3000 3500 4000 45000.810.820.830.840.850.860.870.880.89

0.90.91

f(x) = 2.05519111944471E-05 x + 0.823854786942774R² = 0.972141037761258

A-.5 vs t at 25 C

Time (s)

A-.5

Chart 9.

1000 1500 2000 2500 3000 3500 40000

500

1000

1500

2000

2500

f(x) = 0.379316842273493 x + 857.24443229394R² = 0.981527857879102

A-1 vs t at 40 C

time (t)

A-1

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Chart 10.

1000 1500 2000 2500 3000 3500 40000

0.2

0.4

0.6

0.8

1

1.2

1.4

f(x) = − 0.000117675152492531 x + 1.34386760049228R² = 0.965186977263479

A.5 vs t at 40 C

Time (s)

A.5

Chart 11.

1000 1500 2000 2500 3000 3500 4000

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

f(x) = − 0.000220181537066949 x + 0.638671667903397R² = 0.973430266010731

LnA vs t

TIme (s)

Ln(A

)

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Chart 12.

1000 1500 2000 2500 3000 3500 40000

0.2

0.4

0.6

0.8

1

1.2

f(x) = 0.000103509582377472 x + 0.702162425604686R² = 0.978846818100025

A-.5 vs t at 40 C

Time (s)

A-.5

Regression Analysis for Ln(A) vs t:

SUMMARY OUTPUT first order 0 C

Regression StatisticsMultiple R 0.981621R Square 0.96358Adjusted R Square 0.951441Standard Error 0.00137Observations 5

Coefficients

Standard Error t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.4286170.00116

9366.640

64.47E-

08 0.4248970.43233

80.424897

0.432338

X Variable 1 -2.3E-062.55E-

07-

8.909170.00298

3 -3.1E-06 -1.5E-06 -3.1E-06 -1.5E-06

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Coefficient

sStandard

Error t Stat P-valueLower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.384668 0.01612223.8599

70.00175

20.31530

10.45403

50.31530

10.45403

5

X Variable 1 -4.7E-05 5.88E-06 -7.995980.01528

3 -7.2E-05 -2.2E-05 -7.2E-05 -2.2E-05



CoefficientsStandard


Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.638672 0.053462 11.94617 0.001262 0.46853 0.808813 0.46853 0.808813

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X Variable 1 -0.00022 2.1E-05 -10.4838 0.001853 -0.00029 -0.00015-0.00029 -0.00015

Table 6. k values if reaction is First order

1st order Slope K 1/T lnK0˚ C -0.00022 0.000507 0.003193 -7.58767

25˚ C -2.30E-06 5.3E-06 0.00366 -12.148440˚ C -4.70E-05 0.000108 0.003354 -9.13115

Average 0.000207 Activation Energy 187.22 ± 69.1 kJ/molSD 0.000265

Table 7. k values if reaction is Second order

2nd order slope k (in Cunits) 1/T lnK0˚ C 0.3793 0.3793 0.003193 -0.96943

25˚ C 2.90E-03 0.0029 0.00366 -5.8430440˚ C 6.97E-02 0.0697 0.003354 -2.66355

Average 0.15063333Activation Energy

199.71±33.37 kJ/molSD

0.20082802

Table 8. Comparison of regression values for A1-n vs time graphs

Regression Values for plots for 2nd order vs 1st order 2nd order 1st order

Temp C R2 of A-1 vs time R2 LnA vs time0 0.9744 0.9474

25 0.9464 0.969440 0.9815 0.9474

Avg. r2 values 0.967433 0.954733SD 0.018558 0.012702

Chart 13.

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0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037-14

-12

-10

-8

-6

-4

-2

0

f(x) = − 9778.37957306881 x + 23.6469035873113R² = 0.999950064194088

First Order Activation Energy

1/T (Kelvin)

Ln(K

)

Chart 14.

0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037-7

-6

-5

-4

-3

-2

-1

0

f(x) = − 10430.0281483014 x + 32.3277566587398R² = 0.999989764057088

Second order Activation Energy

1/T (Kelvin)

Ln(K

)

SUMMARY OUTPUT First Order Activation Energy


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Error t Stat P-value Lower 95%Upper 95%

Lower 95.0%

Intercept 23.6469 0.235485 100.4179 0.006339 20.65478 26.63902 20.65478X Variable 1 -9778.38 69.10091 -141.509 0.004499 -10656.4 -8900.37 -10656.4

SUMMARY OUTPUTregression for Activation Energy 2nd

Order




Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 32.32776 0.113718 284.2788 0.002239 30.88283 33.77269 30.88283 33.77269X Variable 1 -10430 33.36965 -312.56 0.002037 -10854 -10006 -10854 -10006

Calculation of Activation energy 1st order from Equation 7:

Slope = -Ea/2.303(R)

Ea= -9778.38molK(8.314x10-3kJmol-1K-1)(2.303)

Ea=187.22 ± 69.1 kJ/mol

118 kJ¿mol<¿Ea ¿ 256.12 kJ/mol

DISCUSSION:

`Overall this experiment was successful. Indeed the proper dilutions were made and the assay

was carried out to the best ability in an undergraduate setting. When selecting the order of the

reaction it was decided that the reaction best fit the strait plot of a first order reaction. The data

indicates however that a second order, and perhaps in some instances a 3/2 order reaction

19


appear to have a better regression value. Despite this, it is important to consider the relevant

literature values before coming to a conclusion. According to similar experiments performed by

Hartung[4], Canning[5] and Wiesman[6] the reaction is nearly unanimously first order with

discrepancies of the mechanism of the formation of an aryl decomposition intermediate

cation. Although obtained regression values may suggest otherwise, it is important to note that

discrepancies between regression values of the various plots as shown in table 8, led to r2

values that were not obviously better than those of other plots obtained. With this in mind, the

standard deviations between the different r2 values were calculated, and it was observed that

the r2 values form the first order plots, despite being marginally further from 1, maintained a

smaller standard deviation. This information was interpreted as evidence of a more accurate

representation of the true order of the reaction, as the r2 values proved to be slightly more

consistent with each other than those of a second order approximation. Despite this

assumption, both 1st order and 2nd order calculations were carried out with 2 final activation

energies obtained from the respective k values (tables 6 and 7). It was determined that the

activation energies were 187.22 ± 69.1 kJ/mol and 199.71±33.37 kJ/mol for first and second

order respectively which are both exceedingly large compared to a literature value obtained by

Canning of approximately 112kJ/mol. Despite these large values, if the extreme low end of the

first order approximation is taken as 187-69.1, a value of 118kJ/mol is obtained which although

still high, is significantly closer to the literature values than doing the same low end

approximation with the second order activation energy. When considering the differences

between literature and obtained values, it is also important to note that results obtained by

Canning produced plots with regression values no smaller than .999[7]. These findings are in

20


stark contrast to the plots obtained by graphing our data which at most did not exceed a .990

value. Clearly then, there was a fairly large amount of error inherent to our experiment.

Possible such sources of this error include the fact that multiple groups were collecting data at

the same time and the samples on ice at some points had to wait up to 3 minutes before being

analyzed in the UV-vis instrument. With this in mind, the reaction likely continued and resulted

in large deviations from the expected values had the reaction truly been halted and measured.

Considering this limitation, it would then most likely be ideal for this experiment to be

performed using a UV-vis spectrophotometer capable of taking multiple measurements from

different samples at once, or simply spacing out the recording intervals further to allow each

group more time on the Uv-Vis.

Despite large activation energies, no disastrous or unexplainable measurements were recorded,

and the few data points that were not in accordance to the predicted decreasing absorbance

trend were effectively able to be neglected in the relevant calculations. If attempting to predict

one of the obtained absorbance values using a first order calculation of k the following would

result in accordance with equation 4:

C = Co e-kt (n=1)

Assuming 20 min at 0˚ (because a 30min point was not taken) with Co= 1.738 (in absorbance values)

K=.00507 s-1 at 0˚ C

C = (1.738) e-(.00507)(20)(60)

C=.0039 M (theoretical)

Measured, A=εcd

C=A/ε

21


C=1.531/(1939.24± 150)=.00078M

These two values are nearly 6.5 times different with the calculated value being greater than the

actual value of concertation calculated with ε. This does raise the issue of error in ε as Chas[5]

had given an estimate of ε to be 1.25x104 cm mol- L which is nearly an order of magnitude

larger than the calculated value of ε from initial concentrations and absorbance values.

Both of the discrepancies in the data as well as values for ε can be described reasonably well if

it is assumed that at 0˚C the reaction does not in fact stop, but proceeds fine and well. This is

clearly evident in the fact that the 0˚ C run consistently yielded a decreasing absorbance

indicating that the benzenediazonium was indeed decaying. With this in mind, it can not be

assumed that putting samples on ice will result in negligible error.

REFERENCES:

1) Science.uwaterloo, Kinetics, http://www.science.uwaterloo.ca/~cchieh/cact/c123/chmkntcs.html (accessed 4/10/16)

2) Gallik, Steve; Beer’s law: http://cellbiologyolm.stevegallik.org/node/8 (accessed 4/12/16)

22


3) https://scholarship.Rice .edu/itstream/Wander/1911/14269/661034) Hartung, Levoy Dee, 1936 Biomolecularity in diazonuim ion hydrolysis Rice, 1966

Organic Chem5) Chas, E Waring; Some Kinetic considerations of thermal decomposition of

Benzenediazonium Chloride J. Am. Chem. Soc., 1941, 63 (10), pp 2757–27626) Wiesman,Floyd Monitoring the Rate if solvolytic Decomposition of Benzenediazonium

Tetrafluroborate in aq. Media using pH electrode; J. Chem. Educ., 2005, 82 (12), p 18417) Cannning, Rates and mechanisms of the thermal solvolytic decomposition of

arenediazonium ions J. Chem. Soc., Perkin Trans. 2, 1999, 2735–27408) . Shoemaker, Garland, Nibler, "Experiments in Physical Chemistry, 8th ed." McGraw-Hill

Publishing Company, Toronto (2009)

APPENDIX:

Regression Analysis for Second Order Plots:

SUMMARY OUTPUT 1/A 0CSecond order

23



Coefficient

sStandard Error t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.651390.00077

7838.474

8 3.74E-090.64891

70.65386

20.64891

70.65386

2

X Variable 1 1.5E-06 1.7E-078.81705

6 0.003074 9.56E-07 2.04E-06 9.56E-07 2.04E-06

SUMMARY OUTPUT 1/A 25C 2nd order




Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.676625 0.011296 59.90016 0.000279 0.628023 0.725228 0.628023 0.725228X Variable 1 3.59E-05 4.12E-06 8.722397 0.01289 1.82E-05 5.37E-05 1.82E-05 5.37E-05

SUMMARY OUTPUT 1/A 40 C 2nd order

Regression Statistics

24


Multiple R 0.990721R Square 0.981528Adjusted R Square 0.97537Standard Error 0.029395Observations 5



Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 0.442052 0.039437 11.20904 0.001522 0.316545 0.567558 0.316545 0.567558X Variable 1 0.000196 1.55E-05 12.62564 0.001071 0.000146 0.000245 0.000146 0.000245

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kinetics of benzene diazonium

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