The Spectrophotometric Multicomponent Analysis of a TernaryMixture of Paracetamol , Aspirin , and Caffeine by the Double Divisor-Ratio Spectra Derivative Method

Double divisor-ratio spectra derivative method based on the spectrophotometric data was developed for the simultaneous analysis of a ternary mixture containing paracetamol, aspirin, and caffeine, without prior separation.is method is based on the use of the derivative of the ratio spectrum obtained by dividing the absorption spectrum of the ternary mixture by a standard spectrum of a mixture of two of the three compounds in the titlemixture.e concentrations of three compounds in theirmixture are determined by using their respective calibration graphs which are obtained by measuring the amplitude at either the maximum or minimum wavelengths selected.e selectedwavelengths for determination of aspirin, caffeine, and paracetamol are 241.5, 256, and 258.5 nm, respectively. All of the solutions adjusted to pH11 before recording the spectra in the range of 220 to 320 nm.Also, themathematical explanation of the procedure is illustrated. e method was applied for the assay of Excedrin containing paracetamol, aspirin, and caffeine.

Salinas et al. [16] and Nevado et al. [17] developed two methods for the resolution of two or more compounds in mixtures by ratio spectra derivative spectrophotometry and the derivative ratio spectra-zero crossing method.Salinas' method is based on the use of the derivative of the ratio spectra for a binary mixture.e absorption spectrum of the mixture is divided by the absorption spectrum of one of the compounds, and the �rst derivative of the ratio spectrum is obtained.e concentrations of active compounds are then determined from the calibration graphs obtained by measuring the amplitudes at points corresponding to the minimum or maximum wavelengths.In Berzas Nevado's method, the simultaneous determinations of three compounds in ternary mixtures are based on the measurements of the amplitude at the zero crossing points in the derivative spectrum of the ratio spectra.
In the present research, a sensitive, selective, accurate, and inexpensive procedure was applied for simultaneous determination of paracetamol (PAR), aspirin (ASP), and caffeine (CAF) by double divisor-ratio spectra derivative method with simultaneous standard additions of three analytes.is method is a novel standard addition method based on the derivative of the ratio spectra concept.In this paper, an attempt was made to calculate the derivative of the double divisor-ratio spectra and attribute them to the analyte concentration using spectrophotometry technique.

Experimental
2.1.Reagents.Paracetamol, aspirin, and caffeine were kindly provided by the Iranian Pharmaceutical Companies (Tehran, Iran).Analytical grade phosphoric acid, boric acid, acetic acid, and sodium hydroxide were supplied from Merck (Darmstadt, Germany).All other reagents were of analytical grade.Britton-Robinson (B-R) buffer (0.1 mol L −1 ) in the pH range of 2-10 was used throughout.
A 1.0 × 10 −3 mol L −1 paracetamol solution was prepared daily by dissolving 0.0074 g PAR (99.0%) in ethanol (96%) and was diluted in a 100 mL volumetric �ask to the mark.A 1.0 × 10 −3 mol L −1 aspirin solution was prepared daily by dissolving 0.0090 g of ASP (99.5%) in ethanol (96%) and diluted in a 100 mL volumetric �ask.A 1.0 × 10 −3 mol L −1 caffeine solution was prepared daily by dissolving 0.0097 g of CAF (99.5%) in double distilled water and diluted into a 100 mL volumetric �ask.ese solutions were kept in a refrigerator at 4 ∘ C in dark.More dilute solutions were prepared by serial dilutions with double distilled water.

Instrumentation and Soware.
UV-visible absorption spectra were recorded by a spectrophotometer (Perkin Elmer) model Lambda 25, with the use of 1.0 cm quartz cells.
A Pentium IV (2.53 GHz) computer controlled all the setting and data processing.e spectrum of each solution were recorded in the wavelength range of 200-320 nm and saved as text �les.Double divisor-ratio derivative spectra calculated in Excel (2007) program.
A pH-meter (Metrohm, Model 827) with a double junction glass electrode was used to adjust the pH of the solutions.

Preparation of Real Samples.
To assay Excedrin tablet containing paracetamol (325 mg), aspirin (325 mg), and caffeine (65 mg) in each tablet, the content of �ve tablets are mixed together.e quantity of 0.0203 g of the powder was accurately weighted and then dissolved in 100 mL of ethanol (96%).Aer being mixed completely, the solution was diluted to the mark with ethanol.is solution was kept in refrigerator at 4 ∘ C.
2.4.General Procedure.e general procedure for the analysis of PAR, ASP, and CAF in a ternary mixture was as follows.To approximately 1.0 mL of sample solution in a 10.0 mL volumetric �ask, 1.0 mL B-R buffer (pH 11.0) is added, and the �nal volume was diluted to the mark with double distilled water aer successive standard additions of the three components (PAR, IBU, and CAF) at the same mole ratio.For simultaneous determination of PAR, ASP, and CAF, the spectra of ternary mixture aer each standard addition divided to the standard binary samples of ASP + CAF, CAF + PAR, and PAR + ASP in the same concentrations of 2.0 mol L −1 for each species.en the ratio spectra were transformed to Matlab soware and converted to derivative ratio spectra, and the values of PAR, ASP, and CAF in the ternary mixtures were determined by standard addition plots at wavelengths 258.5, 241.5, and 256 nm, respectively.For better understanding this phenomenon, let us consider a mixture of PAR, ASP, and CAF in the same concentration of 10.0 mol L −1 for each component.To determine ASP in the presence of PAR and CAF, the absorption spectra of the ternary mixture, aer successive standard additions of three components, were prepared (Figure 2) and divided by the spectrum of the standard mixture solution of PAR and CAF (2.0 mol L −1 each in B-R buffer), and the ratio spectra were plotted (Figure 3).e �rst derivatives of the ratio spectra were plotted with Δ  nm (Figure 4).e amount of ASP was determined by measuring the amplitude at 241.5 nm corresponding to a minimum in the �rst derivative of the ratio spectra in the spectral region selected (Figure 5).

Double Divisor-Ratio Spectra Derivative Method.
As shown in Figure 1, the absorption spectra of paracetamol, aspirin, and caffeine overlapped in the wavelength range of 220-320 nm.erefore, double divisor-ratio spectra derivative method proposed for simultaneous determination of compounds in ternary samples.If Beer's law is obeyed for all compounds over the whole wavelength range used, and if the path length is 1 cm, the absorption spectrum of the ternary mixture can be written in the form of the following equation: where    is the absorbance of the mixture at wavelength   , and  PAR ,  ASP , and  CAF are the absorptivities of PAR, ASP and CAF, respectively.A similar equation for two compounds in the same ternary mixture as in a standard binary mixture can be written as If ( 1) is divided by (2) corresponding to the spectrum of a standard solution of two of the components in the ternary mixture, the ratio spectrum is obtained in Substituting ( 5) into ( 4), ( 6) is derived as follows: If the �rst derivative of ( 6) is taken, since the derivative of a constant is zero, (7)  Equation ( 7) is the mathematical foundation of multicomponent analysis which permits the determination of the concentration of each of the active compounds in solution without interference from the other components of the ternary system.In practice, (7) corresponding to the �rst derivative ratio spectrum of PAR is obtained by dividing the absorption spectrum of the ternary mixture of PAR, ASP, and CAF by the standard spectrum of two of the compounds in the ternary mixture.Also, in (7), the derivative signal of the ratio spectrum of the ternary mixture is dependent only on the concentration values of PAR and  0 CAF , but is independent of the concentration values  ASP and  CAF in the ternary mixture.In the developed method, the concentration of  PAR in the ternary mixture is proportional to the �rst derivative signals corresponding to a maximum or minimum point.
e double divisor spectra of binary mixtures calculated as the following steps.
(a) A standard binary mixture of analytes added to the unknown sample and recorded its spectrum.
(b) e spectrum of unknown sample recorded in the wavelength range of 220 to 320 nm.
(c) e spectrum of double divisor in the presence of matrix effect calculated by the subtract the spectrum of step "b" from step "a".
e stored spectra of the ternary mixture are divided by the spectrum of double divisors aer addition of pure PAR using MATLAB soware.e derivative of the ratio spectra at wavelength 258.5 nm plotted against standard concentrations of PAR.As explained here, this technique can be used for determination of other compounds in the ternary mixture using other double divisors containing PAR + CAF and PAR + ASP for the determination of ASP and CAF, respectively.In this research, simultaneous standard additions of three compounds of PAR, ASP, and CAF into the ternary mixture presented, and the analysis of PAR, ASP and CAF is also applicable using the doubled divisor-ratio derivative method for the �rst time.is technique is very simple and fast in comparison with the individual standard addition method.

Results and Discussions
e absorption spectra of the three compounds, PAR, ASP, and CAF overlapped closely in the region 220-320 nm in Figure 1.For this reason, the determination of the above T 2: Determination of aspirin, caffeine, and paracetamol in some ternary mixtures.

Mixture
Added (mol L −1 ) Found (mol L  compounds was not possible from direct measurements of absorbances in the zero-order spectra.In this research, double divisor-ratio spectra derivative method based on the spectrophotometric data was developed for the simultaneous analysis of the ternary mixtures containing paracetamol, aspirin, and caffeine, without prior separation.ASP decreased, therefore B-R buffer at pH 11.0 was selected to adjust the pH of solutions before recording the spectra.

Selection of the Working Wavelengths.
In the application of this method, the �rst derivative of the ratio spectra of pure compound and its ternary mixture would be coincided in the spectral region corresponding to a maximum point or a minimum point of the wavelength as shown in Figure 7. ese coinciding points of the derivative of the ratio spectra can be selected as working wavelengths for the determinations of the subject compounds in the ternary mixture.e best working wavelengths selected at 258.5, 241.5, and 256 nm for determination of paracetamol, aspirin, and caffeine, respectively.

e Effect of Double Divisor Concentrations.
According to the theory [16], the concentrations of double divisors should be equal, but the slope of the calibration graphs proportionally decreased by increasing concentrations of divisors (Figure 8).ese results con�rm the reliability of the ratio spectra method in the present instance.According to the above results, concentration of 2.0 mol L −1 was chosen as the divisor concentrations.

Figures of Merit.
To check the reproducibility of the proposed method, three replicate experiments for the determination of paracetamol, aspirin, and caffeine in ternary mixtures have been designed (Table 1).e relative standard deviation values are in the range of 0.58 to 5.73%.e limit of detection calculated as LOD = 3  [18], where   is the standard deviation of several ( = 3) replicated measurement of zero concentration of the analyte using the proposed method.e corresponding values obtained were 0.46, 0.53, and 0.68 mol L −1 for PAR, ASP, and CAF, respectively.e calibration plots were linear in the ranges of 0.4-320.0mol L −1 , 0.8-160.0mol L −1 , and 0.4-260.0mol L −1 , respectively, for PAR, ASP, and CAF with the correlation coefficients of 0.9979, 0.9999, and 0.9991.

Application of the Proposed Method in Synthetic and
Real Samples.In order to evaluate the applicability of the proposed method for the determination of PAR, ASP, and CAF in real samples, the utility of the developed method was tested by determining of the compounds in several model (mixed) samples (Table 2) and pharmaceutical formulations (Table 3).e good recoveries of the spiked samples are indicative of the successful applicability of the proposed method for simultaneous determination of paracetamol, aspirin, and caffeine.All of the recoveries in real samples were satisfactory in the range of 94.0% to 106.0%.

Conclusions
is work formulates a new approach to the simultaneous analysis of ternary mixtures of paracetamol, aspirin, and caffeine which have overlapping spectra.In the double divisor-ratio spectra derivative method, for each compound in ternary mixture, without searching for the critical point for the separated peaks, the maximum amplitude of the separated peaks can be measured.is can be considered as an advantage of the new method over alternative methods for the resolution of ternary mixtures.Our new method has great promise for the routine determination of two or more compounds in mixtures and for the analysis of Excedrin tablets in control process of products.

Con�ict of �nterests
It needs to be mentioned that the Merck materials (phosphoric acid, boric acid, acetic acid, and sodium hydroxide) were provided to the author by the Gachsaran Branch, Islamic Azad University where the author work as a member of the faculty, and these materials, which are running very low, have been purchased by the university around the year 2005.

F 3 : 5 F 4 : 4 F 5 :
Double divisor of the ratio spectra for a ternary mixture of aspirin, caffeine, and paracetamol aer simultaneous standard addition of three components in the concentration range of 10-60 mol L −1 (1-6).Double divisors concentrations are CAF, 2.0 mol L −1 + PAR, 2.0 mol L −1 .All of the conditions are as Figure2.First-derivative double divisor-ratio spectra for a ternary mixture of aspirin, caffeine, and paracetamol aer simultaneous standard addition of three components in the concentration range of 10-60 mol L −1 .Δ   nm.All of the conditions are as Figure3.Standard addition plot for the derivative of double divisorratio spectra for a mixture of ASP (50 mol L −1 ), CAF (20 mol L −1 ), and PAR (20 mol L −1 ) aer standard addition of three components in the same mole ratios in the concentration range of 10-60 mol L −1 .e initial solution contains a ternary mixture of ASP (50 mol L −1 ), CAF (20 mol L −1 ), and PAR (20 mol L −1 ).

F 8 :
Effect of double divisor concentrations on the slopes of the calibration curves of (a) ASP, (b) CAF, and (c) PAR.

3. 1 .
Optimization of the Parameters.In the following, the effective parameters involving pH, working wavelengths, and double devisor concentrations studied on the accuracy of the proposed method.3.1.1.Optimization of pH.It has been shown that the maximum absorbances for CAF and PAR are independent of the pH of the solution within the pH range of 1.8 to 11.0 in terms of sensitivity (Figure6(a)).e maximum wavelengths for PAR and ASP are close to each other in the range of 1.8 to 8.0 but at pH > 8.0, overlapping spectra between PAR and ASP    ASP +  CAF    CAF   ASP   ASP +  CAF   CAF  ASP    ASP +  CAF    CAF +  PAR  PAR  ASP    ASP +  CAF    e ratio of the sum of  ASP   ASP and  CAF   CAF to the sum of  ASP    ASP and  CAF    CAF is equal to a constant ( with respect to , in a certain region or point of wavelength.ese coinciding points of the derivative of the ratio spectra can be selected as working wavelengths for the determinations of the subject compounds in the ternary mixture.If the above constant is replaced in (3), we obtain     ASP    ASP +  CAF    CAF   +  PAR  PAR  ASP    ASP +  CAF    ) are equal or very close to each other, we could write  ASP    ASP +  CAF    CAF    CAF  ASP  +  CAF    (5) will be obtained as follows: Determination of paracetamol, aspirin, and caffeine in Excedrin tablets by the proposed method.