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Talanta 77 (2008) 587–592

Contents lists available at ScienceDirect

Talanta

journa l homepage: www.e lsev ier .com/ locate / ta lanta

ovel approach to calibration by the complementary dilution methodith the use of a monosegmented sequential injection system

oanna Kozak ∗, Marzena Wojtowicz, Alicja Wrobel, Paweł Koscielniakepartment of Analytical Chemistry, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland

r t i c l e i n f o

rticle history:eceived 15 November 2007eceived in revised form 14 March 2008ccepted 17 March 2008vailable online 25 March 2008

a b s t r a c t

Novel approach to calibration by the complementary dilution method (CDM) is presented. The CDM inte-grates in a single procedure the set of standards and the standard addition calibration methods. Theapproach is implemented with the use of the fully automated monosegmented sequential injection sys-tem coupled to FAAS as a detector. It relies on generation of a series of standard solutions consistent withthe CDM calibration method in subsequent monosegments using a single stock standard solution, sam-

eywords:alibrationonosegmented flow analysis

equential injection analysis

ple and diluent in appropriate proportions. Two versions of the method, basic and extended have beenverified. They have been tested on the example of magnesium determination in a synthetic sample witherrors of repeatability (R.S.D.) and accuracy (R.E.) less than 3.2%. Subsequently, they have been applied tomagnesium and calcium determinations in water. The results obtained are comparable with the appro-priate certified values as well as with the results received by traditional calibration methods performedseparately in batch system. Using the system, a complete sample analysis takes 8 or 21 min with sampleor standard consumption less than 1 or 2 mL in basic and extended versions, respectively.

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. Introduction

Calibration is an indispensable step of most analytical meth-ds. Its correct performance is important especially on account ofesult accuracy. Several calibration methods have been developedn analytical chemistry, but only two of them became commonmong analysts: the set of standards method (SSM) and the stan-ard addition method (SAM). As they allow an analytical result toe calculated differently, interpolatively (SSM) or extrapolativelySAM), they are characterized by different abilities and limitations.

Flow analysis offers a variety of possibilities of rationalizationr automation of both the SSM and the SAM methods. Underneath,ome of the approaches representing a basis of many others, haveeen quoted: merging zones approach [1] in which segments oftandard and sample can be superimposed and merged in a con-rolled way in a flow injection (FI) system; zone sampling method2] where a small portion of a dispersed standard zone can benjected into another carrier stream; reversed FI system [3] where

tandard is injected into sample carrier; gradient techniques [4–7]sing a concentration–time profile generated by a single standard

njection; peak width measurement method [8]; continuous dilu-ion methods exploiting mixing chamber inserted into a FI system

∗ Corresponding author. Tel.: +48 126632232; fax: +48 126340515.E-mail address: janiszew@chemia.uj.edu.pl (J. Kozak).

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039-9140/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.talanta.2008.03.024

© 2008 Elsevier B.V. All rights reserved.

9], or peristaltic pumps to create linear flow gradients [10]; sequen-ial injection method [11] where several discrete standard volumesre introduced simultaneously into a carrier stream; network [12]r variable tube dimensions [13] methods when dispersion of aingle standard solution is changed by directing it to loops of dif-erent lengths; automatic dilution method [14] where additionalilution loop is used for a standard dilution; SIA approaches exploit-

ng an additional loop to generate concentration gradient of thentroduced standard [15], or exploiting a sample as a carrier [16]r systems using a concept of monosegmented continuous flownalysis (MSFA) [17,18].

The MSFA relies on forming in a reaction coil a zone consistedf a sample and a reagent [19]. In order to reduce dispersion witharrier solution, the zone is located between two air bubbles form-ng a monosegment. The influence of an axial dispersion causedy a thin film of solution linking a monosegment with its liquidarrier on an analyte concentration in the monosegment is veryimited, hence it is usually omitted during results calculation. Theoncept has been exploited for rationalization of the SAM usingn automated manifold with a solenoid valve incorporated [17]. Inhe developed procedure, different quantities of a single standard

olution were added to the sample by controlling the time inter-al in which the solenoid valve was switched on. Since absorbanceersus time analytical curves were obtained it was necessary to cal-brate the system prior the use in order to determine the quantitiesf standard solution added to the sample in each injection. Pinto

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ilva and Masini [18] exploited SIA and MSFA approaches to per-orm in-line SAM method. In the system, standard solutions wereenerated from a single stock standard solution, in monosegmentsf the same total volume by introducing into each monosegmenthe same volume of sample, increasing volumes of standard andecreasing volumes of diluent. As a syringe pump was exploitedor solutions aspiration into the system, the concentration of stan-ard added was calculated directly using the volume of standard

ntroduced into a monosegment and the total volume of monoseg-ent.In the approaches presented above analytical results are always

btained using exclusively one of the calibration methods. Recently,n idea of integrated calibration method (ICM) arose [20]. The con-ept of this approach relies on unification of the SSM and SAMethods in a single calibration procedure. As a consequence, an

nalytical result is able to be estimated at least twice in twoays—interpolatively and extrapolatively. One of the versions of

he ICM method is the complementary dilution method (CDM) [21].he specificity of the CDM is typified by special preparation pro-edure of the calibration solutions. Namely, three solutions, eachontaining two or three constituents (diluent, standard or sampleolutions) in appropriate volumes p or q (where p > q) are gener-ted in two series. The prerequisite is that if in one of the series aonstituent is diluted to degree P (where P = p/(p + q)) in the othereries it is diluted to degree Q (where Q = q/(p + q)), which is comple-entary to degree P, i.e. P + Q = 1. Flow injection systems have been

esigned to perform the CDM calibration [21,22] in such a way,hat the calibration solutions are prepared by strictly controlledartial superimposing and merging zones of standard and sampleolutions propelled in two streams of diluent with different flowates.

In the present work, the calibration procedure based on theDM concept has been developed with the use of monosegmentedequential injection system. The method relies on the subsequenteneration of solutions in monosegments of a defined, constantotal volume, containing standard and/or sample and diluent in var-ous volumetric proportions corresponding to the rules of the CDM

ethod. Two procedures, basic and extended, have been developed.he system has been tested by applying it to the FAAS determinationf magnesium in a synthetic sample and subsequently exploited tohe determination of magnesium and calcium in water samples.

. Experimental

.1. Reagents and solutions

Standard stock solutions of magnesium and calcium of con-entration 1 mg L−1 were prepared from titrisol standards (Merck,ermany). Standard solutions of magnesium and calcium usedirectly for calibration purposes, were prepared by dilution of the

ardat

ig. 1. Instrumental system developed for realization of CDM procedure in monosegmenV, selection valve.

(2008) 587–592

ppropriate standard stock solution with the use of nitric (Merck,ermany) and hydrochloric (Merck, Germany) acids respectively,f concentration 1% (v/v). Analytical-reagent grade chemicals andouble distilled water were used throughout.

SPS-SW2 Batch 105 Reference Material for Measurements of Ele-ents in Surface Waters (SPS Spectrapure Standards AS, Norway)as used for the method verification. Spring water used as a sampleas commercially available in the Polish market.

.2. Instrumentation

Atomic absorption spectrometer PerkinElmer 3100PerkinElmer, USA) was used in the experiments. Air–acetyleneame was applied and nebulizer free uptake rate was fixed to.3 mL min−1. Magnesium and calcium hollow cathode lampsere operated at 12 and 17 mA, respectively. The wavelengthsere set to 285.5 and 423.0 nm, respectively with a spectral slitidth of 0.7 nm. PC AMD K5 computer with program written in

ur laboratory was connected to the spectrometer and served forata collection and handling.

The sequential injection system applied consisted of the fol-owing units: 10-positional selection valve (Valco, Switzerland),wo-positional injection valve (Alitea Instruments, USA), peristalticump (Gilson, France), syringe pump (Alitea Instruments, USA),peration of which was modified in our laboratory, electronicdapter developed in our laboratory that enables remote controlf all the units of sequential injection system.

Tygon tubes for carrier transport with the use of the peristalticump and PTFE tubing of i.d. 0.8 (tubes) or 1.6 mm (a mixing coilnd a holding coil) were used. The length of the holding and theixing coil was 1000 and 300 mm, respectively.

. Results and discussion

.1. Operation of the sequential injection system

The sequential injection system developed for the research isepicted in Fig. 1. The system is operated in three stages: aspi-ation, homogenization and washing. In the first stage (shown inig. 1), strictly controlled volumes of air and diluent, standardnd/or sample are aspirated through the selection valve (oper-ted in anticlockwise direction) to the holding coil with the usef the syringe pump. At the same time carrier is propelled by peri-taltic pump through the two-positional valve to the spectrometer.he total volume of a monosegment was established to 450 �L, to

chieve the possibility of generating several standard solutions ofequired concentrations by appropriate dilution of a single stan-ard solution. Carrier flow rate was fixed to 4.6 mL min−1 and waslittle higher than the nebulizer uptake rate. In the second stage

he position of selection valve is changed into diluent position and

ted sequential injection mode. St, standard; S, sample; TPV, two-positional valve;

J. Kozak et al. / Talanta 77

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00 �L of diluent is introduced into a holding coil with the flowate 2.5 mL min−1, than the flow direction is reversed and 150 �Lf the solution is removed with the same flow rate. The procedures repeated twice. This way, solutions contained in the monoseg-

ent move quickly in reverse directions and are homogenized inecurrent way. In the last stage of system operation, after chang-ng the position of the two-positional valve (clockwise, Fig. 1), thearrier propelled by peristaltic pump is directed to the holding coildashed line in the scheme of the two-positional valve, Fig. 1) andashes the whole monosegment to the detector. Simultaneously,

he carrier is removed from the syringe pump. As the flame atomicbsorption spectrometer was used as the detector there was noecessity of removing air segments before detection.

The performance of the system was checked in terms of itspplicability for dilution. For the aim, the repeatability of signalsenerated in the system has been checked in the following way.ine solutions of increasing standard concentration were subse-uently generated in the system. Firstly, 50 �L of Mg standard

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able 1onditions of signals generation according to the CDM method in basic and extended ver

ilution degree Monosegment compositiona (�L)

tandard Sample Diluent Stan

– Continuous stream –Q 300 –Q – 300– 150 300– 300 150P – 150P 150 –Q 100 200Q 200 100– 250 200– 350 100– 350 100– 400 50P 50 100P 100 50

a Air volume at both sides of monosegment: 100 �L.

(2008) 587–592 589

olution of concentration 0.8 mg L−1 and 400 �L of diluent wereubsequently aspirated into a holding coil between two air seg-ents. The solution was homogenized, as described in the previous

ection, and directed to the detector. The absorbance correspondingo the plateau of the signal registered was regarded as an ana-ytical signal. Afterwards, the procedure was repeated for higherolumes of standard (in sequence: 100, 150, 200, 250, 300, 350,00 and 450 �L) and respectively lower volumes of diluent (inequence: 350, 300, 250, 200, 150, 100, 50 and 0 �L) aspirated intohe holding coil. The whole procedure was repeated eight times andverage values of the signals registered as well as relative standardeviations were calculated. The values of R.S.D. always lower than.5% and linear calibration curve were obtained (R = 0.9999). Theepeatability of a single measurement, when only a stock standardolution was inserted between air segments lower than 0.8% wasund.

.2. Calibration procedure

Two versions of the procedure consistent with the rules of theDM method have been proposed. They differ in the number oftandard solutions containing two or three constituents – diluent,tandard and sample – in the basic procedure a blank solution andix standard solutions are created, whereas in the extended pro-edure the blank and 14 standard solutions are generated. In eacholution (in the form of a monosegment) a constituent is diluted inhe complementary mode.

The constant volumes of p = 300 �L and q = 150 �L were selectedo receive analytical curves of considerably different slopes (seeig. 2) and to achieve the total volume of monosegment equal50 �L. As the total volume of a monosegment was always con-tant, the dilution degree for standard or sample could be calculatednd was always equal P or Q, respectively. In case of the solutionsenerated in the extended version of the procedure, the dilutionegree was calculated including the diluent volume necessary toeceive the complementary volume p or q. The detailed composi-ion of monosegments containing subsequent standard solutions,he appropriate dilution degrees and the corresponding analyticalignals are shown in Table 1.

On the basis of the registered signals in both procedures, four

nalytical curves can be constructed as shown in Fig. 2. In the basicrocedure each analytical curve is based on two analytical sig-als, whereas in the extended procedure on four analytical signals.ence, the latter procedure can be useful in such a case when thenalytical curves are suspected to be nonlinear.

sions of the proposed procedure

Signal for procedure

dard Sample Basic Extended

– R0 R0150 R1 R1150 R2 R2

– R3 R3– R4 R4

300 R5 R5300 R6 R6150 – R2′

150 – R2′′

– – R3′

– – R3′′

– – R4′

– – R4′′

300 – R5′

300 – R5′′

590 J. Kozak et al. / Talanta 77 (2008) 587–592

Table 2Determination of Mg in a synthetic sample; n = 6

Element Concentration expected (mg L−1) Procedure CDM calibration Concentration found (mg L−1) R.S.D. (%) R.E. (%)

Mg 0.200 Basic Interpolative cx1 0.201 1.80 0.51cx2 0.198 2.15 −0.90

Extrapolative ICM cx3 0.201 2.29 0.54cx4 0.201 3.13 0.55

Extrapolative cx5 0.203 1.19 1.33cx6 0.194 1.64 −3.09Mean 0.200 1.60 −0.17

0.200 Extended Interpolative cx1 0.203 1.72 1.27cx2 0.197 2.08 −1.33

Extrapolative ICM cx3 0.197 1.94 −1.47

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In the basic procedure the analytical result is estimated in thenterpolative mode from the following analytical equations:

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x2 = R1

R4· cSt (2)

nd in the extrapolative mode characteristic for the ICM methodith no necessity to determine dilution degrees P and Q [21]:

x3 = R6

R2 − R1· cSt (3)

x4 = R1

R5 − R6· cSt (4)

nd finally in the traditional extrapolative mode using calculatedalues of dilution degrees:

x5 = R6

R5 − R6· Q

P· cSt (5)

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able 3pplication of the developed method to the determination of Mg and Ca in surface water

lement Concentration certified (mg L−1) Procedure Calibration

g 2.00 ± 0.01 Basic Interpolative

Extrapolative ICM

Extrapolative

Extended Interpolative

Extrapolative ICM

Extrapolative

a 10.00 ± 0.05 Basic Interpolative

Extrapolative ICM

Extrapolative

Extended Interpolative

ExtrapolativeICMExtrapolative

cx4 0.199 2.50 −0.28cx5 0.198 1.29 −1.02cx6 0.194 1.35 −3.15Mean 0.198 1.50 −1.01

x6 = R1

R2 − R1· P

Q· cSt (6)

here R1–R6 are signals registered for the generated standard solu-ions (see Table 1) and cSt is the analyte concentration in the stocktandard solution.

In the extended version of the proposed procedure, the param-ters of analytical curves are determined and than the values ofppropriate standard concentrations are related to the mathemati-al model obtained. Next, the values of signals received in this modeerve for the analyte concentration calculation with the use of thebove analytical equations.

The calculated values of concentrations, cx1–cx6 can be com-ared and verified mutually. If they do not differ statistically, theirverage value can be considered as the analytical result [22].

.3. Test examinations and procedure verification

The proposed procedures were tested on the example of Mgetermination in a synthetic sample. Stock standard solution of

, CI: confidence interval (˛ = 0.05)

Developed method Traditional method

Concentration found ± CI (mg L−1) Concentration found ± CI (mg L−1)

cx1 2.13 ± 0.03 2.06 ± 0.01cx2 2.16 ± 0.01cx3 2.11 ± 0.02 –

cx4 2.01 ± 0.01cx5 2.09 ± 0.04 2.12 ± 0.09cx6 2.03 ± 0.05Mean 2.09 ± 0.05cx1 2.13 ± 0.04 2.06 ± 0.02cx2 2.14 ± 0.01cx3 2.11 ± 0.03 –

cx4 2.01 ± 0.05cx5 2.06 ± 0.04 2.10 ± 0.05cx6 1.99 ± 0.06Mean 2.07 ± 0.05

cx1 10.27 ± 0.34 9.89 ± 0.13cx2 9.93 ± 0.12cx3 10.90 ± 0.29 –

cx4 10.74 ± 0.32cx5 11.08 ± 0.41 11.36 ± 0.14cx6 10.03 ± 0.15Mean 10.49 ± 0.38cx1 10.33 ± 0.37 9.75 ± 0.14cx2 9.90 ± 0.11cx3 10.92 ± 0.27 –

cx4 10.80 ± 0.27cx5 10.96 ± 0.38 11.85 ± 0.25cx6 9.91 ± 0.24Mean 10.47 ± 0.39

J. Kozak et al. / Talanta 77 (2008) 587–592 591

Table 4Application of the developed method to the determination of Mg and Ca in spring water, CI: confidence interval (˛ = 0.05)

Element Concentration declared (mg L−1) Procedure Calibration Developed method Traditional method

Concentration found ± CI (mg L−1) Concentration found ± CI (mg L−1)

Mg 4.91 Basic Interpolative cx1 4.54 ± 0.05 4.65 ± 0.05cx2 4.60 ± 0.05

Extrapolative ICM cx3 4.48 ± 0.09 –

cx4 4.41 ± 0.14Extrapolative cx5 4.66 ± 0.13 4.69 ± 0.14

cx6 4.27 ± 0.09Mean 4.49 ± 0.11

Extended Interpolative cx1 4.55 ± 0.07 4.67 ± 0.06cx2 4.56 ± 0.03

Extrapolative ICM cx3 4.48 ± 0.09 –

cx4 4.40 ± 0.13Extrapolative cx5 4.49 ± 0.15 4.62 ± 0.19

cx6 4.15 ± 0.05Mean 4.44 ± 0.12

Ca 28.00 Basic Interpolative cx1 32.60 ± 0.77 31.76 ± 0.52cx2 32.35 ± 0.83

Extrapolative ICM cx3 32.52 ± 0.81 –

cx4 32.66 ± 1.19Extrapolative cx5 34.81 ± 1.23 32.06 ± 0.56

cx6 30.54 ± 1.15Mean 32.58 ± 1.21

Extended Interpolative cx1 32.80 ± 0.83 31.50 ± 0.51cx2 32.20 ± 0.64

Extrapolative ICM cx3 32.57 ± 0.77 –

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oncentration of Mg 0.400 mg L−1 were used. The sample was ana-yzed six times and the results are presented in Table 2. It is seenhat both procedures provide results with precision (R.S.D.) andccuracy (R.E.) less than 3.2%. Comparable precision of the resultsbtained in interpolative and extrapolative ways were obtained.t can be noticed, that in case of the results obtained with these of the traditional extrapolative method, that exploits values

f dilution degrees, in case when the widen range of extrapolationas employed (cx6), the results of worsen accuracy (R.E. = −3.09

nd −3.15%) than accuracy of the results of the other methods|R.E.| ≤ 1.47%) were obtained.

In order to verify the proposed procedures, Mg and Ca wereetermined in the reference sample of surface water and in com-ercially available spring water. Stock standard solutions of Mg and

−1

a of concentration 0.400 and 4.00 mg L , respectively, were used.ntire procedures were repeated six times. Samples were dilutedefore the determination. For comparison, the same samples werexamined according to traditional interpolative (SSM) and extrap-lative (SAM) calibration methods with using of an appropriate

bt

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able 5omparison of chosen analytical parameters when performing calibration using batchwiseersions

Calibration method

Batchwise approach

I + Ea I + Ea

Basicb Extendedb

umber of standard solutions 2 + 2 4 + 4umber of analytical curves 1 + 1 1 + 1umber of analytical results 1 + 1 1 + 1ime of analysis, min 10 20tandard consumption (mL) 0.4 3.2ample consumption (mL) 4 8

a Interpolative and extrapolative methods performed separately.b Procedures.

cx4 32.34 ± 1.06cx5 34.06 ± 1.23 31.80 ± 0.16cx6 30.28 ± 1.50Mean 32.38 ± 0.98

ingle analytical curve. In the traditional basic procedures ana-ytical curves were based on two analytical signals whereas inraditional extended procedures they were based on four signals.esults of determinations in surface and spring water are presented

n Tables 3 and 4, respectively.Regarding the analysis of surface water (Table 3), the results

btained with the use of the propose procedures agree with theertified values and with the values determined with the use of theraditional calibration methods. No differences have been observed,etween the results obtained using the basic or the extended pro-edures. It can be noticed, that despite the fact that in the samplef surface water potential interferents were contained (as Al, Fe,, Na, Pb, Sr or V) no interference effect was detected. The resultsbtained for the spring water samples differ from those declared

y a producer but they are in agreement with results obtained byraditional calibration methods.

In Table 5 the comparison between some parameters of inter-olative and extrapolative calibration methods are presented whenhey are realized separately in traditional batch way as well as in

method or CDM method in flow injection and monosegmented sequential injection

FI approach [22] Developed approach

CDM CDMBasic Extended Basic Extended

7 15 7 154 4 4 44 (or 6) 4 (or 6) 6 63.6 12 8 214 12 0.9 1.74 12 0.9 1.8

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ccordance with the complementary dilution calibration methoderformed in flow injection system and in the proposed monoseg-ented sequential injection system. The presented values were

stablished for cases when appropriate complete calibration pro-edures were performed for each of a sample analyzed. It is seen,hat complementary dilution calibration method provides rich ana-ytical information in the form of at least four analytical results.s far as the performance of the CDM method in flow injection or

he proposed system is concerned, the latter system is competitiven terms of low standard and sample consumption. Regarding theime of analysis, the proposed procedures last longer than FI CDMrocedures and the time necessary to perform them is comparableith the time of realization of traditional batch interpolative and

xtrapolative methods separately. The reason is that in monoseg-ented sequential injection procedures calibration solutions are

enerated separately one after another and each of them must beomogenized before reaching the detector. However, during theomparable time the CDM procedure performed in the proposedystem provides more analytical results than traditional calibrationethods performed separately.The advantage of the proposed CDM calibration procedures

ealized in the developed system in relation to CDM methodserformed in flow injection systems is that they do not exploiterging of two streams of diluent [21,22]. Hence, they are not

rone to random fluctuations of the streams flow rates. In theI extended system [22] each subsequent calibration solution isenerated from the previous one by its controlled dilution sohere is a risk of accumulation of errors arising during the suc-essive dilutions. In the developed system calibration solutionsre generated independently from each other and a number ofolutions of required analyte concentration can be generated.his can be exploited for both, an analytical curve nonlinearityetection and subsequently CDM calibration performance in thextended version. Differently from FIA systems, for the systemeveloped it is easy to calculate directly dilution degrees P and Qnd exploit them for results calculation in traditional extrapolativeode.In the system, unlike in the other systems known from liter-

ture [18], solutions are introduced into a monosegments in twor three segments and homogenized afterwards, and there is no

ecessity of introducing them using ‘sandwich’ way. Although theystem has been applied for realization of the CDM calibrationethod, it can be also used to perform interpolative or extrapola-

ive calibration methods separately or for the dilution purposes asell.

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(2008) 587–592

. Conclusions

The proposed monosegmented sequential injection system wasuccessfully employed for rationalization of calibration stage ofnalysis using the complementary dilution calibration method. Thepproach provides reach analytical information with the use of aingle stock standard solution and minimum reagent consumption.wo procedures of the realization of the CDM method in the pro-osed system, basic and extended, were developed and verified.he basic procedure can be exploited when linear calibration ranges confirmed whereas the extended procedure in each case whenhere is necessary to establish linear calibration range or when cali-ration curve is not linear. The proposed system is versatile and cane adapted to various analyzes performed with atomic absorptionetection. It is also worth to emphasize, that complete automationf the procedures constrains the risk of random errors during cali-ration solutions generation and allows the analytical results to bebtained in less laborious way.

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