SIMULTANEOUS DETERMINATION OF MIXTURES OF WEAK ACIDS BY SPECTROPHOTOMETRIC METHODS

1 SIMULTANEOUS DETERMINATION OF MIXTURES OF WEAK ACIDS BY SPECTROPHOTOMETRIC METHODS GÜZIDE PEKCAN ERTOKUŞ* and A.HAKAN AKTAŞ * Department of Chemistry, Faculty of Science&Art, Süleyman Demirel University, 32260 Isparta-Turkey *To whom correspondence should be addressed Telephone: +90 246 211 41 68 Fax: +90 246 237 11 06 E-mail: guzide@fef.sdu.edu.tr

2 Abstract: A method is proposed for the simultaneous determination of mixtures of weak acids by PLS and PCR.The weak acids are benzoic acids contain nitro group- 4- nitrobenzoic acid, 2- nitrobenzoic acid, 3- nitrobenzoic acid.the chemometric techniques are based on a solid mathematical and statistical background. The spectra of the analytes recorded between 200-500 nm against a blank and the partial least squares multivariate (PLS) calibration was used to otain the results. The results were compared with PCR methods. Samples were prepared in 25 ml calibrated flasks containing different concentration of pure weak acids and their ternary mixtures. The absorption spectra of weak acids in the same mixture were strongly overlapping. Keywords: PLS,PCR, simultaneous determination, benzoic acids.

3 INTRODUCTION A multivariate calibration has historically been a major cornerstone of the chemometrics as applied to the analytical chemistry. Most of the chemometrics involves the multivariate calibration. Some groups have based much of their development over the past two decades primarily on applications of the partial least squares (PLS) algorithm. The PLS is often regarded as the major regression technique for multivariate data. In fact, in many cases it is applied inappropriately and is not justified by the data. In areas outside the main stream of the analytical chemistry, or even biometrics and psychometrics, the PLS certainly is an invaluable tool, because the underlying factors have little or no physical meaning so a linearly additive model in which each underlying factor can be interpreted chemically is not expected. 1 Derivative techniques and multivariate statistical analysis, such as multiple linear regression (MLR), principal component regression (PCR), partial least squares (PLS) and Kalman filter, have been successfully applied to the multi-component analysis of mixtures by ultraviolet/visible molecular absorption spectrophotometry 2. During the last decade the powerful chemometric methods classical least-square (CLS), inverse least-square (ILS), principal component regression (PCR) and partial least-square (PLS) were used in the spectral data analysis for the mixtures containing two or more compounds with overlapping spectra. These methods have a huge range of applications, e.g. spectrophotometric, chromotographic and electrochemical quantitative analysis 3. Benzoic acids,c 6 H 5 COOH, are members of the class of compounds knowns as carboxylic acids. Carboxylic acids are one of the earliest types of organic

4 compounds to be explored by ancient chemists ; they are present in or derived from many natural substances 4. A scheme of acid-base equilibria set up between acids (both molecular and cationic) and organic bases in non-aqueous media is very complicated and depens on properties of medium 5. IUPAC has remarked on the importance of the knowledge of ph values of buffers in mixed solvents in order to achieve complete and effective ph standardization in these media.the establishment of reference ph values of the acid-base pk values of the acids and bases that compose the buffer in the mixed solvent 6. The PLS regression, one of multivariate calibration methods, was applied to potentiometric titration for determination of acid mixture 7. In this study three chemometric methods were applied to analyse the synthetic mixtures and natural waters in the presence of interferences of the absorption spectra.

5 Experimental part Apparatus Absorbance measurements were carried out by using a Perkin-Elmer Lambda 20 double beam UV-visible spectrophotometer interfaced to an IBM SX-486 microcomputer for the spectral acquisition provided with a UV-Win Lab software and subsequent manipulation of experimental data. The absorbance measurements were carried out in two matching quartz 1.0 cm cells with a 1 mm path length. The e.m.f measurements to evaluate the ph of the solution were performed with a model Metleer-Toledo MA 235 ph/ion analyzer with Hanna HI 1332 Ag/AgCl combined ph electrode system (±0.1 mv). Reagents Analytical reagent grade chemicals were used, unless otherwise indicated. Studied benzoic acids are shown in Figure 1. These compoumds were purchased from Merck( Darmstadt, Germany) Water, with conductivity lower than 0.05 S cm -1, was obtained with a Milli-Q water purification system (Millipore Corp.). NaOH ( Merck ), NaCl ( Merck ), HCl ( Merck ) were purchased from Merck( Darmstadt, Germany), too. All the solutions were prepared in 0.1 mol L -1 potassium chloride to adjust the ionic strength. The calibration of the electrode system was done potentiometrically by Gran s method [15].

6 COMPOUNDS 4-Nitrobenzoic acid FORMULA CO 2 H 3-Nitrobenzoic acid NO 2 CO 2 H 2-Nitrobenzoic acid CO 2 H NO 2 NO 2 Figure 1. Structural formulae of studied benzoic acids compounds 2.3. Absorbance measurements In a typical titration, suitable amounts of individual acids or acids mixture was added into the cell. The solution was then stirred and titrated with the titrant. After every about 10 µl of titrant was added, spectra scanning was carried out in the wavelength range of 200-500 nm. In the first step, the electrodic system was calibrated by Gran s method as in the case of potentiometric measurements in order to obtain E o value in water at 25 C ± 0.1 and in 0.1 mol l -1 ionic strength (NaCl). Previously, a suitable amount of a solution containing the compound to be analyzed at the required conditions of temperature, ionic strength and solvent composition, was added to the pre-titrated background solution and 10 µl of NaOH solution were then added. The spectral data were obtained by adding small amounts of acid or base to change the ph in the range of 2.0 11.0. At each ph, UV-Vis spectra were recorded with 1 nm resolution in order to obtain different spectra around the maximum λ for each benzoic acids. After each addition, the potential was allowed to stabilize and the potential value was used to calculate the ph of the solution using the value of E o calculated in the calibration step. In the UV-Vis spectrometric titrations, the test solution was pumped to a spectrophotometric flow-cell by means of a peristaltic pump. After each addition of

7 titrant, and after waiting for the potential reading to be stable, a spectrum was recorded, all relevant data were stored, and a new volume of titrant was added to restart the cycle. Data were processed using the programme phab which has been written for the determination of equilibrium constants from spectrophotometric data obtained from solutions at known ph. Principal Component Regression (PCR) In the spectral work, the following steps can explain the fundamental concept of PCR : a) The original data obtained in absorbances (A) (or derivative absorbance (da/dλ) and concentration (C) of analyte were reprocessed by mean-centring as A o and C o, respectively. b) The covariance dispersion matrix of the centered matrix A o was computed. The normalized eigenvalues and eigenvectors were calculated starting from square covariance matrix. The number of the optimal principal components (eigenvectors) is selected by considering only the highest values of the eigenvalues. The other eigenvalues and their corresponding eigenvectors are eliminated from our study. Using the ordinary linear regression C=/a+bxA we calculated the coefficients, a and b. To reach this objective firstly, we determined the coefficient b as b=pxq, where P is the matrix of eigenvectors and q is the C-loadings given by q= DxT T xa o. Here T T is the transpose of the score matrix T. D is a diagonal matrix having on the components the inverse of the selected eigenvalues. Knowing b we can easily find a by using the formula a=c mean -/A T meanxb, where A T mean represents the transpose of the matrix having the entries the mean absorbaces values and C mean is the mean concentration of the calibration set 8.

8 Partial Least Squares Method (PLS) The PLS calibration using the orthogonalized PLS algorithm developed by Wold and extensively discussed by Martens and Naes involves simultaneously the independent and the dependent variables on the data compression and decomposition operations. In the spectrophotometry, the PLS calibration is done by decomposition of both concentration and absorbance matrix into latent variables, A=TP T +E and C=UQ T +F. The vector, b is given as b=w(p T W) _1Q, where W is a weight matrix. By using the linear regression C=/a+bxA, the constant, a is calculated by a=c mean -/A T meanxb. As in PCR method, the PLS calibration is used for the estimation of the compounds in the samples 9.

9 Results and Discussion The absorption spectra of benzoic acid compounds in water and various ph values at 200-500 nm intervals were recorded. 4-Nitrobenzoic acid, 3-nitrobenzoic acid and 2- nitrobenzoic acid were titrated spectrophotometrically in water with sodium hydroxide as the titrant. The absorption spectra of their mixtures are shown Figs. 2. It is obvious that the titration curves of these three agents seriously overlap.in this work, Both the pka values were determinated and concentration could be estimated by PLS and PCR. Table1. The pka values of benzoic acid compounds obtained by spectrophotometric method in water and The theorical pka values of benzoic acid compounds Compounds 4-Nitrobenzoic Acid 3-Nitrobenzoic Acid 2-Nitrobenzoic Acid a: Ref [10] b: Ref [11] c: Ref [12] Experimental design of calibration sets H 2 O ( theorical) pk a 3,43 a 3,44 b 3,43 c 3,49 a 3,49 b 3,46 c 2,22 a 2,17 b 2,17 c The calibration set of standart solution of studied benzoic acids is showed in Table This ternary calibration set for multivariate calibration is a three level and three component system contain ten calibration samples. H 2 O pk a 3,4400±0,0105 3,4532±0,0110 2,3586±0,0217 1,89 1,8 1,6 1,4 1,2 A 1,0 0,8 0,6 0,4 0,2 0,00 200,0 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350,0 NM

10 Figure2. Titration absorption spectra of mixture solution studied of benzoic acids. Table2. Analytical results of prediction set of synthetic mixtures.(mmol ml -1 ) a) PCR Sythetic mixture 2-nitrobenzoic 3-nitrobenzoic acids 4-nitrobenzoic acid Actual Predicted Residual Actual Predicted Residual Actual Predicted Residual 0.050 0,0689-0,0189 0,0400 0,0444-0,0044 0,0450 0,0404 0,0046 0,100 0,1223-0,0223 0,0800 0,0852-0,0052 0,0900 0,0989-0,0089 0,150 0,1159 0,0341 0,1200 0,1171 0,0029 0,1350 0,1367-0,0017 0,200 0,1963 0,0037 0,1600 0,1530 0,0070 0,1800 0,1730 0,0070 0,200 0,1930 0,0070 0,0400 0,0387 0,0013 0,0900 0,0864 0,0036 0,150 0,1698-0,0198 0,0800 0,0793 0,0007 0,0450 0,0439 0,0011 0.100 0,0839 0,0161 0,1200 0,1196 0,0004 0,1800 0,1758 0,0042 a) PLS Sythetic mixture 2-nitrobenzoic 3-nitrobenzoic acids 4-nitrobenzoic acid Actual Predicted Residual Actual Predicted Residual Actual Predicted Residual 0.050 0,0500 0,0000 0,0400 0,0397 0,0003 0,0450 0,0443 0,0007 0,100 0,1001-0,0001 0,0800 0,0789 0,0011 0,0900 0,0867 0,0033 0,150 0,1497 0,0003 0,1200 0,1219-0,0019 0,1350 0,1402-0,0052 0,200 0,2003-0,0003 0,1600 0,1592 0,0008 0,1800 0,1781 0,0019 0,200 0,2000 0,0000 0,0400 0,0402-0,0002 0,0900 0,0907-0,0007 0,150 0,1497 0,0003 0,0800 0,0806-0,0006 0,0450 0,0460-0,0010 0.100 0,1002-0,0002 0,1200 0,1195 0,0005 0,1800 0,1790 0,0010

11 4-Nitrobenzoic acid mm (Predicted) 0,2 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 0 0,05 0,1 0,15 0,2 mm (Actual) PCR mm(predicted) PLS mm(predicted) Figure3. The results of actual and predicted for 3-nitrobenzoic acid and 4-nitrobenzoic acid. SAMPLE FUNCTION OF CORRELATION CALIBRATION COEFFICIENTS 2-nitrobenzoic acid y = 0,021x - 0,0035 0,9985 3-nitrobenzoic acid y = 0,0991x + 0,0186 0,9953 4-nitrobenzoic acid y = 0,1054x + 0,0075 0,9997 Acid concentrations of these spectrophotometric titrations could be estimated by Principal Component Regression (PCR) and Partial Least Squares Method (PLS).. 3-Nitrobenzoic Acid mm(predicted) 0,18 0,16 0,14 0,12 0,1 0,08 0,06 0,04 0,02 0 0 0,05 0,1 0,15 0,2 mm(actual) PCR mm(predicted) PLS mm(predicted)

12 Conclusion In this paper, a spectrophotometric titration method coupled with chemometrics was proposed for the simultaneous determination of mixtures of weak acids, using the mixtures of sodium hydroxide as a titrant and using ph-meter. In this method, the concentration of each component in mixture can be obtained simultaneously only using the absorption spectra of some titration points. For all acids, low prediction errors and high correlations coefficients emphasize the high linear relationship between the predicted and actual concentrations. The results obtained with this ternary mixture and some ratios of component concentrations show excellent predictive ability of this methods.

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