Embed Size (px)
Citation preview
Application of the split-plot experimental design for the optimizationof a catalytic procedure for the determination of Cr(VI)
CeÂsar Reis1,a, JoaÄo Carlos de Andradea,*, Roy E. Brunsa, Regina C.C.P. Moranb
a Universidade Estadual de Campinas, Instituto de QuõÂmica, CP 6154, 13083-970 Campinas±SP, Brazilb Universidade Estadual de Campinas, Instituto de MatemaÂtica, EstatõÂstica e CieÃncias da Computac,aÄo, Departamento de EstatõÂstica, CP
6065, 13093-970 Campinas±SP, Brazil
Received 19 September 1997; received in revised form 26 February 1998; accepted 3 March 1998
Abstract
A kinetic catalytic procedure for the determination of Cr(VI), based on the o-dianisidine oxidation reaction with hydrogen
peroxide in a weakly acid medium was optimized with respect to both reactants [HCl, o-dianisidine and H2O2] and solvent
composition [mixtures of water, acetone and N, N-dimethylformamide], in order to achieve higher sensitivities. This was
accomplished by making use of a split-plot experimental design which permitted simultaneous variations in both mixture and
process variables, using a response surface approach. Ten mixture experiments were randomized at each one of the 23 factorial
levels and error analysis was performed using a split-plot approach. The optimal mixture [water±acetone 70±30% m/m] and
process variables [HCl: 6.0�10ÿ4 mol/l, o-dianisidine: 1.9�10ÿ2 mol/l and H2O2: 0.79 mol/l] values resulted in a signi®cant
sensitivity increase compared with a similar procedure described in the literature. # 1998 Elsevier Science B.V. All rights
reserved.
Keywords: Split-plot design; Factorial design; Mixtures design; Optimization; Response surface analysis
1. Introduction
The use of solvent mixtures as a reaction medium
has been widely used in analytical chemistry [1±8].
Larger determination sensitivities [3,7] and greater
solubilities of organic reagents [2], as well as the
determination of water insoluble substances [5] and
better selectivities [1,8] have been reported using
organic±aqueous systems.
A catalytic kinetic spectrophotometric method using
the hydrogen peroxide oxidation of o-dianisidine (3,
30-dimethoxybenzidine) in an acid medium has been
used to determine Cr(VI) concentration [9]. Since the
o-dianisidine reagent is slightly soluble in water, use
of an organic solvent miscible with water is necessary
to provide an appropriate reaction medium. Dolma-
nova et al. [2] used an ethanol±water mixture to
determine microquantities of Cr(VI) in AlCl3. Later,
they studied the effect of the organic±aqueous medium
on the reaction of Cr(III) with o-dianisidine using
binary systems of water with each of the following
solvents: methanol, ethanol, n-propanol, iso-propanol,
ethyleneglycol, acetone and N, N0-dimethylforma-
Analytica Chimica Acta 369 (1998) 269±279
*Corresponding author. Fax: +55 19 7883023; e-mail:
[email protected] leave from the Universidade Federal de Vic,osa, Departa-
mento de QuõÂmica, 36570-000 Vic,osa±MG, Brazil
0003-2670/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved.
P I I S 0 0 0 3 - 2 6 7 0 ( 9 8 ) 0 0 2 4 6 - 3
mide (DMF) [10]. However, their attempts [2,10] to
improve the solvent mixture proportions and reaction
conditions in order to provide better sensitivities
were performed without using statistical designs, such
as those frequently employed to optimize solvent
mixtures for chromatographic analysis [11±14].
In statistical mixture designs [11], chemical and
physical properties are studied as a function of varying
proportions of the mixture components. The propor-
tions used in individual experiments are not indepen-
dent, since their sum must always be constant (100%).
On the other hand, other factors besides component
proportions, such as temperature, pressure and pH, as
well as concentrations of reagents, can also in¯uence
the properties measured in the reaction medium.
These variables, known as process variables [15], in
contrast to the mixture variables, are statistically
independent and can be freely varied within the
physical and chemical constraints of the system. Ide-
ally optimization of all factors, both process and
mixture variables, should be undertaken simulta-
neously. However this endeavour can result in opera-
tional dif®culties since the large number of
experiments involved in combined process±mixture
designs should be executed randomly to obtain accu-
rate error estimates for testing the signi®cance of
model parameters. Special designs with restricted
randomization requirements can be used to overcome
these dif®culties [16±18].
The objective of this work is to determine simulta-
neously the optimum values of the proportions of
water, acetone and dimethylformamide as a reaction
medium and the concentrations of HCl, o-dianisidine
and H2O2 as reagents for the analytical determination
of Cr(VI), using the 450 nm absorption of the oxidized
species of o-dianisidine as the system response. The
split-plot design proposed by Wooding [19] is used to
provide an operationally viable optimization proce-
dure for both these mixture and process variables.
2. The split-plot experimental design
The simultaneous optimization of mixture and pro-
cess variables involves performing p different factorial
runs on m different mixtures. The large number of
experiments to be made (mxp) results in operational
dif®culties since an accurate error estimate implies
randomization of all the experiments. These dif®cul-
ties can be reduced using the split-plot strategy [19].
Different mixture experiments (Fig. 1(a)) are carried
out for each of the p conditions of the factorial design
as shown in Fig. 1(b). These are randomized as
recommended for any simple mixture design. The p
different factorial blocks are also executed randomly.
This procedure is considerably simpler to execute than
a complete randomization of all experiments. Instead
of obtaining one variance estimate evaluated from
replicates of all experiments, two experimental error
sources are obtained with the split-plot approach, one
from the subplot or mixture treatments and the other
from the factorial or main plot treatments. To obtain
accurate measures of the main and subplot variances,
duplicate determinations of all experiments are
recommended and were carried out in this work. These
two error sources can be analyzed using a conven-
tional analysis of variance (ANOVA) of the mixture±
component process variable model with
Yijk � �� Ri � Zj � RZij � Xk � ZXjk � �ijk (1)
where i�1, 2; j�1, 2,..., 8 and k�1, 2,..., 10. Yijk is the
response value taken from the kth mixture at the jth
factorial point and for the ith replicate. Also
� general mean
Ri effect of the ith replication, R�NID�0; �2R�
Zj effect of the jth process (main plot) treat-
ment
RZij replicate by main plot treatment interaction
effects used for main plot estimate,
RZij�NID�0; �2RZ�
Xk effect of the kth mixture (subplot) treatment
ZXjk interaction effect of the jth process and kth
mixture treatments and
�ijk subplot error consisting of replicate�sub-
plot and replicate�main plot�subplot
interactions, ��NID�0; �2e�:
Note that interaction effects involving replicates are
used to estimate the main plot and subplot errors since
replication is not expected to alter process or mixture
variable effect values.
270 C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279
Fig. 1. The split-plot experimental design. (a) Mixture design (b) representation of each point for the 23 process variable complete factorial
design.
C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279 271
Assuming quadratic models for both mixture and
process variables, the dependence of the response on
the Xk mixture and Zj process variables can be written
as
Y�X; Z� �X3
k
gokXk �
X3
k<
X3
k0go
kk0Xk;Xk0
�X3
j
X3
k
gjkXk �
X3
k<
X3
k0g
jkk0XkXk0
" #Zj
�X3
i<
X3
j
X3
k
gijk Xk�
X3
k<
X3
k0g
ijkk0XkXk0
" #ZiZj:
(2)
The ®rst six terms correspond to the linear and non-
linear portions of the mixture model since they do not
involve process variables. The summation term that is
the coef®cient of Zj represents the effect of changing
the jth process variable level in terms of the linear and
non-linear mixture parameters. The last summation in
Eq. (2) represents the interaction effect of the two
process variables written in terms of mixture model
parameters.
3. Experimental
All experiments were carried out using deionized
water and analytical grade reagents. The stock solu-
tion of HCl (0.01 mol/l) was prepared by dilution from
the concentrated acid and concentrated H2O2
(9.7 mol/l) was used directly, after standardization.
In addition, o-dianisidine solutions (0.05 mol/l) were
prepared by dissolving appropriate amounts of this
reagent (Aldrich) in acetone or in N, N0- dimethyl-
formamide (DMF). These solutions can be used for a
period of 1 week if stored in darkened bottles [20]. A
500 mg/ml standard stock solution of Cr(VI) was also
prepared using K2Cr2O7 (>99.5%, Merck). All runs
were carried out in 30 ml snap-cap glass ¯asks with
plastic lids. The solvents were transferred to the
reaction ¯asks using precision dispensers. All glass
and plastic materials were washed with non-ionic
detergent and then exhaustively rinsed with distilled
water and later with deionized water.
Each point of the 23 factorial for HCl (z1),
o-dianisidine (z2) and H2O2 (z3) was investigated with
a three-component mixture design involving water
(x1), acetone (x2), and DMF, (x3). The experimental
region covered by the design was restricted owing to
the low solubility of o-dianisidine in water, especially
in the presence of HCl and H2O2. Table 1 shows the
mass percent proportions of the mixtures along with
their pseudocomponent values. The mixture variables
were measured in terms of % m/m with a 10 g total
mass for each mixture.
The z1, z2, and z3 variables were then adjusted by
adding 50 ml (ÿlevel) and 500 ml (�level) of the stock
0.01 mol/l HCl solution, 300 ml (ÿlevel) and 600 ml
(�level) of the stock 0.05 mol/l o-dianisidine solution
and 300 ml (ÿlevel) and 600 ml (�level) of the stock
H2O2 solution. Table 2 contains the concentrations
and the scaled values for these process variables. The
Table 1
Experimental design for the mixture
Components (% m/m) Pseudocomponentsa
Mixture Water Acetone DMF X1 X2 X3
1 70 30 0 5/8 3/8 0
2 20 80 0 0 1 0
3 20 0 80 0 0 1
4 70 0 30 5/8 0 3/8
5 45 55 0 5/16 11/16 0
6 20 40 40 0 1/2 1/2
7 45 0 55 5/16 0 11/16
8 45 27.5 27.5 5/16 55/160 55/160
9 57.4 21.3 21.3 374/800 213/800 213/800
10 32.5 16.9 50.6 5/32 169/800 253/400
a The following equations were used to calculate pseudocomponent
values:
X1 � CH2O ÿ 20
80; X2 � CAcetone
80; X3 � CDMF
80
Table 2
Concentration and scaled values of the complete 23 factorial design
Original variables (mol/l) Scaled variables
Run HCl o-Dianisidine H2O2 z1 z2 z3
1 5.0�10ÿ5 1.5�10ÿ3 0.29 ÿ1 ÿ1 ÿ1
2 5.0�10ÿ4 1.5�10ÿ3 0.29 �1 ÿ1 ÿ1
3 5.0�10ÿ5 3.0�10ÿ3 0.29 ÿ1 �1 ÿ1
4 5.0�10ÿ4 3.0�10ÿ3 0.29 �1 �1 ÿ1
5 5.0�10ÿ5 1.5�10ÿ3 0.58 ÿ1 ÿ1 �1
6 5.0�10ÿ4 1.5�10ÿ3 0.58 �1 ÿ1 �1
7 5.0�10ÿ5 3.0�10ÿ3 0.58 ÿ1 �1 �1
8 5.0�10ÿ4 3.0�10ÿ3 0.58 �1 �1 �1
272 C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279
concentrations used for the process variables during
the optimization step were calculated in terms of mol/
l, assuming ideal solvent behaviour. This approxima-
tion does not signi®cantly affect the optimization
results.
The ®nal concentration of Cr(VI) in each mixture of
the factorial design was 0.2 mg/ml. The H2O2 and
Cr(VI) solutions were added after all the others and
the system was then allowed to react for 20 min. All
experiments were carried out at ambient temperature,
controlled within (22�2)8C. The transfer of micro-
quantities of reagents was performed by using vari-
able±volume Eppendorff micropipettes. Absorbance
readings were made at 450 nm with a HITACHI U-
2000 spectrophotometer, using a 10 mm optical path
¯ow cell coupled to a ¯ow system. Blanks were
prepared using the same procedure, except for the
addition of Cr(VI). The experiments were done in
duplicate and both the MATLAB computational pack-
age and the SAS statistical package were used for the
split-plot calculations.
3.1. Sample preparation for chromium determination
Two plant samples, one furnished by the Interna-
tional Plant±Analytical Exchange (IPE) of the Wagen-
ingen University (Holland) and the other, a SRM
pepperbush with a reference value for chromium from
the National Institute for Environmental Studies
(NIES ± Japan), as well as two samples of wastewater
from a pulp mill analysed by graphite furnace atomic
absorption spectroscopy, were used to demonstrate the
applicability of the proposed method.
The vegetal samples were prepared by taking
0.2000±0.5000 g portions in triplicate, then ashing
them at 6008C for 5 h. After ashing, 10 ml of
1�1 v/v water-concentrated HCl solution were added
and heated until dryness. To the residuals, previously
moistened with water, 1 ml of concentrated HNO3 and
10 ml of water were added. The resulting mixture was
®ltered into 150 ml beakers. The solution pH was
increased to a value between 3±5 and all chromium
contained in the samples was then oxidized to Cr(VI)
by the addition of 2 ml of 1 mol/l ammonium persul-
fate solution and 2 ml of 30 mg/ml AgNO3 solution,
followed by slow heating for 30 min. Excess persul-
fate was decomposed by boiling. The water samples
were simply ®ltered with Whatman 40 paper and
40.0 ml aliquots were taken to initiate the chromium
oxidation treatment step as indicated above.
Since catalytical determinations are subject to many
chemical interferents, Cr(VI) was extracted with
methylisobutylketone in accordance with the Pilking-
ton and Smith procedure [21] for all samples, after the
oxidation process. Accordingly, the total solution
volume was increased to about 50 ml with water to
obtain a ®nal HCl concentration of about 1 mol/l,
cooled in an ice bath and transferred to a previously
cooled separatory funnel. 10 ml of ice-cold methyli-
sobutylketone saturated with 1 mol/l HCl were added
and the funnel was agitated for 1 min. After phase
separation, the aqueous phase was discharged and the
organic phase was re-extracted with 10 ml of 708Cwater. Then, 4.00 ml of each aqueous extract were
pipetted into a 10 ml volumetric ¯ask along with 2 ml
of 0.15 mol/l potassium biphtalate pH 5 buffer solu-
tion, 3.5 ml of 0.05 mol/l o-dianisidine solution in
acetone and 0.7 ml 30% m/m H2O2. The solutions
were completed to volume with water and rested for
20 min, after which spectrophotometric measure-
ments at 450 nm were performed. For comparison
purposes, the wastewater samples were also analysed
for chromium by graphite furnace atomic absorption
spectroscopy, using the Cr resonance line at 357.9 nm
and Zeeman background correction.
4. Results and discussion
Table 3 contains duplicate absorbance results of the
split-plot design. Each line represents a mixture
experiment and each column a factorial design point.
The ANOVA results for these data applied to Eq. (1)
are given in Table 4.
Some explanation of how the values in Table 3 are
transformed into the sums of squares in Table 4 is
useful to understand the signi®cance of the split-plot
analysis of variance. The procedure is analogous to
conventional ANOVA [16]. The main plot sum of
squares is determined by calculating averages over
all mixture formulations for each point of the 23
factorial and subtracting the grand average. The
sum of these squares, times the number of experiments
at each point of the 23 factorial (20), yields the main
plot sum of squares. For this reason it has 23ÿ1�7
degrees of freedom. The subplot error with nine
C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279 273
degrees of freedom consists of differences between
averages over all 23 factorial conditions for each
mixture formulation and the grand average, multiplied
by 16, the number of experiments for each mixture
formulation. The replicates' sum of squares is com-
posed of differences between the averages of each
duplicate in Table 3 and the grand average and has a
multiplier equal to the number of replicates (80).
Interaction sums of squares for the split-plot ana-
lysis of variance are also analogous to those in more
conventional ANOVA. The replicate main plot inter-
action sum of squares has terms obtained by summing
each replicate±factorial combination average with the
grand average and subtracting the respective replicate
and factorial point averages. The main plot±subplot
interaction involves averages for each factorial±mix-
ture design combination, respective factorial point and
mixture point averages and the grand average.
Signi®cance testing is similar to that in regular
ANOVA, except that there are two error terms. The
main plot error mean sum of squares is used to test the
signi®cance of the factorial process variable effects,
Table 3
Absorbances values [�A]a for each point of the split-plot design, in duplicate
Run Complete 23 factorial design experimental set
ÿ ÿ ÿ � ÿ ÿ ÿ � ÿ � � ÿ ÿ ÿ� � ÿ � ÿ � � � � �1 0.550 0.545 0.828 1.230 0.446 0.699 0.810 1.194
0.534 0.558 0.732 1.233 0.409 0.654 0.777 1.251
2 0.227 0.096 0.290 0.183 0.184 0.111 0.279 0.203
0.228 0.071 0.273 0.193 0.154 0.114 0.288 0.219
3 0.000 0.019 0.017 0.052 0.015 0.060 0.054 0.111
0.000 0.021 0.014 0.049 0.010 0.051 0.046 0.120
4 0.199 0.141 0.446 0.429 0.333 0.205 0.507 0.462
0.213 0.158 0.416 0.416 0.294 0.186 0.498 0.473
5 0.337 0.272 0.452 0.702 0.274 0.352 0.474 0.831
0.340 0.254 0.425 0.663 0.272 0.359 0.486 0.832
6 0.030 0.122 0.102 0.193 0.039 0.144 0.115 0.206
0.059 0.118 0.102 0.211 0.056 0.126 0.077 0.214
7 0.118 0.051 0.191 0.141 0.169 0.122 0.277 0.228
0.115 0.059 0.170 0.114 0.161 0.100 0.232 0.250
8 0.269 0.153 0.385 0.349 0.249 0.242 0.409 0.524
0.251 0.186 0.347 0.338 0.233 0.213 0.370 0.523
9 0.350 0.232 0.535 0.662 0.336 0.369 0.548 0.846
0.328 0.238 0.480 0.574 0.287 0.370 0.492 0.751
10 0.059 0.114 0.191 0.182 0.042 0.178 0.192 0.270
0.058 0.120 0.177 0.173 0.053 0.159 0.109 0.263
a [�A] means corrected Absorbances against the blank (A�AtotalÿAblank). Runs 9 and 10 were used as verification points.
Table 4
Analysis of variance for the split-plot designa responses, taken in terms of absorbance
Variation source Degrees of freedom Sum of squares Mean sum of squares Fcalc.
Replicates (R) 1 0.0045 0.0045
Main plot (Z) 7 1.7322 0.2474 412b
Main plot error (RZ) 7 0.0039 0.0006
Sub-plot (X) 9 6.9664 0.7740 1935b
Interaction (ZX) 63 1.3615 0.0216 54b
Subplot error (E) 72 0.0281 0.0004
Total 159 10.0967
a The equations used in these calculations are given in [16].b Significant at the level ��0.01.
274 C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279
whereas the signi®cance of mixture variable effects
and the mixture±process variable interaction effects
use the subplot error to obtain Fcalc. The interactions
between replicate and factorial or mixture effects, as
well as all higher order interactions are assumed to be
zero as should be the case when experiments are
performed randomly within the factorial and mixture
blocks.
These results show that process and mixture vari-
able effects, as well as their interactions, are signi®-
cant at the 99% con®dence level. Hence one cannot
assume that mixture and process variables are inde-
pendent of one another for this system. Individual
parameters of the quadratic mixture±quadratic process
model, calculated using the standard least squares
procedure, are given in Table 5. Only those signi®cant
at the 99% con®dence level are shown.
The mean quadratic sums of replicate and the main
plot and subplot error values are also given in Table 4.
The parameters with large absolute values describe
how the absorbance changes for variations in the
mixture and process variable values. For example,
for the line labelled x1 in Table 5, the mean effect
for the ®rst pseudocomponent has a �0.911 value,
indicating that increasing proportions of water, within
the limits studied here, result in a larger blank-cor-
rected absorbance value. This mixture parameter aver-
age is most affected by the levels of the z1 and z2
process variables. Increases in HCl and o-dianisidine
concentrations result in absorbance increases for 70±
30% water±acetone solvent mixtures, as can be
observed in the ®rst row of Table 3. Although absor-
bance increases in this table are always observed when
the o-dianisidine level increases while the other fac-
tors remain constant, the opposite is often true for
increases in the HCl level. The combined mixture±
process variable model explains this adequately, since
other interaction terms involving x have coef®cients
whose absolute values are larger than the one for the
z1x1 term. This is particularly notable for the large
negative value of the z1x1x3 term (ÿ0.894). For the
coef®cients of x2, the 0.176 value represents an aver-
age absorbance increase owing to an increase in the
acetone proportion. This is three times larger than the
average increase caused by DMF concentration
increases, 0.051.
The average synergic and antagonistic mixture
interaction parameters in column 1 of Table 5 can
also be more easily understood by referring to the data
in Table 3. For example, the average interaction para-
meter for the ®rst and third pseudocomponents in
Table 5 (ÿ0.895) indicates a lower corrected absor-
bance when these pseudocomponents are mixed than
the average absorbance values for the pure pseudo-
components. The data in Table 3 con®rm this inter-
pretation. The average absorbance value in line 7
(corresponding to 50±50% x1x3 pseudocomponent
mixture), is 0.156, somewhat lower than the average
value of the line for points 3 and 4 of the mixture
design, 0.188 (see Fig. 1(a)).
In order to understand more completely the results
of the combined mixture±process variable model, the
Table 5
Combined model coeficients and their respective errorsa
Mean z1 z2 z3 z1z2 z1z3 z2z3
x1 0.911 0.139 0.278 ± ± ± ±
(�0.038) (�0.038) (�0.038)
x2 0.176 ÿ0.044 0.045 ± ± ± ±
(�0.011) (�0.011) (�0.011)
x3 0.051 0.032 ± ± ± ± ±
(�0.011) (�0.011)
x1x2 0.466 0.266 ± ± ± 0.248 ±
(�0.088) (�0.088) (�0.088)
x1x3 ÿ0.895 ÿ0.513 ÿ0.242 0.233 ± ± ±
(�0.088) (�0.088) (�0.088) (�0.088)
x2x3 ± 0.188 ± ± ± ± ±
(�0.048)
a Significant at the level a�0.01
C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279 275
simple Scheffe mixture model [22] was determined at
each of the eight points of the factorial design using all
the mixture data
y�x� � b1x1 � b2x2 � b3x3 � b12x1x2 � b13x1x3
� b23x2x31 (3)
The mixture parameters which are signi®cant at the
99% con®dence level are shown in Table 6. Note the
large variations in the mixture model coef®cients for
the different levels of the factorial design. The b1
coef®cient has a low value of 0.569 at the (ÿ ÿ �)
factorial point, whereas it is 1.607 at the (� � ÿ)
point. In spite of large variations in Table 6, as cited
above, the mixture response surfaces at each point of
the 23 factorial have somewhat similar shapes. All
show maxima for the corrected absorbance values at
point 1 of the mixture design, as can be seen in Fig. 2
(see also Fig. 1(a)). These results indicate that the
largest absorbance values for the H2O2 oxidation of o-
dianisidine occur for the 70% m/m water±30% m/m
acetone reaction medium.
For these reasons the factor effects of the 23 design
at this mixture point were calculated using the results
in the ®rst line of Table 3. These effect values are
presented in Table 7, along with their standard error
values even though these values are all the same. The
peroxide concentration does not show a signi®cant
principal effect and only participates in very small
interaction effects, while the HCl and o-dianisidine
concentration factors provoke almost all of the cor-
rected absorbance dependence for this factorial. Their
principal and binary interaction effects are all positive
and the largest corrected absorbance occurs for the
factorial point with all three factors at their highest
levels. As such, to achieve even higher absorbance
values, steepest ascent path analysis suggests new
experimentation at the factor levels given in Table 8.
There, a central composite design (23 factorial � star
design � central replicated point) and its corrected
Table 6
Coeficients of the quadratic models for all factorial points (Scheffe Model)
Factorial Scheffe model coefficientsa
points x1 x2 x3 x1x2 x1x3 x2x3
ÿ ÿ ÿ 0.526 0.203 ± ± ± ±
(�0.097) (�0.028)
� ÿ ÿ 0.692 ± ± ± ÿ1.119 ±
(�0.094) (�0.217)
ÿ � ÿ 1.006 0.250 ± ± ± ±
(�0.115) (�0.033)
� � ÿ 1.607 0.175 ± ± ÿ2.370 ±
(�0.137) (�0.039) (�0.316)
ÿ ÿ � 0.569 0.162 ± ± ± ±
(�0.070) (�0.020)
� ÿ � 0.744 ± ± ± ÿ1.046 ±
(�0.113) (�0.260)
ÿ � � 0.985 0.266 ± ± ± ±
(�0.103) (�0.030)
� � � 1.159 0.195 0.121 1.746 ÿ1.096 ±
(�0.113) (�0.033) (�0.033) (�0.260) (�0.260)
a Significant at the level ��0.01.
Table 7
Calculated effects for the 23 factorial design at mixture point
(0.7:0.3:0.0)
Efects Value Error
Average 0.781 �0.008
Z1 (HCl) 0.285 �0.016
Z2 (o-dianisidine) 0.458 �0.016
Z3 (H2O2) 0.004a �0.016
Z1Z2 (HCl X o-dianisidine) 0.156 �0.016
Z1Z3 (HCl X H2O2) 0.054 �0.016
Z2Z3 (o-dianisidine X H2O2) ÿ0.002a �0.016
Z1Z2Z3 (HCl X o-dianisidine X H2O2) ÿ0.060 �0.016
a Not significant at the level ��0.005.
276 C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279
absorbance results are presented. A quadratic model
provides a statistically satisfactory ®t to the experi-
mental data and the corrected absorbance (�A) is
given by Eq. (4)
where only signi®cant 99% con®dence level terms
have been included. This function has a maximum
value at z1�ÿ4.8, z2�7.3 and z3�0.6. Since these
values are outside the range of the experimental
Fig. 2. Response surfaces for the quadratic model at each point of the factorial design. The numbers are the predicted absorbance values which
are close to those observed. Mixtures producing highest responses are indicated in the shaded regions.
y�z1; z2; z3�� 0:856 �0:0952z2 ÿ0:015z21 ÿ0:012z2
2 ÿ0:022z23 ÿ0:018z1z2 ÿ0:022z1z3 ÿ0:011z2z3
��0:002� ��0:001� ��0:001� ��0:001� ��0:001� ��0:002� ��0:002� ��0:002�(4)
C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279 277
design, Eq. (4) was examined ®xing the z2 value at the
studied maximum [4�����23p
; see Table 8]. For this con-
dition, the optimum values found were 6.0�10ÿ4 mol/
l, 1.9�10ÿ2 mol/l and 0.79 mol/l for HCl, o-dianisi-
dine and H2O2 concentrations, respectively, which
should be used in the 70±30% water±acetone solvent
medium. Under these experimental conditions, the
calibration graph is linear up to at least 40 ng/ml,
according to [�A]�0.035�0.030CCr (ng/ml), with
r2�0.9996, where [�A] is the absorbance value cor-
rected against the blank. A relative standard deviation
of 0.5% was calculated from 10 replicate measure-
ments at the 10 ng/ml level of chromium (VI) and a
detection limit of about 1.1 ng/ml was estimated from
the blank measurements [23]. The reliability of the
method under the optimized conditions for total chro-
mium determination can be con®rmed by the results
shown in Table 9 for plant and wastewater samples.
Results obtained using the procedure described above
agree favourably with those reported, demonstrating
its promise as an alternative and sensitive method for
the determination of chromium traces.
Using our experimental set-up, but with the solvent
mixture and the reagent concentrations formerly
recommended by Dolmanova et al. [2] for the deter-
mination of traces of Cr(VI) led to a calibration graph
given by [�A]�ÿ0.007�0.0067CCr (ng/ml) with a r2
value of 0.9914, showing that sensitivity under our
optimized conditions increased by a factor of about
4.5, attesting to the ef®ciency of multivariate split-plot
designs in optimization work.
Acknowledgements
The authors wish to thank Professor John A. Cornell
for his attention in the early stages of this work. C.R.
acknowledges CAPES-PICD for a doctorate fellow-
ship.
References
[1] G. Goldstein, D.L. Manning, O. Menis, Anal. Chem. 30
(1958) 539.
[2] I.F. Dolmanova, G.A. Zolotova, L.V. Tarasova, V.M. Peshko-
va, Anal. J. Chem. USSR, 24 (1969) 827 (Zh Analit. Khim.
24, 1969, 1035).
[3] A.B. Carel, J.W. Wimberley, Anal. Lett. 15 (1982) 493.
[4] M.C. Brennan, B. Svehla, Fresenius Z. Anal. Chem. 335
(1989) 893.
[5] W. Puacz, Fresenius Z. Anal. Chem. 329 (1987) 43.
[6] M. Otto, G. Schobel, G. Werner, Anal. Chim. Acta 147 (1983)
287.
[7] T.R. Gilbert, B.A. Penney, Spectrochim. Acta 38B (1983)
297.
[8] S.V. Manjarekar, A.P. Argekar, Anal. Lett. 28 (1995)
1711.
[9] F. BuscaroÂns, J. Artigas, Anal. Chim. Acta 16 (1957) 452.
[10] I.F. Dolmanova, G.A. Zolotova, T.N. Shekhovtsova, V.D.
Bubelo, N.A. Kurdyukova, J. Anal. Chem. USSR, 33 (1978)
213 (Zh. Analit. Khim., 33 (1978) 274).
[11] J.A. Cornell, Experiments with Mixtures: Designs, Models,
and the Analysis of Mixture Data, Wiley, New York, 1990.
[12] P.F. Vambel, J.A. Gilliard, B. Tilquim, Chromatographia 36
(1993) 120.
[13] M. Righezza, J.R. ChreÂtien, Chromatographia 36 (1993)
125.
[14] C. Reis, J.C. de Andrade, Quim. Nova 19 (1996) 313.
[15] J.A. Cornell, J.C. Deng, J. Food Sci. 47 (1982) 836.
[16] J.A. Cornell, J. Qual. Technol. 20 (1988) 2.
Table 8
Levels of the central composite design used in the Response
Surface Analysis
Levels HCl (z1) o-dianisidine (z2) H2O2 (z3)
(mol/l) (mol/l) (mol/l)
ÿ4�����23p
4.6�10ÿ4 1.08�10ÿ2 0.45
ÿ1 6.0�10ÿ4 1.25�10ÿ2 0.58
0 8.0�10ÿ4 1.5�10ÿ2 0.78
1 1.0�10ÿ3 1.75�10ÿ2 0.974�����23p
1.14�10ÿ3 1.92�10ÿ2 1.11
Table 9
Comparison of total chromium determination results using the
optimized catalytic procedure and reported reference values
Sample Cr(VI)
Reference value Founda
(mg/kg) (mg/kg)
Plants
NIES ± Pepperbush SRM 1300 1277�77
IPE ± Sample 6378b 4872�571 4725�122
Wastewater (mg/l)c (mg/l)
Sample 1 13.1 12.8�0.6
Sample 2 13.2 13.0�0.2
a Average results of triplicate samples.b Bimonthly Report 91.1 ± January/February 1991. International
Plant-analytical Exchange (IPE).c From GF-AAS measurements.
278 C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279
[17] J.A. Cornell, J. Am. Stat. Assoc. 66 (1971) 42.
[18] D.C. Montgomery, Design and Analysis of Experiments, 3rd.
edn., Wiley, New York, 1991, p. 468.
[19] W.M. Wooding, J. Qual. Technol. 5 (1973) 16.
[20] B.M. Kneebone, H. Freiser, Anal. Chem. 47 (1975) 595.
[21] E.S. Pilkington, P.R. Smith, Anal. Chim. Acta 39 (1967) 321.
[22] H. ScheffeÂ, J. R. Stat. Soc. B20 (1958) 344.
[23] Nomenclature, symbols, units and their usage in spectro-
chemical analysis II. Data Interpretation, Spectrochim. Acta,
33B (1978) 245.
C. Reis et al. / Analytica Chimica Acta 369 (1998) 269±279 279
