Talanta 49 (1999) 155 – 163
A chemometric study of the simultaneous determination of calcium and magnesium in natural waters F. Blasco Go´mez, F. Bosch Reig, P. Campı´ns Falco´ * Departament de Quı´mica Analı´tica, Facultad de Quı´mica, Uni6ersidad de Valencia, C/ Doctor Moliner 50. Burjassot, Valencia, E-46100, Spain Received 29 July 1998; received in revised form 23 October 1998; accepted 12 November 1998
Abstract A method for the simultaneous spectrophotometric determination of calcium and magnesium in mineral waters with an FIA system is tested. The method is based on the reaction between the analytes and arsenazo(III) at pH 8.5. The calculations of the amounts of both analytes in the samples are carried out with the H-point standard addition method (HPSAM) for ternary mixtures, and with a partial least squares (PLS) model after a proper variable selection. The results obtained for the determination of calcium were comparable using both methods. The employment of the HPSAM brings to our attention the influence of the calcium concentration in the sample to the development of the reaction between magnesium and arsenazo(III). HPSAM also permits to estimate the concentration of magnesium in the samples. © 1999 Elsevier Science B.V. All rights reserved. Keywords: H-point standard addition; Partial least-squares regression; Calcium; Magnesium; Simultaneous determination; Arsenazo(III)
1. Introduction The control of the concentrations of magnesium and calcium in waters is important, as they are the responsible for water hardness and their presence at high concentrations lowers the quality of drinking waters. From a physiological point of view, calcium and magnesium, along with sodium and potassium, are the most important ions affecting cardiology, owing to their role in nervous impulse conduction and cell contraction. * Corresponding author. Tel.: +34-96-398-3002; fax: +3496-386-4436. E-mail address:
[email protected] (P. Campı´ns Falco´)
Titrimetry, spectrophotometry and atomic spectrometry are the most frequently used techniques for such determinations [1]. The traditional method in quality control of calcium and magnesium in water and waste water is complexometry using EDTA as titrant. By the other side this technique is time consuming since the determination of both cations is not simultaneous, otherwise sequential. In order to obtain a higher sampling rate several flow injection (FI) assemblies have been designed [2,3] making use of EDTA and the usual indicators. These complexometric methods cannot be applied when Ca and Mg are present at concentrations lower than ap-
0039-9140/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 9 1 4 0 ( 9 8 ) 0 0 3 5 2 - X
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proximately 20 ppm (total hardness) owing to their lack of sensitivity. Several attempts have been made to develop suitable spectrophotometric methods for the determination of Ca(II) and Mg(II) [4–6]. Several reagents have been proposed to carry out the spectrophotometric determination of those cations, some of them are: 4-(2-pyridylazo)resorcinol (PAR) [7 – 10], arsenazo(I) [11], arsenazo(III) [12– 15], emodin [16], chlorphosphonazo(I) [17], chlorphosphonazo(III) [18], 3,3%-bis[N,Nbis(carboximethyl)aminomethyl)] -o-cresolphthalein [19], o,o%-dihydroxyazo-compounds [20], beryllon(II) [21], methylthymol blue [22], o-cresolphtalein [23], alizarin red S [24], azochromotropic acid [25] and PA-FPNS [26]. Ca(II) and Mg(II) react with the proposed reagents yielding to similar spectra. To allow the analyst the assessment of one cation in presence of the other one, by using a single reagent, several strategies have been developed. Some of them are a change in the pH value [18,27], avoiding the formation of the complex of one cation, and the use of masking agents [19] with a great difference between the log K value for the complex of one cation and the log K value for the complex of the other one. In that cases the determination of calcium and magnesium should be described as sequential not as simultaneous, since two consecutive measurements are required while the simultaneous determination should be related to the determination of more than one parameter per measurement. Simultaneous determinations are among the major issues of analytical chemistry as they avoid the need to separate a mixture of components by using one of the many techniques available for this purpose [28] making use of simpler, faster and cheaper techniques such as UV/VIS spectrophotometry. On the other hand, the main drawback of UV/VIS spectrophotometry is its lack of selectivity. Sometimes multivariate analysis of data permits the treatment of the non-specific data obtained with UV/VIS detectors. This strategy allows the simultaneous determination of calcium and magnesium avoiding a previous separation or a mod-
ification of the experimental conditions. Multiple linear regression (MLR) [8,9,12], partial least squares regression (PLS) [7,13,22,28] or H-point standard additions method (HPSAM) [14,15], have been proposed for the simultaneous determination of Ca(II) and Mg(II) in waters by spectrophotometry. PAR and arsenazo(III) are generally the most employed reagents for the simultaneous determination of both ions. PAR presents a too high molar absorptivity in relation to that of the Ca(II) and Mg(II) complexes in the working wavelength range, and it offers a narrow spectral window from a multivariate perspective. In this paper, an FIA method for the simultaneous spectrophotometric determination of calcium and magnesium, in mineral waters, with arsenazo(III) at pH 8.5 is chemometrically studied from the point of view of the model used for the calibration and from the point of view of the prediction. The usefulness of the method for the prediction of the concentration of calcium and magnesium in commercial waters is discussed.
2. Experimental
2.1. Apparatus and software A detection system consisting of a Hewlett Packard HP8453 UV–Visible spectrophotometer was used. The spectrophotometer was interfaced to a Hewlett Packard Vectra XM 5/90 personal computer, furnished with the G1115AA software. The FI assembly (Fig. 1) was built using a peristaltic pump (Minipuls 3, Gilson, Middleton, WI, USA), an injection valve (Model 5020, Rheodyne, Cotati, CA, USA), a 10-mm path length
Fig. 1. FI assembly employed for the determination of Ca2 + and Mg2 + . C1: arsenazo(III), C2: sample/standard, C3: carrier, D: detector.
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flow cell (Model 178.712-QS, Hellma, Mu¨lheim/ Baden, Germany) and 0.5mm i.d. PTFE tubes. FI conditions were: flow rate 1.75 ml min − 1, sample volume 50 ml and a 100-cm length reactor coil. The pH was measured using a Crison micropH 2000 pH-meter. HPSAM calculations were carried out with MICROSOFT EXCEL . PLS calculations were done with Parvus 1.3 (ISBN: 0-444-43012-1). ®
2.2. Reagents and standards Individual stock solutions of Ca(II) and Mg(II) 0.125M of each metal were made by dissolving the appropriate amounts of CaCl2 (Probus S.A., Badalona (Barcelona), Spain) and MgCl2 × 6H2O (Probus) respectively. The reagent solution was 0.245 g l − 1 in arsenazo(III) (BDH Chemicals, Poole, UK) and 0.1 M in NH3/NH4+ (pH =8.5). A stock solution of NH3/NH4+ buffer 10 M at pH =10 from NH3 (Probus) and NH4Cl (Probus); NaOH (Probus) and HCl (Panreac, Barcelona, Spain). Ethylendiamintetraacetic acid disodium salt, EDTA (Probus); Eriochrome black T and murexide (Probus, used as solid reagents diluted in NaCl (Probus)). Water was distilled and then deionized using a Sybron/Barnstead (IZASA, Madrid, Spain) Nanopure II purification system, including a filtration system (Hollow Fibre Filter 0.2 m (Barnstead D3750)).
157
Table 1 Calibration set concentrations for the determination of calcium and magnesium Magnesium (ppm)
0 1.82 3.65 5.47 7.30
Calcium (ppm) 0
3.09
6.19
9.27
12.36
1A 1B 1C 1D 1E
2A 2B 2C 2D 2E
3A 3B 3C 3D 3E
4A 4B 4C 4D 4E
5A 5B 5C 5D 5E
shown in Table 1. The samples of commercial waters were diluted with NH3/NH4+ pH= 8.5 buffer to give concentrations of Ca(II) and Mg(II) included in the calibration set.
2.3.2. Titrimetric determination The total hardness of the waters by using EDTA titration was measured at pH=10, buffered with NH3/NH4+ buffer; Eriochrome black T was used as indicator. Ca(II) determination by using EDTA titration was performed at pH\ 12, and murexide was used as indicator. The Mg(II) concentration was then obtained by difference. The titrations were made three times a day for 3 consecutive days.
3. Results and discussion
2.3. Procedures 3.1. H-point standard additions method 2.3.1. Spectrophotometric determination. Calibration sets The spectrophotometric determination of Ca(II) and Mg(II) was done with the FI system shown in Fig. 1 using as carrier NH3/NH4+ pH= 8.5, 0.1 M, and as reagent arsenazo(III), the spectra were recorded each second from 0 to 60 s, and each nanometer from 200 to 800 nm every 1 nm. The spectra at the time which gave the maximum signal were selected. A calibration set consisting of 25 standards was used, a code with a number and a letter was assigned to each standard. The first one refers to the Ca(II) concentration and the second to the Mg(II) concentration, their concentrations are
As it was explained in the Experimental section the calibration set consisted on 25 standards that contained different concentrations of both cations. The aim of the employment of the HPSAM for ternary mixtures is to find couples of wavelengths that allow the building of calibration curves that only respond to one analyte in the sample. It is then necessary to find pairs of wavelengths which accomplish the condition expressed in the Eq. (1) of the appendix, which means that both species considered as interferents present the same relationship of absorbances at the two selected wavelengths. A possible way to locate these couples of wavelengths is to plot the quotient
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Fig. 2. Isolation of the signal of Calcium. Absorbance increment: A655 −rYZ A688, being Y = Mg and Z= Arsenazo(III).
spectra of the interferents (the reagent and the other cation considered as interferent). So to determine the amount of Ca(II) in the sample we should plot the quotient spectra between arsenazo(III) and Mg(II) complex and select couples of wavelengths with the same quotient value. We considered that two wavelengths had the same quotient value when the difference between their values was lower than 5%. There are always several pairs of wavelengths which meet that condition, the best results in prediction of the analyte concentration will be provided by those increments with the highest slope in the calibration equation for the analyte. For the determination of Ca(II) (Mg(II) and arsenazo(III) considered as interferents) the selected pairs of wavelengths were those with the highest slope in the calibration line for Ca(II) and a correlation coefficient equal or higher than 0.995. Those pairs of wavelengths were 655 – 684, 655– 685, 655–686, 655 – 687 and 655 – 688. The calibration graphs best fitted to a two order polynomial, no dependence of the signals for
Ca(II) on the Mg(II) concentration in the sample was observed (i.e. for the increment A655 − rYZA688 the curve equation was y= −0.0022x 2 + 0.0877x − 0.0053, r 2 = 0.997, n= 25). As can be observed in Fig. 2, the absorbance increment does not depend on the amount of Mg(II), but only on the concentration of Ca(II). 1A-1E series corresponds to a calibration plot of Mg(II), where Ca(II) is not present, and as it can be seen the analytical signal is equal to zero. So, accurate results could be obtained by the method regardless of the Mg(II) content in the sample. Six samples were tested, one of them was a synthetic water and the rest were commercially available waters for consumption. The results, summarized in Table 2, were compared with those reported by the complexometric titration with EDTA. As can be seen the HPSAM provides accurate results, the precision is also good, with relative standard deviations lower than 5%. To determine the amount of Mg(II) it is necessary to proceed in the same way as previously, so the first step is to plot the quotient spectra be-
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Table 2 Results of the prediction of calcium and magnesium in commercial and synthetic waters, with different calibration methodsa Method/results (ppm)
Font vella
Lanjaron
Synthetic
Solan de cabras
Solares
Viladrau
EDTA Ca Mg
38 9 1 9.0 9 0.1
23.0 9 0.6 8.9 9 0.7
80 9 5 33.7 9 0.7
52 9 3 26.1 9 0.9
71 9 2 13.0 9 2.0
16 9 0.5 3 . 9 9 0. 2
HPSAM Ca Mg
39. 91 11 9 2
25.19 0.8 9.690.9
84 94.3 33 99
52.0 9 2 26 9 7
76 93 20 95
19.6 90.7 4.5 90.6
PLS Ca Mg
399 1 —
269 1 —
97 93 —
50 9 2 —
75 93 —
20.1 90.8 —
PLSb Ca Mg
369 1 —
25.29 0.7 —
79 9 4 —
— —
70 9 3 —
19.8 90.6 —
Mean of nine samples 9 S.D. PLS model without the standards with Ca(II) concentration higher than 6.2 ppm.Bold: relative error in absolute value lower than 10%. a
b
tween arsenazo(III) and Ca(II) complex. 597–627, 599–630, 604 – 631, 609 – 630 and 611 – 626 increments were selected among all the increments that accomplished the condition established in Eq. (1) of the appendix. Those increments presented the highest value of the slope in the calibration lines and a correlation coefficient equal or higher than 0.99. Using those increments it was possible to isolate the signal due to the Mg(II) in the sample [12], but five calibration curves were found instead of only one, this is due to the influence of Ca(II) in the formation of the Mg(II) complex. The analytical signal provided by Mg(II) decreases as the Ca(II) present in the sample increases, therefore, a different calibration equation is obtained depending on the amount of Ca(II) in the sample. Even so the intercept of every curve was equal to zero, this means that the signal only depend on the Mg(II) concentration in the sample. The resolution of Mg(II) concentration as a ternary mixture is not a good form, because the slopes of the calibration curves obtained were very low, but it is possible to work in another way. To solve the problem we followed the HPSAM for binary mixtures selecting wavelengths that cancel the signal of arsenazo(III). Once the wavelengths have been selected, the absorbance due to the amount of Ca(II) in the standards at
those wavelengths was subtracted. The result was a signal that only depended on the amount of Mg(II) since the influence of arsenazo(III) and Ca(II) had been eliminated. The absorbance increments used to cancel the signal of arsenazo(III) were 622–478, 621–479, 618–484, 621–478 and 624–475. In the Fig. 3 can be seen the calibration curves obtained for the absorbance increment A622 –A478, after the subtraction of the calcium signal. It can be seen that when there is no Mg(II) in the standard the analytical signal is zero value, so the isolation of the Mg(II) signal was achieved successfully. Fig. 3 shows the importance of the amount of Ca(II) in the sample for the Mg(II) complex formation (the same concentration of Mg(II) gives a higher analytical signal when Ca(II) is absent), so depending on the concentration of Ca(II) in the sample a different calibration equation for determining Mg(II) must be used. There is a linear relationship between the amount of Ca(II) in the sample and the analytical signal of Mg(II), so once the amount of Ca(II) in a sample is known, it is possible to calculate the equation that will allow the calculation of Mg(II) concentration in the sample. This is very important because the results obtained for the Mg(II) will depend on the accuracy of the Ca(II) prediction.
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Fig. 3. Calibration curves for the determination of Mg(II) in presence of different amounts of Ca(II). Absorbance increment: A622 – A478.
The results obtained are given in Table 2 and show that the accuracy and precision of the predictions of both analytes are suitable for almost all the samples.
3.2. Analysis of PLS models The data was also treated with a PLS algorithm (PLS-1). For this purpose the concentration of the standards were used as the Y-block in combination with the X-block data. For the first model studied, the X-block consisted on the full centered spectra from 250 to 798 nm every 4 nm, so 138 spectral variables were introduced. This model gave a percentage of explained variance in crossvalidation (%EVCV) of 99.2% for Ca(II) and 86.5% for Mg(II), with 5 factors for both of them. The first factor was clearly related with the Ca(II) concentration (it explained 95.1% of variance in cross-validation for Ca(II) while 0.8% for Mg(II)), and the second one was related with Mg(II) concentration (it only raised an additional 0.4% of the total Y variance of the calibration for Ca(II)
while for Mg(II) it raised 49.5%). In order to select the relevant spectral information the B-coefficients corresponding to the equation Y = B0 + BX for each analyte were studied. The magnitude of the B-coefficients (in absolute values) should be related to the importance of the original variables in the prediction of the analytes. Fig. 4 shows the B-coefficients versus the original variables corresponding to the model built with one and two factors. It can be seen that the range 580–680 nm is the most important for the prediction of both analytes. A new PLS model was tested, it used as X-block data the absorbances of the standards in the range 580-680 nm. The %EVCV was 99.4 and 96.7% for Ca(II) and Mg(II) respectively, using four factors for both of them, so a great improvement, specially for Mg(II), was achieved reducing the number of spectral variables. Several models with the absorbances at different spectral windows within the range 580–680 nm were assayed. The best results were those provided by the model built with the absorbances in the range 600–680 nm, with
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161
Fig. 4. Regression coefficients B versus the original wavelengths. PLS models built with one () and two ( ) factors.
%EVCVs of 99.6 and 97.0% for Ca(II) and Mg(II) respectively with four factors for both of them. As can be seen in Table 2 the prediction of Ca(II) in the samples was appropriate for almost all of them. The wrong prediction of the amount of Ca(II) in some samples may be due to non-linearities of the signals at high concentrations of Ca(II), in order to test that fact a new PLS model was constructed, with the same spectral window (600–680 nm) but without the standards with a concentration higher than 6.2 ppm of Ca(II). With this new model, the %EVCVs obtained were 99.5 and 97.7% with two and four factors for Ca(II) and Mg(II) respectively. The amount of Ca(II) in all samples was suitably predicted except for Viladrau. The content of Ca(II) in Solan de Cabras is not given since this water was out of the calibration. In spite of having high values of %EVCVs for Mg(II), the prediction of this analyte in the
samples was wrong with both models, this means that though the models are able to predict the concentration of Mg(II) in the standards, they are not able to do it in the samples. A calibration set consisting on real samples may result in better predictions for Mg(II) concentration, as it was found by Ruisa´nchez et al. [11]. They reported a methodology for the automatic, simultaneous determination of Ca(II) and Mg(II) in natural waters based on a Sinusoidal Injection Analysis (SIA) system with diode array spectrophotometric detection. They measured the complex formed by both cations with arsenazo(III), using as calibration set samples of natural water fit for human consumption. The amount of Ca(II) and Mg(II) in the samples was previously determined by atomic absorption spectrometry. This model, built with real samples, provided a mean square error (MSE) in prediction lower for Mg(II) than for Ca(II) using four and two factors respectively.
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Fig. 5. Signals of the three components of the sample (X, Y and Z) at the wavelengths l1 and l2 before the employement of the correction rYZ factor (a) and final signals after using the rYZ factor (b). Since the rYZ factor operate in l2, AX,l 1, AY,l 1 and AZ,l 1 have the same value in a and b cases.
4. Conclusions
Acknowledgements
It has been proved the ability of the HPSAM and PLS methods to calculate the amount of an analyte in presence of an interference and in presence of the reagent, when the three compounds absorb the UV/VIS radiation in the same spectral range, and the overlap is severe. The results obtained for Ca(II) with the PLS models are suitable if a variable selection is done properly, it has been shown a possible way to make the variable selection. Ca(II) determination is easier than Mg(II) determination since its signal is much larger than the Mg(II) signal. By the other side the determination of Mg(II) is conditioned by the presence of Ca(II) in the sample. This fact became evident upon isolating the Mg(II) signal with the HPSAM method. The prediction of Mg(II) in the standards is successfully achieved by the PLS model, but it was not able to predict this cation in the samples, so the use of real samples (i.e. mineral water) to build the calibration set may give more robust and reliable models for the prediction of Mg(II) content in commercial waters.
The authors are grateful to the DGICYT (Project No. PB 94-0984) for its financial support.
Appendix A. Fundamentals of the HPSAM for ternary samples If we consider a sample in which X and Y are the analytes to be determined with Z reagent [29], the concentration of X can be calculated by finding pairs of wavelengths which satisfy the following equation AY,l 1 AZ ,l 1 = = ry,z AY,l 2 AZ,l 2
(1)
Only one spectrum of the species Y and another of the species Z are needed. Although this relationship depends on the concentration of Y and Z, it will be equal at the two selected wavelengths, regardless of the concentrations chosen. There are generally several pairs of wavelengths to choose from. The rY, Z factor transforms the original situation (a) into (b), as can be seen in Fig. 5. Since the
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signals of Y and Z are the same at both wavelengths after the correction made using the rY, Z factor, the absorbance increment calculated depends only on the concentration of X. If we consider that the response variable (absorbance increment) follows the Beer-Lambert law, the concentration of X (CH(X)) can be calculated from the equation: −CH(X) =
AS,l 1 −rY,ZAS,l 2 A 0X,l 1 −rY,ZA 0X,l 2 = rY,ZMX,l 2 −MX,l 1 rY,ZMX,l 2 − MX,l 1 (2)
where AS, l 1 and AS, l 2 are the absorbance values measured for the sample at the two chosen wavelengths, MX, l 1 and MX,l 2 are the slopes of the standard additions method for X or, if the matrix effect is known not to be present, the molar absorption coefficients for the species X at the two wavelengths. A 0X, l 1 and A 0X, l 2 are the absorbance values of the species X in the sample. Therefore, the calculated concentration corresponds to compound X. Similar equations can be described for resolving species Y from rX, Z factor.
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