Factorial design in oxidation reactions
n
49 zyxwvut
Original Research Paper
and Intelligent Laboratory Systems, 12 (1991) 49-55
Elsevier Science Publishers B.V.. Amsterdam
Chemometrics
Factorial design in oxidation reactions and analysis
of variance of initial rates of reaction
N.C. Sadiris, NC. Thanasoulias
and N.P. Evmiridis *
Laboratory of Analytical Chemistry, Department of Chemistry, University of loannina,
451 10 Ioannina (Greece)
(Received 23 August 1990; accepted 25 January 1991)
Sadiris, N.C., Thanasoulias, N.C. and Evmiridis, N.P., 1991. Factorial design in oxidation reactions and analysis of variance of initial
rates of reaction. Chemometrics and Intelligent Laboratory Systems, 12: 49-55.
An illustration is given of how the factorial experiment and analysis can provide the basis for the deduction of information about
the chemistry of a reaction and/or reaction kinetics with three oxidation reaction examples.
INTRODUCTION
In the world of chemical reactions a molecule
of a particular compound goes through a change
from one form to another by colliding either with
inert molecules to give reaction products composed of its constituent atoms, or with active
molecules that act either (i) as reagents, giving
reaction products that are composed of atoms that
belong to both types of reacting molecules, or (ii)
as catalysts that cause an effective collision to
occur, changing the chemical nature of the molecule or allowing it to react with other molecules.
The dissociation species of the reagents, residual reactivity and/ or instability of reaction products and catalyst intermediates are some of the
factors that complicate the reaction process in
solution, leading to the expression
reaction paths that are occurring in the system at
any moment during the reaction period. However,
the rate equation (1) can be considerably simplified by replacing the rate by the initial rate (IR)
and the rate equations by the much simpler initial
rate equations, thus obtaining the equation
IR(observed)
= C(IR,)
(2)
where
II+@
I
0
and nXi
is the product of u factors of Xi where
u is 1 for-first order, 2 for second order, and 3 for
a third order kinetics, or for some more complicated catalytic reactions in solution [1,2], and
where ki are constants and Xi is the concentration of the jth compound or, in the most complex
case, it is a function of the compound’s concentrar (observed) = Cr,
(I)
tion, and subscripts 1, 2, 3 refer to compounds 1,
where zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
r, are the rate contributions from all the
2, 3, respectively, and subscript i refers to the
Chemometrics and Intelligent Laboratory Systems
50 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
simultaneous changes that contribute to the overall change in the initial part of the reaction and u
represents the number of the factors involved in
the product. The establishment of the specific
equation that is followed by the reacting system
under examination is a matter of discovering the
effects and interactions of concentration factors,
which is simple since, in most cases, there are no
more than two dominant terms involved in eq. (2).
A useful method used to investigate effects and
interactions is the factorial experiment, which is
conventionally used as a ‘precursor’ method for
generating linear mathematical models which represent the response surface [3] for a response
optimization procedure in analytical chemistry.
The establishment of the significance of effects
and interactions proceeds with the factorial analysis procedure described by Yates [3].
The factorial procedure consists of the following stages:
1. Establishment of the factors involved in the
determination of the response size.
2. Decision making about the levels ( - , + ) of
each factor. The decision has to be taken in
such a way that the levels convey the necessary
information for the correct representation of
the response surface.
3. The execution of the trials of the factorial
experiment, which must be done in a random
order.
4. The statistical analysis of the factorial experiment.
The factorial experiment is a general method
and is applicable to all types of responses. However, if the response is the rate of the reaction and
such factors involved are the concentrations of the
reactants the factorial experiment provides a study
of the kinetics of the reaction and such factorial
experiments have been applied in the assessment
of the validity of proposed kinetic models [4,5].
However, the factorial experiment can also be
used to provide information about the actual
chemistry and kinetics of complex reacting systems, as explained above.
In this work we present the factorial experiments for the oxidation of (1) p-phenylenediamine (PDA), (2) N, N, N ‘, N ‘-tetramethyl-p-phenylenediamine (TMPDA), and (3) pyrogallol, and
n
we use these experiments to draw conclusions
about the chemistry and the kinetics of the oxidation reactions. The conclusions drawn are further
supported by other methods.
APPLICATIONS
Example 1. Oxidation of p-phenylenediamine
Introduction
The oxidation reaction of PDA with hydrogen
peroxide in aqueous solutions forms coloured
products [6-81 which increase in quantity with
time until a stage is reached where a coloured
precipitate is formed. The overall reaction is given
by the following equation
PDA + H,O, --* oxidation products
and proceeds at a rate which is very slow but,
upon the addition of formaldehyde, becomes much
more rapid. The oxidation products formed during
the whole oxidation cycle are products of a consecutive oxidation path that, at some stage,
branches to give condensation products which are
oxidized much more slowly. Of all the oxidation
products, two products are intensely coloured and
absorb significantly
at 485 nm. The coloured
product that is formed earlier in the reaction path
is the so called ‘Wurster salt’, which has the
formula
Wurster
ion
Because of its ionic form this product is readily
soluble in water. The other coulored product is
formed later on along the reaction path and is a
product of the condensation branch of the path. It
has the following formula and is called the
‘Badrowski base’. This product is quite stable and
slightly soluble in water.
Bodrowski
base
zyxwvut
w
51 zyxwvuts
Original Research Paper
TABLE 1
The initial rate (IR) of oxidation followed by
the absorbance at 485 nm is weakly dependent on
Factorial experiment of PDA oxidation
the rate of formation of the Badrowski base;
Factors
Response l,
whereas it depends strongly on the rate of formaR**
B **
**
A**
D**
C
tion of the Wurster salt. Upon the addition of
-1
-1
-1
-1
0.0007
formaldehyde the rate of reaction is significantly
+1
-1
-1
-1
0.0025
increased, thus suggesting that the formaldehyde
-1
+1
-1
-1
0.0035
molecule is a ‘catalyst’ of the oxidation reaction.
+1
+1
-1
-1
0.0128
The ‘catalytic’ properties of formaldehyde are as-1
-1
+1
-1
0.0062
+1
-1
+1
-1
0.0192
sumed to stem from the formation of peroxy acids
-1
+1
+1
-1
0.6750
which readily form peroxy radicals [9] by the
+1
+1
+1
-1
5.8000
reaction: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
H- C =0
I
+
HP2 -
H
+1
0.0008
Total
1.88
2.57
1.87
C
1.87
AC
BC
ABC
D
AD
BD
ABD
CD
ACD
BCD
ABCD
2.56
1.86
-1
-1
0.96
+1
-1
+1
-1
-1
+1
0.0030
0.59
+1
-1
+1
0.0030
0.97
+1
-1
+1
0.0300
0.59
-1
-1
+1
+1
0.0180
0.96
+1
-1
+1
+1
0.0440
0.59
+1
+1
+1
2.1800
0.96
H- C - 00*
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
-0 OH
+1
+1
+1
+1
12.0000
0.58
I
OH
i
-
The peroxy radicals provide a lower activation
energy for the oxidation of PDA. The oxidation
process can then proceed via a peroxy radical
mechanism through the formation of the Wurster
salt [lo] as follows:
A
B
AB
2.59
-1
i
H-C
-1
Effects ***
* M ean value from duplicate measurements.
l
* A = [PDA],
B = pH,
C = [HCHO],
D = [H,O,],
R = IR
(absorbance units/min).
l
** Residuals, $
= 0.0042;
Ftb = 4.49.
TABLE 2
Ratio of IR between levels of each factor
Oxidant level
[H z4 1 = (+)
[H z4 1 = C-1
The Wurster salt is further oxidized to quinonediA. Ratio behveen [reagent] levels
imine, which is very unstable [ll] and partly con[HCHO]
pH
densed to form the Badrowski base, which is in
2.4
6.0
2.4
6.0
turn oxidized very slowly to quinone, and partly
hydrolysed and oxidised to quinone [7,8]. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
4.0
4.0
0.00 ppm
4.0
10.0
500.0
Results
The reaction system described above was investigated using the factorial experiment procedure after the performance of preliminary experiments to establish the range within which each
factor affects the rate. The results are tabulated in
Table 1.
From the factorial experiment analysis (F test)
it is apparent that all effects and interactions
between the factors are statistically significant,
which is commonly found in such experiments.
ppm
2.5
B. Ratio between [HCHO]
V’DAI
5.5
3.0
9.0
levels
PH
2.4
6.0
2.4
6.0
0.1%
30.0
700.0
9.0
200.0
1.0%
15.0
400.0
8.0
450.0
C. Ratio between pH levels
[HCHO]
lPD-41
0.1%
0.00 ppm
500.0 ppm
1.0%
0.1%
1.0%
3.0
10.0
5.0
5.0
100.0
250.0
108.0
302.0
Chemometrics and Intelligent Laboratory Systems
52
The initial rates given above, however, can be
manipulated to provide information about the initial rate equation. Such a manipulation is based
on the ratios of IR between the two levels of each
factor at different combinations of the levels of
the other factors. A comparison of these ratios is
presented in Table 2.
The values of ratios obtained in Table 2A between [PDA] levels at all combinations of levels of
the other factors do not differ very much and they
fall within the numerical range of l-10. Since the
ratio of PDA concentration levels is 10, this suggests that the rate equation may be approximated
by the expression.
IR = k,[PDA],
where k, = constant
(3)
On the other hand, the values obtained between
[HCHO] levels at all combinations of levels of the
other factors in Table 2B fall into two groups. One
group is characterized by small values and is obtained at a low pH level, and the other group is
characterized by relatively large values being obtained at a high pH level. This leads to the following rate equation,
IR = ~,/L[HCHO]
(4)
where k, = constant and p is a factor depending
on the pH value. Finally, the values obtained in
Table 2C between pH levels at all combinations of
other factor levels once again fall into two groups.
One group is characterized by low values and is
found when HCHO is absent and the other group
is characterized by relatively high values and is
found in experiments where HCHO is added at
the 500 ppm level. This leads to a rate equation of
the form
IR = k,Nh
(5)
where k, = constant, N is a factor depending on
the HCHO concentration and X is a factor that
depends on pH.
Discussion
The expression for IR, deduced from Table 2
for each level of [H20z], is therefore approximately given by the expression
IR = k/A [PDA] [HCHO]
(6)
n
where A = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO
f(pH), p is a factor that depends on
the interaction between pH and [HCHO], and
k = the kinetic constant.
The contribution of [H202] to the overall rate
response can be deduced from Table 1, from which
it is clear that, in the absence of formaldehyde,
[H202] has no effect while, in the presence of
formaldehyde, the contribution of [H20J to the
IR is much less than the change in [H20z] ( - 5).
The final picture that the factorial experiment
conveys by the method of ratios is that, in the
absence of HCHO, the initial rate equation is
IR = kh [PDA]
(7)
and, in the presence of HCHO,
IR= kXp[PDA][HCHO]{
f(H,O,)}
0)
which demonstrates that all factors and the interactions of any number of factors are significant,
which is in agreement with the factorial analysis of
the data of the factorial experiment.
The evidence that the IR depends on the pH is
reasonable if the rate is different for the different
dissociation species of PDA .2HCl since the wncentration of the species depends on pH. Also, the
dependence of IR on the interaction of pH and
[HCHO] is reasonable and can be explained by
the reaction of peroxy-radical formation if this is
assumed to be pH-dependent. Finally, the dependence of the IR on [H,O,] in the presence of
HCHO suggests once again the existence of the
peroxy-radical formation reaction, which occurs
when both HCHO and H,Oz are present.
Example 2. Oxidation of N,N,N’,N ‘-tetramethylp-phenylene diamine
Introduction
The oxidation of TMPDA is relatively slow and
follows the overall chemical equation [Et]
TMPDA + oxidant + oxidation products
The reaction with H,Oz as oxidant starts with the
formation of a product that develops a blue wlour
in the solution, becoming more intense with time.
However, after a long time the solution decolorises
once again. The formation of the blue wlour is
due to the formation of the Wurster salt, which is
l
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Original ResearchPaper
TABLE 3
Factorialexperimentof T’MPDA oxidation
Factors
A**
B**
C
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
-1
-1
-1
+1
+1
+1
+1
-1
-1
-1
-1
+1
+1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
l
*
Response*,
R **
Effects l **
D **
-1
-1
-1
-1
-1
-1
-1
-1
+1
+1
+1
+1
+1
+1
+1
+1
0.0007
0.0050
0.0100
0.0600
0.0001
0.0200
0.0125
0.0682
0.0020
0.0012
0.0280
0.1460
0.0009
0.0095
0.0231
0.1440
Total
0.046
A
0.059
B
0.040
AB
-0.0014
c
0.0001 AC
0.0006 BC
0.0012 ABC
0.0280 D
0.0190 AD
0.0237 BD
0.0158 ABD
-0.0025
CD
0.0002 ACD
-0.0024
BCD
0.0002 ABCD
53
Eq. (9) is in agreement with the factorial analysis results and this relationship provides evidence
that the HCHO molecule is not acting as a ‘catalyst’ in this oxidation reaction. If one considers
the change of IR between the levels of [H202] one
realizes that the ratio is close to unity, which
suggests that the H,O, is not the oxidizing agent
in this example. On the other hand the IR is
proportional to the concentration of TMPDA and
the pH. The dependence on pH suggests that the
rate of oxidation is different among the various
dissociation species of TMPDA * 2HCl that exist
in aqueous solution.
Example 3. Oxidation of pyrogallol
Introduction
The oxidation
of pyrogallol (Pg) may be
accomplished with a variety of oxidant molecules,
* Mean value from duplicatemeasurements.
a few of which can generate chemihnninescence
l * A = [TMPDA];
B = pH; C = [HCHO]; D = [H20z]; R =
(CL)
emission [12]. Periodate ion is one of the
IR (absorbanceunits/min).
oxidants that generates CL emission during the
l ** Residuals, $
= 9.0 xzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
lo-$ F:6 = 4.49.
oxidation of pyrogallol according to the chemical
reaction [13-151
quite zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
stable in the reacting mixture, being readily
Pg + IO; + oxidation products + hv(light)
soluble in aqueous solutions. This compound abThe CL emission generated is dependent on the
sorbs at 560 nm. In this example there is no
inner filter effect, the sensitizing effect and the
‘catalytic’ effect due to HCHO, and H,O, is not
rate of the reaction. When the experiment is caran effective oxidant for the reaction.
ried out under conditions that eliminate the inner
filter effect and there are no sensitizers in the
Results
reaction
mixture the CL emission provides a meaA similar factorial experiment was performed
sure
of
the
rate of the reaction. However, in this
as in the previous example and the data obtained
particular
CL
reaction it has been shown that the
are shown in Table 3. The factorial analysis of the
CL
emission
is
generated through energy transfer
data in Table 3 shows that the effect of [HCHO] is
between
primary
CL oxygen excimer species and
not significant. Neither are most of the interacsecondary
CL
species
originating from Pg oxidations involving [HCHO] and interactions that intion
products
[16]
as
shown
below
volve more than two factors.
(lo,):
Disctmion
Following the procedure of determining IR
ratios between the levels of each factor at constant
combinations of the other factor levels, as in the
previous example, it is found that the equation for
IR at each [H202] level is approximated by
IR = kX [TMPDA]
where k = kinetic constant and X = f(pH).
(9)
+F+230,+F*
F*+F+hv
where F is the fluorescent secondary species. In
this case both the concentration of oxygen excimer
and the concentration of the F species determine
the intensity of CL emission. The intensity of CL
emission depends on the ratio of these two concentration factors, which in turn depends on the
kinetics of the pyrogallol oxidation reaction since
Chemometrics and Intelligent Laboratory Systems
54 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
545
385
Wavclcngth,nm
n
225
Fig. 1. UV -visible spectra of (a) pyrogallol; (b) hydroxylamine
hydrochloride; and (c) molar mixture (1: 1) of pyrogallol and
hydroxylamine solutions.
both the oxygen excimer and the F are products of
the same reaction. However, since the oxygen extimer is a short-living sequence product originating from the oxidant reagent while the F is a
sequence product originating from pyrogallol, the
ratio also depends on the degree of overlap of the
reaction profiles of the two products within the
reaction period, or on the extent of other parallel
reactions that occur before the CL emission step,
thus decreasing the concentration of F. The addition of a thud compound to the reaction system
may produce a change in the intensity of CL
emission because it may change the ratio of the
oxygen excimer to the F molecule concentration
by acting as a reagent or catalyst of the oxidation
reaction, or it may change the quantum yield
because of a change of the structure of the F
molecule.
The overall rate of reaction, up to the step of
CL emission, depends on the pH of the aqueous
solution; it is relatively rapid and it is monitored
with a photomultiplier after mixing the Pg solution with the oxidant solution in a flow injection
analysis manifold system. From previous work it
was found that CL emission intensity is increased
270
w.vctength,nm
470
Fig. 2. Fingerprint fluorescence spectra with AX = 25 mn of
(A ) pyrogallol;
(B)
hydroxylamine
hydrochloride;
and (C)
molar mixture (1: 1) of pyrogallol and hydroxylamine solutions.
TABLE 4
Factorial experiment of Pg oxidation (pH = 7.8)
Factors
*
Response,
Effects
l
*
M ean
Sign/NCE
square
level
A*
g*
C*
-1
-1
-1
230
+1
-1
-1
4
121.0
A
29282
Yes
-1
+1
-1
1
112.5
B
25312
Yes
+1
+1
-1
38
432.9
AB
373248
Yes
-1
-1
+1
440
335.5
c
225120
Yes
+1
-1
+1
45
216.0
93312
Yes
-1
+1
+1
35
210.0
+1
+1
+1
1100
300.0
AC
BC
ABC
R*
95%
*A = [Pg], B = [NH,OH],
l
Total
88200
Yes
180600
Yes
C = [IO,- ), R = hr (mv).
* Residuals from 12 repeat measurements, $
4.84.
= 379.5;
FtrI =
n
55
Original ResearchPaper
about five-fold by the addition of hydroxylamirte
at optimum concentration
[13]. The hydroxyl-
amine is rapidly oxidized by periodate but this
oxidation process is not accompanied by light
emission. In order to discover the origin of the CL
enhancement upon the addition of hydroxylamine
we proceeded with the design of a factorial experiment.
Results
The data obtained
from the factorial experiment, together with the results of the factorial
analysis, are presented in Table 4.
Discussion
From Table 4 it can be seen that the order of
effects and interactions from the factorial experiment has the following sequence:
AB>C>ABC>AC>BC>A>B
The interaction AC between the factors of [Pg]
and [IO;], as well as the interaction BC between
the factors of [NH,OH] and [IO;] are expected,
since periodate reacts with both of them sirnultaneously in parallel oxidation reactions. However,
the strong interaction between [Pg] and [NH,OH]
was not expected. One possibility for such a strong
interaction between [Pg] and [NH,OH] was to
consider the association of Pg with NH,OH in the
formation of species that are oxidized by periodate with higher quantum yield. This suggestion
was investigated by obtaining the absorption spectra and fingerprint fluorescence spectra of Pg and
NH,OH solutions alone and in admixture. These
spectra are shown in Figs. 1 and 2, and they
provide evidence of the formation of such a PgNH,OH association compound.
CONCLUSION
The three examples presented in this work show
clearly how the factorial experiment is able to
provide useful information
about the chemistry
involved during a reaction process and how the
initial rate data can provide the kinetics of reactions in a simplified model, apart from providing
linear mathematical
models
of the response
surface.
REFERENCES
1 O.A. Hougen, K.M. Watson, Chemical Process Principles,
Part 3, Kinetics and Catalysis, Wiley, New York, 1947, pp.
815-863.
2 H.A. Mottola, Kinetic Aspects of Ana&tical Chemistry, Wiley, New York, 1988, pp. 25-30.
3 F. Yates, Design and Analysis of Factorial Experiments,
ImperialBureauof Soil Sciences, London, 1937.
4 W.G. Hunter and R. Mezaki, Catalyst selection by group
screening, Industrial and Engineering Chemistry, 56 (1964)
38-40.
5 G.E.P. Box and W.G. Hunter, The experimental study of
physical mechanics, Technometrics, 7 (1965) 23-42.
6 B.W. Bailey and J.M. Rankin, New spectrophotometric
method for determination of formaldehyde, Analytical
Chemistry, 43 (1971) 782-784.
7 N.P. Evmiridis and M.I. Karayannis, Determination of
formaldehyde using a spectrophotometric
method. Part I.
Oxidation of p-phenylenediamine
with hydrogen peroxide,
The Analyst (London), 112 (1987) 831-835.
8 N.P. Evmiridis, N.C. Sadiris and M.I. Karayannis, De-
termination of formaldehydeusing a kinetic-speotrophoto
metric method. Part II. Oxidation of N-methyl-substituted
1,4-phenylenediamineswith hydrogenperoxide,TheAnalyst
(London), 115 (1990) 1103-1107.
9 G. Woker, Ein Be&rag zur Theorie der Oxidations-fermente
ilber “Peroxidase” und “Katalase’‘-Reaktionen
des Formaldehydes und Acetaldehydes, Chemische Berichte, 47 (1914)
1024-1029.
for10 C.E. Boozer and G.S. Hammond, Molecular-complex
mation in free radical reactions, Journal of the American
Chemical Society, 76 (1954) 3861-3862; Air oxidation of
hydrocarbons. II. The stoichiometry and fate of inhibitors
in benzene and chlorobenzene,
Journal of the American
Chemical Society, 77 (1955) 3233-3237.
11 R. Adams and A.S. Nagarkatti,
Quinone imides. I. pQuinone disulfonimides,
Journal of the American Chemical
Society, 72 (1950) 4601-4606.
12 NC. Thanasoulias and N.P. Evmiridis, presented at the
EuropeanConferenceof Analytical Chemistry“Euroanalysis VII”, Vienna, 26-31 August, 1990.
13 N.P. Evmiridis, Effect of hydroxylamineon chemiluminescence intensity generatedduring the oxidation of pyrogallol
with periodate, The Analyst (London), 112 (1987) 825-829.
14 N.P. Evmiridis, Prospects of using chemihuninescence
emission generated during oxidation of pyrogallol with
periodate for the determination
of pyrogallol with flow
injection, The Analyst (London), 113 (1988) 1051-1056.
15 N.P. Evmiridis, Periodate determination by FIA with CL
emission detection and its application to ethylene glycol,
Tafanta, 36(3) (1989) 357-362.
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88 (1964) 1574.
49 zyxwvut
Original Research Paper
and Intelligent Laboratory Systems, 12 (1991) 49-55
Elsevier Science Publishers B.V.. Amsterdam
Chemometrics
Factorial design in oxidation reactions and analysis
of variance of initial rates of reaction
N.C. Sadiris, NC. Thanasoulias
and N.P. Evmiridis *
Laboratory of Analytical Chemistry, Department of Chemistry, University of loannina,
451 10 Ioannina (Greece)
(Received 23 August 1990; accepted 25 January 1991)
Sadiris, N.C., Thanasoulias, N.C. and Evmiridis, N.P., 1991. Factorial design in oxidation reactions and analysis of variance of initial
rates of reaction. Chemometrics and Intelligent Laboratory Systems, 12: 49-55.
An illustration is given of how the factorial experiment and analysis can provide the basis for the deduction of information about
the chemistry of a reaction and/or reaction kinetics with three oxidation reaction examples.
INTRODUCTION
In the world of chemical reactions a molecule
of a particular compound goes through a change
from one form to another by colliding either with
inert molecules to give reaction products composed of its constituent atoms, or with active
molecules that act either (i) as reagents, giving
reaction products that are composed of atoms that
belong to both types of reacting molecules, or (ii)
as catalysts that cause an effective collision to
occur, changing the chemical nature of the molecule or allowing it to react with other molecules.
The dissociation species of the reagents, residual reactivity and/ or instability of reaction products and catalyst intermediates are some of the
factors that complicate the reaction process in
solution, leading to the expression
reaction paths that are occurring in the system at
any moment during the reaction period. However,
the rate equation (1) can be considerably simplified by replacing the rate by the initial rate (IR)
and the rate equations by the much simpler initial
rate equations, thus obtaining the equation
IR(observed)
= C(IR,)
(2)
where
II+@
I
0
and nXi
is the product of u factors of Xi where
u is 1 for-first order, 2 for second order, and 3 for
a third order kinetics, or for some more complicated catalytic reactions in solution [1,2], and
where ki are constants and Xi is the concentration of the jth compound or, in the most complex
case, it is a function of the compound’s concentrar (observed) = Cr,
(I)
tion, and subscripts 1, 2, 3 refer to compounds 1,
where zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
r, are the rate contributions from all the
2, 3, respectively, and subscript i refers to the
Chemometrics and Intelligent Laboratory Systems
50 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
simultaneous changes that contribute to the overall change in the initial part of the reaction and u
represents the number of the factors involved in
the product. The establishment of the specific
equation that is followed by the reacting system
under examination is a matter of discovering the
effects and interactions of concentration factors,
which is simple since, in most cases, there are no
more than two dominant terms involved in eq. (2).
A useful method used to investigate effects and
interactions is the factorial experiment, which is
conventionally used as a ‘precursor’ method for
generating linear mathematical models which represent the response surface [3] for a response
optimization procedure in analytical chemistry.
The establishment of the significance of effects
and interactions proceeds with the factorial analysis procedure described by Yates [3].
The factorial procedure consists of the following stages:
1. Establishment of the factors involved in the
determination of the response size.
2. Decision making about the levels ( - , + ) of
each factor. The decision has to be taken in
such a way that the levels convey the necessary
information for the correct representation of
the response surface.
3. The execution of the trials of the factorial
experiment, which must be done in a random
order.
4. The statistical analysis of the factorial experiment.
The factorial experiment is a general method
and is applicable to all types of responses. However, if the response is the rate of the reaction and
such factors involved are the concentrations of the
reactants the factorial experiment provides a study
of the kinetics of the reaction and such factorial
experiments have been applied in the assessment
of the validity of proposed kinetic models [4,5].
However, the factorial experiment can also be
used to provide information about the actual
chemistry and kinetics of complex reacting systems, as explained above.
In this work we present the factorial experiments for the oxidation of (1) p-phenylenediamine (PDA), (2) N, N, N ‘, N ‘-tetramethyl-p-phenylenediamine (TMPDA), and (3) pyrogallol, and
n
we use these experiments to draw conclusions
about the chemistry and the kinetics of the oxidation reactions. The conclusions drawn are further
supported by other methods.
APPLICATIONS
Example 1. Oxidation of p-phenylenediamine
Introduction
The oxidation reaction of PDA with hydrogen
peroxide in aqueous solutions forms coloured
products [6-81 which increase in quantity with
time until a stage is reached where a coloured
precipitate is formed. The overall reaction is given
by the following equation
PDA + H,O, --* oxidation products
and proceeds at a rate which is very slow but,
upon the addition of formaldehyde, becomes much
more rapid. The oxidation products formed during
the whole oxidation cycle are products of a consecutive oxidation path that, at some stage,
branches to give condensation products which are
oxidized much more slowly. Of all the oxidation
products, two products are intensely coloured and
absorb significantly
at 485 nm. The coloured
product that is formed earlier in the reaction path
is the so called ‘Wurster salt’, which has the
formula
Wurster
ion
Because of its ionic form this product is readily
soluble in water. The other coulored product is
formed later on along the reaction path and is a
product of the condensation branch of the path. It
has the following formula and is called the
‘Badrowski base’. This product is quite stable and
slightly soluble in water.
Bodrowski
base
zyxwvut
w
51 zyxwvuts
Original Research Paper
TABLE 1
The initial rate (IR) of oxidation followed by
the absorbance at 485 nm is weakly dependent on
Factorial experiment of PDA oxidation
the rate of formation of the Badrowski base;
Factors
Response l,
whereas it depends strongly on the rate of formaR**
B **
**
A**
D**
C
tion of the Wurster salt. Upon the addition of
-1
-1
-1
-1
0.0007
formaldehyde the rate of reaction is significantly
+1
-1
-1
-1
0.0025
increased, thus suggesting that the formaldehyde
-1
+1
-1
-1
0.0035
molecule is a ‘catalyst’ of the oxidation reaction.
+1
+1
-1
-1
0.0128
The ‘catalytic’ properties of formaldehyde are as-1
-1
+1
-1
0.0062
+1
-1
+1
-1
0.0192
sumed to stem from the formation of peroxy acids
-1
+1
+1
-1
0.6750
which readily form peroxy radicals [9] by the
+1
+1
+1
-1
5.8000
reaction: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
H- C =0
I
+
HP2 -
H
+1
0.0008
Total
1.88
2.57
1.87
C
1.87
AC
BC
ABC
D
AD
BD
ABD
CD
ACD
BCD
ABCD
2.56
1.86
-1
-1
0.96
+1
-1
+1
-1
-1
+1
0.0030
0.59
+1
-1
+1
0.0030
0.97
+1
-1
+1
0.0300
0.59
-1
-1
+1
+1
0.0180
0.96
+1
-1
+1
+1
0.0440
0.59
+1
+1
+1
2.1800
0.96
H- C - 00*
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
-0 OH
+1
+1
+1
+1
12.0000
0.58
I
OH
i
-
The peroxy radicals provide a lower activation
energy for the oxidation of PDA. The oxidation
process can then proceed via a peroxy radical
mechanism through the formation of the Wurster
salt [lo] as follows:
A
B
AB
2.59
-1
i
H-C
-1
Effects ***
* M ean value from duplicate measurements.
l
* A = [PDA],
B = pH,
C = [HCHO],
D = [H,O,],
R = IR
(absorbance units/min).
l
** Residuals, $
= 0.0042;
Ftb = 4.49.
TABLE 2
Ratio of IR between levels of each factor
Oxidant level
[H z4 1 = (+)
[H z4 1 = C-1
The Wurster salt is further oxidized to quinonediA. Ratio behveen [reagent] levels
imine, which is very unstable [ll] and partly con[HCHO]
pH
densed to form the Badrowski base, which is in
2.4
6.0
2.4
6.0
turn oxidized very slowly to quinone, and partly
hydrolysed and oxidised to quinone [7,8]. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
4.0
4.0
0.00 ppm
4.0
10.0
500.0
Results
The reaction system described above was investigated using the factorial experiment procedure after the performance of preliminary experiments to establish the range within which each
factor affects the rate. The results are tabulated in
Table 1.
From the factorial experiment analysis (F test)
it is apparent that all effects and interactions
between the factors are statistically significant,
which is commonly found in such experiments.
ppm
2.5
B. Ratio between [HCHO]
V’DAI
5.5
3.0
9.0
levels
PH
2.4
6.0
2.4
6.0
0.1%
30.0
700.0
9.0
200.0
1.0%
15.0
400.0
8.0
450.0
C. Ratio between pH levels
[HCHO]
lPD-41
0.1%
0.00 ppm
500.0 ppm
1.0%
0.1%
1.0%
3.0
10.0
5.0
5.0
100.0
250.0
108.0
302.0
Chemometrics and Intelligent Laboratory Systems
52
The initial rates given above, however, can be
manipulated to provide information about the initial rate equation. Such a manipulation is based
on the ratios of IR between the two levels of each
factor at different combinations of the levels of
the other factors. A comparison of these ratios is
presented in Table 2.
The values of ratios obtained in Table 2A between [PDA] levels at all combinations of levels of
the other factors do not differ very much and they
fall within the numerical range of l-10. Since the
ratio of PDA concentration levels is 10, this suggests that the rate equation may be approximated
by the expression.
IR = k,[PDA],
where k, = constant
(3)
On the other hand, the values obtained between
[HCHO] levels at all combinations of levels of the
other factors in Table 2B fall into two groups. One
group is characterized by small values and is obtained at a low pH level, and the other group is
characterized by relatively large values being obtained at a high pH level. This leads to the following rate equation,
IR = ~,/L[HCHO]
(4)
where k, = constant and p is a factor depending
on the pH value. Finally, the values obtained in
Table 2C between pH levels at all combinations of
other factor levels once again fall into two groups.
One group is characterized by low values and is
found when HCHO is absent and the other group
is characterized by relatively high values and is
found in experiments where HCHO is added at
the 500 ppm level. This leads to a rate equation of
the form
IR = k,Nh
(5)
where k, = constant, N is a factor depending on
the HCHO concentration and X is a factor that
depends on pH.
Discussion
The expression for IR, deduced from Table 2
for each level of [H20z], is therefore approximately given by the expression
IR = k/A [PDA] [HCHO]
(6)
n
where A = zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO
f(pH), p is a factor that depends on
the interaction between pH and [HCHO], and
k = the kinetic constant.
The contribution of [H202] to the overall rate
response can be deduced from Table 1, from which
it is clear that, in the absence of formaldehyde,
[H202] has no effect while, in the presence of
formaldehyde, the contribution of [H20J to the
IR is much less than the change in [H20z] ( - 5).
The final picture that the factorial experiment
conveys by the method of ratios is that, in the
absence of HCHO, the initial rate equation is
IR = kh [PDA]
(7)
and, in the presence of HCHO,
IR= kXp[PDA][HCHO]{
f(H,O,)}
0)
which demonstrates that all factors and the interactions of any number of factors are significant,
which is in agreement with the factorial analysis of
the data of the factorial experiment.
The evidence that the IR depends on the pH is
reasonable if the rate is different for the different
dissociation species of PDA .2HCl since the wncentration of the species depends on pH. Also, the
dependence of IR on the interaction of pH and
[HCHO] is reasonable and can be explained by
the reaction of peroxy-radical formation if this is
assumed to be pH-dependent. Finally, the dependence of the IR on [H,O,] in the presence of
HCHO suggests once again the existence of the
peroxy-radical formation reaction, which occurs
when both HCHO and H,Oz are present.
Example 2. Oxidation of N,N,N’,N ‘-tetramethylp-phenylene diamine
Introduction
The oxidation of TMPDA is relatively slow and
follows the overall chemical equation [Et]
TMPDA + oxidant + oxidation products
The reaction with H,Oz as oxidant starts with the
formation of a product that develops a blue wlour
in the solution, becoming more intense with time.
However, after a long time the solution decolorises
once again. The formation of the blue wlour is
due to the formation of the Wurster salt, which is
l
zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
Original ResearchPaper
TABLE 3
Factorialexperimentof T’MPDA oxidation
Factors
A**
B**
C
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
-1
-1
-1
+1
+1
+1
+1
-1
-1
-1
-1
+1
+1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
l
*
Response*,
R **
Effects l **
D **
-1
-1
-1
-1
-1
-1
-1
-1
+1
+1
+1
+1
+1
+1
+1
+1
0.0007
0.0050
0.0100
0.0600
0.0001
0.0200
0.0125
0.0682
0.0020
0.0012
0.0280
0.1460
0.0009
0.0095
0.0231
0.1440
Total
0.046
A
0.059
B
0.040
AB
-0.0014
c
0.0001 AC
0.0006 BC
0.0012 ABC
0.0280 D
0.0190 AD
0.0237 BD
0.0158 ABD
-0.0025
CD
0.0002 ACD
-0.0024
BCD
0.0002 ABCD
53
Eq. (9) is in agreement with the factorial analysis results and this relationship provides evidence
that the HCHO molecule is not acting as a ‘catalyst’ in this oxidation reaction. If one considers
the change of IR between the levels of [H202] one
realizes that the ratio is close to unity, which
suggests that the H,O, is not the oxidizing agent
in this example. On the other hand the IR is
proportional to the concentration of TMPDA and
the pH. The dependence on pH suggests that the
rate of oxidation is different among the various
dissociation species of TMPDA * 2HCl that exist
in aqueous solution.
Example 3. Oxidation of pyrogallol
Introduction
The oxidation
of pyrogallol (Pg) may be
accomplished with a variety of oxidant molecules,
* Mean value from duplicatemeasurements.
a few of which can generate chemihnninescence
l * A = [TMPDA];
B = pH; C = [HCHO]; D = [H20z]; R =
(CL)
emission [12]. Periodate ion is one of the
IR (absorbanceunits/min).
oxidants that generates CL emission during the
l ** Residuals, $
= 9.0 xzyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
lo-$ F:6 = 4.49.
oxidation of pyrogallol according to the chemical
reaction [13-151
quite zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
stable in the reacting mixture, being readily
Pg + IO; + oxidation products + hv(light)
soluble in aqueous solutions. This compound abThe CL emission generated is dependent on the
sorbs at 560 nm. In this example there is no
inner filter effect, the sensitizing effect and the
‘catalytic’ effect due to HCHO, and H,O, is not
rate of the reaction. When the experiment is caran effective oxidant for the reaction.
ried out under conditions that eliminate the inner
filter effect and there are no sensitizers in the
Results
reaction
mixture the CL emission provides a meaA similar factorial experiment was performed
sure
of
the
rate of the reaction. However, in this
as in the previous example and the data obtained
particular
CL
reaction it has been shown that the
are shown in Table 3. The factorial analysis of the
CL
emission
is
generated through energy transfer
data in Table 3 shows that the effect of [HCHO] is
between
primary
CL oxygen excimer species and
not significant. Neither are most of the interacsecondary
CL
species
originating from Pg oxidations involving [HCHO] and interactions that intion
products
[16]
as
shown
below
volve more than two factors.
(lo,):
Disctmion
Following the procedure of determining IR
ratios between the levels of each factor at constant
combinations of the other factor levels, as in the
previous example, it is found that the equation for
IR at each [H202] level is approximated by
IR = kX [TMPDA]
where k = kinetic constant and X = f(pH).
(9)
+F+230,+F*
F*+F+hv
where F is the fluorescent secondary species. In
this case both the concentration of oxygen excimer
and the concentration of the F species determine
the intensity of CL emission. The intensity of CL
emission depends on the ratio of these two concentration factors, which in turn depends on the
kinetics of the pyrogallol oxidation reaction since
Chemometrics and Intelligent Laboratory Systems
54 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA
545
385
Wavclcngth,nm
n
225
Fig. 1. UV -visible spectra of (a) pyrogallol; (b) hydroxylamine
hydrochloride; and (c) molar mixture (1: 1) of pyrogallol and
hydroxylamine solutions.
both the oxygen excimer and the F are products of
the same reaction. However, since the oxygen extimer is a short-living sequence product originating from the oxidant reagent while the F is a
sequence product originating from pyrogallol, the
ratio also depends on the degree of overlap of the
reaction profiles of the two products within the
reaction period, or on the extent of other parallel
reactions that occur before the CL emission step,
thus decreasing the concentration of F. The addition of a thud compound to the reaction system
may produce a change in the intensity of CL
emission because it may change the ratio of the
oxygen excimer to the F molecule concentration
by acting as a reagent or catalyst of the oxidation
reaction, or it may change the quantum yield
because of a change of the structure of the F
molecule.
The overall rate of reaction, up to the step of
CL emission, depends on the pH of the aqueous
solution; it is relatively rapid and it is monitored
with a photomultiplier after mixing the Pg solution with the oxidant solution in a flow injection
analysis manifold system. From previous work it
was found that CL emission intensity is increased
270
w.vctength,nm
470
Fig. 2. Fingerprint fluorescence spectra with AX = 25 mn of
(A ) pyrogallol;
(B)
hydroxylamine
hydrochloride;
and (C)
molar mixture (1: 1) of pyrogallol and hydroxylamine solutions.
TABLE 4
Factorial experiment of Pg oxidation (pH = 7.8)
Factors
*
Response,
Effects
l
*
M ean
Sign/NCE
square
level
A*
g*
C*
-1
-1
-1
230
+1
-1
-1
4
121.0
A
29282
Yes
-1
+1
-1
1
112.5
B
25312
Yes
+1
+1
-1
38
432.9
AB
373248
Yes
-1
-1
+1
440
335.5
c
225120
Yes
+1
-1
+1
45
216.0
93312
Yes
-1
+1
+1
35
210.0
+1
+1
+1
1100
300.0
AC
BC
ABC
R*
95%
*A = [Pg], B = [NH,OH],
l
Total
88200
Yes
180600
Yes
C = [IO,- ), R = hr (mv).
* Residuals from 12 repeat measurements, $
4.84.
= 379.5;
FtrI =
n
55
Original ResearchPaper
about five-fold by the addition of hydroxylamirte
at optimum concentration
[13]. The hydroxyl-
amine is rapidly oxidized by periodate but this
oxidation process is not accompanied by light
emission. In order to discover the origin of the CL
enhancement upon the addition of hydroxylamine
we proceeded with the design of a factorial experiment.
Results
The data obtained
from the factorial experiment, together with the results of the factorial
analysis, are presented in Table 4.
Discussion
From Table 4 it can be seen that the order of
effects and interactions from the factorial experiment has the following sequence:
AB>C>ABC>AC>BC>A>B
The interaction AC between the factors of [Pg]
and [IO;], as well as the interaction BC between
the factors of [NH,OH] and [IO;] are expected,
since periodate reacts with both of them sirnultaneously in parallel oxidation reactions. However,
the strong interaction between [Pg] and [NH,OH]
was not expected. One possibility for such a strong
interaction between [Pg] and [NH,OH] was to
consider the association of Pg with NH,OH in the
formation of species that are oxidized by periodate with higher quantum yield. This suggestion
was investigated by obtaining the absorption spectra and fingerprint fluorescence spectra of Pg and
NH,OH solutions alone and in admixture. These
spectra are shown in Figs. 1 and 2, and they
provide evidence of the formation of such a PgNH,OH association compound.
CONCLUSION
The three examples presented in this work show
clearly how the factorial experiment is able to
provide useful information
about the chemistry
involved during a reaction process and how the
initial rate data can provide the kinetics of reactions in a simplified model, apart from providing
linear mathematical
models
of the response
surface.
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815-863.
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3 F. Yates, Design and Analysis of Factorial Experiments,
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Oxidation of p-phenylenediamine
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