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Physical Measurements Goux Spring 2016 Daniel Gonzalez
Kinetics of benzene Diazonium
Physical Measurements
Goux
Spring 2016
Daniel Gonzalez
Partner: Jenny J.
1
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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:
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
−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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
intervals subsequently until the last point was 100min.
For 40˚ C a sample was taken after 20 minutes (equilibrium temp), and then at 10 minute
intervals subsequently until the last point was 100min.
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.
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Table 3. 25˚ C Absorbance Vs Time
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
Table 4. 40˚ C Absorbance Vs Time
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
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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
)
12
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
13
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
15
Physical Measurements Goux Spring 2016 Daniel Gonzalez
SUMMARY OUTPUT first order 25 C
Regression StatisticsMultiple R 0.984717R Square 0.969667Adjusted R Square 0.954501Standard Error 0.011835Observations 4
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
SUMMARY OUTPUT first order 40 C
Regression StatisticsMultiple R 0.986626R Square 0.97343Adjusted R Square 0.964574Standard Error 0.039849Observations 5
CoefficientsStandard
Error t Stat P-valueLower 95%
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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Physical Measurements Goux Spring 2016 Daniel Gonzalez
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.
17
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Regression StatisticsMultiple R 0.999975R Square 0.99995Adjusted R Square 0.9999Standard Error 0.023182Observations 3
18
Physical Measurements Goux Spring 2016 Daniel Gonzalez
CoefficientsStandard
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
Regression StatisticsMultiple R 0.999995R Square 0.99999Adjusted R Square 0.99998Standard Error 0.011195Observations 3
CoefficientsStandard
Error t Stat P-valueLower 95%
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
Regression StatisticsMultiple R 0.981246R Square 0.962844Adjusted R Square 0.950459Standard Error 0.00091Observations 5
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
Regression StatisticsMultiple R 0.98711R Square 0.974385Adjusted R Square 0.961578Standard Error 0.008292Observations 4
CoefficientsStandard
Error t Stat P-valueLower 95%
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
Physical Measurements Goux Spring 2016 Daniel Gonzalez
Multiple R 0.990721R Square 0.981528Adjusted R Square 0.97537Standard Error 0.029395Observations 5
CoefficientsStandard
Error t Stat P-valueLower 95%
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
NOTEBOOK PAGES:
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