Double divisor mean centering of ratio spectra as a developed spectrophotometric method for the...

Journal of Saudi Chemical Society (2014) xxx, xxx–xxx

King Saud University

Journal of Saudi Chemical Society

www.ksu.edu.sawww.sciencedirect.com

ORIGINAL ARTICLE

Double divisor mean centering of ratio spectra as

a developed spectrophotometric method for the analysis

of five-component mixture in drug analysis

R’afat Mahmoud Nejema,*, Mahmoud Mohamed Issa

b, Alaa Abu Shanab

c,

Nahed Talab Shaat d

a Analytical Chemistry, Department of Chemistry, Alaqsa University, P.O. Box 4051, Gaza, Palestineb Pharmaceutical Analytical Chemistry, Department of Chemistry, Alaqsa University, P.O. Box 4051, Gaza, Palestinec Inorganic Analytical Chemistry, Department of Chemistry, Alaqsa University, P.O. Box 4051, Gaza, Palestined R and D Department, Middle East Pharmaceuticals and Cosmetics Laboratories, Gaza, Palestine

Received 23 September 2013; revised 19 February 2014; accepted 2 March 2014

*

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Pe

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Pth

KEYWORDS

Methylparaben;

Propylparaben;

Chloropheniramine;

Pseudoephedrine;

Double divisor mean

centering ratio;

Classical least square

Corresponding author. Tel.:

mail address: rafatnejem@al

er review under responsibilit

Production an

19-6103 ª 2014 King Saud U

tp://dx.doi.org/10.1016/j.jscs.

lease cite this article in press ae analysis of five-component

+970 599

aqsa.edu

y of King

d hostin

niversity

2014.03.0

s: R.M. Nmixture

Abstract In this paper a simple method was developed for the simultaneous determination of five-

component mixtures, without prior separation steps. The method is based on the combination of

double divisor-ratio derivative method and mean centering of ratio spectra method. The mathemat-

ical explanation of the procedure is illustrated. The linear determination ranges were 0–30, 0–20,

0–20, 0–45 and 0–100 lg ml�1 for paracetamol, methylparaben, propylparaben, chloropheniramine

maleate and pseudoephedrine hydrochloride in 0.1 M HCl, respectively. The proposed method was

validated by using synthetic five-component mixtures and applied to the simultaneous determina-

tion of these drugs in Decamol Flu syrup. No published spectrophotometric method has been

reported for simultaneous determination of the five components of this mixture. So the results of

the double divisor mean centering of ratio method (DD-MCR) were statistically compared with

those of a proposed classical least squares method (CLS).ª 2014 King Saud University. Production and hosting by Elsevier B.V. All rights reserved.

1. Introduction

Paracetamol (PA) is an analgesic and antipyretic agent [1],which is associated with pseudoephedrine hydrochloride

603459; fax: +970 82845488.

.ps (R.M. Nejem).

Saud University.

g by Elsevier

. Production and hosting by Elsev

01

ejem et al., Double divisor mean cin drug analysis, Journal of Saud

(PS), a direct- and indirect-acting sympathomimetic agent [2]

and chloropheniramine maleate (CM), a potent antihistaminic[3], in addition to methylparaben (MP) and propylparaben,which are used as preservatives. This combination is used for

symptomatic treatment of coughs and the common cold.The UV absorption spectra of PA, MA, PP, CH, and PS

display considerable overlap, where the application of the con-

ventional spectrophotometry failed to resolve it. No spectro-photometric analytical method has been reported for thesimultaneous determination of PA, MP, PP, CH, and PS ina multicomponent mixture.

ier B.V. All rights reserved.

entering of ratio spectra as a developed spectrophotometric method fori Chemical Society (2014), http://dx.doi.org/10.1016/j.jscs.2014.03.001

mailto:[email protected]

http://dx.doi.org/10.1016/j.jscs.2014.03.001


http://www.sciencedirect.com/science/journal/13196103



2 R.M. Nejem et al.

While official [4] and spectrophotometric methods [5–14]are available for the determination of each of these drugsalone or in mixture with other drugs, the most prominent

method for simultaneous determination of PA, MP, PP,CH, and PS is the HPLC, GC–MS or LC–MS [15–21]. How-ever, these reported methods suffered from time-consuming

extraction procedure and long chromatographic analysistime. Additionally the United States pharmacopeia [22] sug-gested the reduction in the amount of toxic organic solvents

used in HPLC assays that cause harm to human health andenvironment. Therefore, chemometric-assisted spectropho-tometry as a simple, quick and low cost method may be agood alternative if it is combined with multivariate calibra-

tion methods for determination of a complex in pharmaceu-tical quality control laboratories.

Salinas et al. [23] proposed a ratio-derivative spectropho-

tometric method. Their method is based on the derivativeof the ratio spectra for a binary mixture which divided bythe spectra of a standard solution (one divisor). Berzas Neva-

da et al. [24] developed a derivative ratio spectrum-zero cross-ing for the simultaneous determination of three compoundsin ternary mixtures (no divisor used). Dinc et al. [25–27] pro-

posed a double divisor-ratio spectra derivative method for thesimultaneous determination of ternary mixtures. Recently,Afkhami and Bahram proposed a new mean centering of ra-tio spectra method for the simultaneous determination of ter-

nary mixtures [28–30]. Their method is based on the meancentering of the ratio spectra for a binary or ternary mixturewhich divided by the spectra of a standard solution (one

divisor).Unfortunately, the advantages of all these methods are at

least partially offset because they are used only for the determi-

nation of binary or ternary mixtures.In this paper a new and simple method was developed for

the simultaneous determination of five-component mixtures,

without prior separation steps. This method is based on thecombination of double divisor-ratio spectra method andmean centering of ratio spectra method. This method elimi-nates derivative steps and therefore signal to noise ratio is en-

hanced [31]. The technique can be used for other systems,particularly for more than five component systems. It maybe also used more than double divisor (three or four) for

the five component mixtures.No published method has been reported for simultaneous

determination of PA, MP, PP, CH and PS. So the results of

the double divisor mean centering of ratio spectra (DD-MCR) method were compared with those of a proposed clas-sical least squares (CLS) method.

2. Theoretical background

2.1. Double divisor mean centering of ratio spectra method (DD-MCR)

If a mixture of five compounds (PA, MP, PP, CH and PS) is

considered and if Beer’s law is obeyed for all compounds overthe whole wavelength range used, then

Am ¼ aPACPA þ aMPCMP þ aPPCPP þ aCHCCH þ aPSCPS ð1Þ

where Am is the vector of the absorbance of the mixture, aPA,aMP, aPP, aCH, and aPS are the absorptivity vectors of PA, MP,

Please cite this article in press as: R.M. Nejem et al., Double divisor mean cthe analysis of five-component mixture in drug analysis, Journal of Saud

PP, CH and PS and CPA, CMP, CPP, CCH, and CPS are the con-

centrations of PA, MP, PP, CH and PS, respectively. Absorp-tivity A: (1%, 1 cm) values were calculated by using theabsorbance for zero-order spectra for each of the compounds

in the five-component mixture.If Eq. (1) is divided by aMPC

�

MP þ aPPC�

PP

ðC�MP ¼ C�

PP=1 lg ml�1) corresponding to the spectrum of astandard solution of CMP and CPP the first ratio spectrum is

obtained [25,28]:

x¼ Am

aMPþaPP

¼ aMPCMPþaPPCPP

aMPþaPP

þ aPACPA

aMPþaPP

þ aCHCCH

aMPþaPP

þ aPSCPS

aMPþaPP

ð2Þ

Here in our method, in the synthetic mixture, CMP and CPP areequal and in the real sample, standard addition method is used(CMP = CPP + CPP,x)

x ¼ Am þ aPPCPP;x

aMP þ aPP

¼ aMPCMP þ aPPbCPP þ CPP;xcaMP þ aPP

þ aPACPA

aMP þ aPP

þ aCHCCH

aMP þ aPP

þ aPSCPS

aMP þ aPP

ð3Þ

If Eq. (2), (3) are mean centered, therefore

mcx ¼ mcaPACPA

aMP þ aPP

þmcaCHCCH

aMP þ aPP

þmcaPSCPS

aMP þ aPP

ð4Þ

By dividing Eq. (4) by mc aCHaMPþaPP

, the second ratio spectrum isobtained

y ¼ mcx

mc aCHaMPþaPP

¼ CCH þ ðZÞ CPA þmc aPS

aMPþaPP

mc aCHaMPþaPP

CPS

mcy ¼ mcZ CPA0 þ mcmc aPS

aMPþaPP

mc aCHaMPþaPP

ð5Þ

Finally we obtain the third ratio spectrum

mcmcy

mcZ¼ ðconstantÞCPS ð6Þ

Eq. (6) is the mathematical foundation of multicomponent

analysis which permits the determination of the concentrationof each compound without interference from the other compo-nents of the mixture.

In practice, the signal of third ratio spectrum of PS is

dependent only on the concentration values CPS and Am

aMPþaPP

(also Cx in real sample), but is independent of the concentra-tion values CPA, CMP, CPP, and CCH in the mixture. The dou-

ble divisor concentration used in our developed method isshown in Table 1, therefore, the concentration CPS in themixture is proportional to the amount of mc mcy

mcZcorrespond-

ing to a maximum or minimum point.A calibration curve could be constructed by plotting

mc mcymcZ

against different concentrations of PS. As explainedhere, this technique can be used for other systems, particularlyfor more than five component systems. By using the calibra-

tion curve, the concentration of PS is determined in the samplecontaining PA, MA, PP and CH. The concentrations of othercomponents are determined by analogous procedures.



https://www.researchgate.net/publication/23435651_Simultaneous_determination_of_propacetamol_and_paracetamol_by_derivative_spectrophotometry?el=1_x_8&enrichId=rgreq-a1d8336c-181c-469f-b075-5c9607afa05b&enrichSource=Y292ZXJQYWdlOzI2MDkxNDA1MTtBUzoxOTA5MjA0ODc5NTY0ODFAMTQyMjUzMDM5OTU2Mw==

Table 1 The first, second and third ratio spectral data.

Drug x y z Double divisor (lgml�1) Cx added (lgml�1)

PS Am

aMP þ aPP

mcx

mc aCH

aMPþaPP

mc aPA

aMPþaPP

mc aCH

aMPþaPP

0.1 MP+ 0.1 PP CPP = 0.32

CHAm

aMP þ aPP

mcx

mc aPS

aMPþaPP

mc aPA

aMPþaPP

mc aPS

aMPþaPP

1 MP+ 1 PP CPP = 0.32

PPAm

aPA þ aCH

mcx

mc aPS

aPAþaCH

mc aMP

aPAþaCH

mc aPS

aPAþaCH

0.1 PA+ 0.1 CH CCH = 12.72

MP Am

aPA þ aCH

mcx

mc aCH

aPAþaCH

mc aPP

aPAþaCH

mc aPS

aPAþaCH

0.1 PA+ 0.1 CH CCH = 12.72

PAAm

aCH þ aPS

mcx

mc aCH

aCHþaPS

mc aPP

aCHþaPS

mc aMP

aCHþaPS

1 CH+ 1 PS CCH = 1.12

Double divisor mean centering of ratio spectra 3

2.2. Classical least squares method (CLS)

The mathematical formulations of this method, in the matrixcompact form, can be written as

A ¼ aCþ E ð7Þ

where the matrix A represents the absorbance matrix, C is theconcentration matrix, a is the absorptivity and E is a matrix of

concentration prediction error. This expression implies thatthe absorbance is a function of the concentration at a seriesof given wavelength. The a matrix can be solved by computing:

C ¼ a�1A ð8Þ

If the a matrix is not square, the pseudo-inverse must be usedinstead:

C ¼ ða0aÞ�1a0A ð9Þ

3. Materials and methods

3.1. Instrumentation and software

A shimadzu (Kyoto, Japan) UV-1650 PC, UV–Visible double-beam spectrophotometer with two matched 1 cm path-lengthquartz cells was used. The subsequent statistical manipulationswere performed by transferring the spectral data to Microsoft

Excel 2010 program and processing them with the standardcurve fit package and matrix calculation.

3.2. Regents and materials

Pharmaceutical grade PA, MP, PP, CH and PS with claimedpurities of 99.8%, 99.9%, 99.7%, 99.7% and 99.9%, respec-

tively according to the manufacturer’s certificate were kindlydonated by the middle east pharmaceuticals and cosmetics lab-oratories, Palestine.

Decamol Flu syrup (batch number 1943) (Middle Eastpharmaceuticals and cosmetics laboratories, Palestine) wasused. Each 5 ml contains 160 mg PA, 5 mg MP, 1 mg PP,1 mg CH and 15 mg PS.


3.3. Stock standard and working solutions

A stock solution of PA (1.6 mg ml�1) was prepared by dissolv-ing 0.16 g of PA in 100 mL of 0.1 M HCl. A stock solution ofMP (0.5 mg ml�1) was prepared by dissolving 0.05 g of MP in100 mL of 0.1 M HCl. A stock solution of PP (0.1 mg ml�1)

was prepared by dissolving 0.01 g of PP in 100 mL of 0.1 MHCl. A stock solution of CH (0.1 mg ml�1) was prepared bydissolving 0.01 g of CH in 100 mL of 0.1 M HCl. A stock solu-

tion of PS (1.5 mg ml�1) was prepared by dissolving 0.15 g ofPS in 100 mL of 0.1 M HCl.

3.4. Procedure

3.4.1. DD-MCR method

Accurate aliquots equivalent to 1.0–300 lg PA, 1.0–200 lgMP, 1.0–200 lg PP, 1.0–450 lg CH and 1.0–1000 lg PS weretransferred from their respective working standard solutionsinto three series of 10 ml volumetric flasks, the volume was

completed to the mark with 0.1 M HCl to obtain final concen-tration range 0.1–30 lg ml�1 PA, 0.1–20 lg ml�1 MP, 0.1–20 lg ml�1 PP, 0.1–45 lg ml�1 CH and 0.1–100 lg ml�1 PS.

The absorption spectra of the prepared solution were mea-sured in the range of 220–280 nm.

For PS, the recorded spectra were divided by standard spec-

trum of 0.1 lg ml�1 MP and 0.1 lgml�1 PP to obtain the firstratio spectra which were then mean centered. These vectorswere then divided by the mean center of aCH

aMPþaPPand therefore

the mean centering of the second ratio spectra was obtained.

In the same way, according to Eq. (6), the third ratio spectracan be obtained as shown in Table 1.

The mean centered values of the third ratio spectra at 250,

265, 265, 235 and 250 nm for PA, MP, PP, CH and PS, respec-tively were measured and plotted against the correspondingconcentration of each drug to construct their calibration

curves.Different synthetic mixtures containing different ratios each

of PA, MP, PP, CH and PS within their calibration ranges

were prepared. The spectra of these mixtures were then re-corded and the procedure that was previously explained was



Table 2 Experimental parameters calculated for the determi-

nation of PA, MP, PP, CH and PS by using DD-MCR and

CLS methods.

k (nm) aPA aPS aPP aCH aMP

230 523.81 4.22 254.83 130 217.86

235 595.24 2.83 387.5 250 159.82

240 639.88 5.83 591.66 440 135.71

245 642.86 7.35 795.83 620 125.0

250 595.24 9.57 950 780 130.37

255 479.17 10.96 1029 850 166.07

260 345.23 9.57 950 790 204.46

265 325.11 6.39 787.5 640 219.64

270 157.74 1.74 587 470 202.68

Figure 1 The zero order spectra of (1) 3.36 lg ml�1 PA; (2)

2.40 lg ml�1 MP; (3) 2.00 lg ml�1 PP; (4) 5.50 lg ml�1 CH; (5)

23.0 lg ml�1 PS in 0.1 M HCl.

4 R.M. Nejem et al.

performed to predict the concentration of each compound inthe mixture.

Two ml of Decamol Flu syrup was transferred to 100 ml

volumetric (five time) and dissolved in 0.1 M HCl. Then 1 mlof the solution was transferred to 25 ml volumetric flask andthe volume was completed with the same solvent. The pro-

posed DD-MCR was applied to the prepared solutions. Eq.(3) is used instead of Eq. (2) and the Cx used can be shownin Table 1.

3.4.2. Classical least squares (CLS)

The absorption spectra of different synthetic mixtures contain-ing different ratios each of PA, MP, PP, CH and PS in the

range 230–270 nm were recorded. The absorptivity (a) was cal-culated for each drug by using the absorbances at nine pointswith intervals of Dk = 5 nm in the spectrum. By using a value

(Table 2), a system of equations with five unknowns can bewritten for the drugs in the five component mixture, as follows:

aPA;230 aMP;230 aPP;230 aCH;230 aPS;230

aPA;235 aMP;235 a9m;235 aCH;235 aPS;235








26666666666666666666664

37777777777777777777775

9X5

CPP

CMA

CPP

CCH

CPS

26666666666666666666664

37777777777777777777775

5X1

¼

A230

A235

A240

A245

A250

A255

A260

A265

A270

26666666666666666666664

37777777777777777777775

9X1

This matrix can be solved and the CLS procedure that waspreviously explained was performed to determine the concen-tration of each drug in the mixture. The proposed method

was applied to the previously prepared solutions of DecamolFlu syrup.

4. Results and discussion

The absorption spectra of PA, MP, PP, CH and PS, Fig. 1,display considerable overlap, where the application of conven-

tional spectrophotometry failed to resolve these overlappings.To the best of our knowledge, there are no other techniques forthe simultaneous spectrophotometry determination of these

drugs by chemometric method.


4.1. DD-MCR method

The developed method is a combination of the double divisor-

ratio spectra and mean centering of ratio spectra. The methoddepends on the use of spectra of the mean centering ratio spec-tra obtained by using a ‘‘double divisor’’ (sum of two spectra)

and measuring at either the maximum or minimum wave-length. The ratio of the concentrations of double divisorshould be the same in calibration and unknown samples.

The method eliminates derivative steps and therefore signalto noise ratio is enhanced. Finally, this method can be usedfor other systems, particularly for more than five component

systems.In order to optimize the developed DD-MCR method, ef-

fect of double divisor on the selectivity of the method has beentested. Different concentrations each of PA and CH, MP and

PP or CH and PS were tested. As Table 1 shows the doubledivisor had a great effect on the selectivity of determinationof PA, MP, PP, CH and PS, where reproducible and good re-

sults have been obtained upon using concentration of0.1 lg ml�1 of MP and 0.1 lg ml�1 PP (for PS), 1 lg ml�1

CH and 1 lg ml�1 PS (for PA), 0.1 lg ml�1 PA and

0.1 lg ml�1 CH (for PP and MP), and 1 lg ml�1 MP and1 lg ml�1 PP (for CH) as double divisors. On the other hand,changing the concentration of the double divisor had a greateffect on the slop, intercept and correlation coefficient of cali-

bration equation (Table 3). The amount of Dk had no effect onthe mean centering of ratio spectra. A Dk of 5 nm was used.

The absorption spectra of the standard solutions of PS were

divided by the spectrum of 0.1 lg ml�1 MP +0.1 lg ml�1 PPand the first ratio spectra were obtained (Fig. 2a). After thatthe third ratio spectra according to Eq. (6) were obtained.

The concentration of PS was determined by measuring theamplitude at 250 nm corresponding to a minimum wavelengthin the third ratio spectra as shown in (Fig. 2b). For the predic-

tion of concentration of PS in synthetic mixtures and real sam-ples, the same procedure was used.

In the same way, the first ratio spectra for CH (Fig. 3a), PP(Fig. 4a), MP (Fig. 5a) and PA (Fig. 6a) were obtained. The



Table 3 Analytical characteristics for analysis of PA, MP, PP, CH and PS by DD-MCR method.

Drug k (nm) Calibration equations R2 Linear range LOD (lg ml�1) LOQ (lg ml�1) Intra-day (RSD) Inter-day (RSD)

PA 250 y= 85.987C+ 3.7005 0.9995 0–30 0.09 0.273 0.875 0.861

MP 65 y= -3.7467C � 0.2667 0.9999 0–20 0.07 0.212 0.738 0.745

PP 265 y= -2.993C + 0.6667 0.9991 0–20 0.07 0.212 0.598 0.613

CH 235 y= 28.657C - 2.285 0.9989 0–45 0.08 0.242 0.791 0.822

PS 250 y= -1.1427C+ 0.2133 0.9981 0–100 0.08 0.242 0.671 0.701

Figure 2 The first ratio spectra of different concentrations (2.5, 5 and 10 lg ml�1) of PS (a) and third ratio spectra (b).

Figure 3 The first ratio spectra of different concentrations (2.5, 5 and 10 lg ml�1) of CH (a) and third ratio spectra (b).


Please cite this article in press as: R.M. Nejem et al., Double divisor mean centering of ratio spectra as a developed spectrophotometric method forthe analysis of five-component mixture in drug analysis, Journal of Saudi Chemical Society (2014), http://dx.doi.org/10.1016/j.jscs.2014.03.001


Figure 4 The first ratio spectra of different concentrations (2.5, 5 and 10 lg ml�1) of PP (a) and third ratio spectra (b).

Figure 5 The first ratio spectra of different concentrations (2.5, 5 and 10 lg ml�1) of MP (a) and third ratio spectra (b).

6 R.M. Nejem et al.

third ratio spectra were also obtained for other drugs. The con-centration of CH, PP, MP, and PA was determined by measur-

ing the amplitude at 235 (Fig. 3b), 265 (Fig. 4b), 265 (Fig. 5b)and 250 nm (Fig. 6b), respectively.

Beer’s law was obeyed in the concentration 0–30 lg ml�1 for

PA, 0–20 lg ml�1 for MP, 0–20 lg ml�1 PP, 0–45 lg ml�1 CHand 0–100 lg ml�1 PS. Table 3 shows the linear regressionparameters for calibration data for simultaneous determination

of PA, MP, PP, CH and PS in their five-component mixtures.Limit of detections (defined as the concentration equivalentto three times the standard deviation of five replicate


measurements of the blank) and limit of quantitation are alsoshown in Table 3.

To ascertain accuracy of the method, recovery studies wereperformed by the standard addition method as per ICH guide-lines. Results of the recovery study are summarized in Table 5.

The percent recoveries for PA, MP, PP, CH and PS were foundin the range of 99.20–100.6% with standard deviation (<2.0)indicating accuracy of the method.

To check the repeatability of the method, the relative stan-dard deviation (R.S.D) for five replicate determinations of10 lg ml�1 each of PA, MP, PP, CH and PS, in five-component



Figure 6 The first ratio spectra of different concentrations (2.5, 5 and 10 lg ml�1) of PA (a) and third ratio spectra (b).

Table 4 Results of several synthetic mixtures for analysis of PA, MP, PP, CH and PS by DD-MCR method.

Taken (lg ml�1) Found (lg ml�1) Recovery (%)

PA MP PP CH PS PA MP PP CH PS PA MP PP CH PS

20* 0.8 0.16 5.0 2.4 19.98 0.81 0.164 5.06 2.35 99.9 101.3 102.5 101.2 97.9

15* 2.0 4.0 2.0 5.0 14.97 2.03 4.04 2.01 5.06 99.8 101.5 101.0 100.5 101.2

20* 1.0 2.0 0.16 5.0 20.10 0.99 2.03 0.16 4.92 100.5 99.0 101.5 100.0 98.4

25.6* 1.0 2.0 5.0 5.0 25.50 0.98 1.98 4.97 10.0 99.6 98.0 99.0 99.4 100.0

15 15 15 15 15 15.11 15.0 14.93 15.0 14.96 100.7 100.0 99.5 100.0 99.7

10 10 10 10 10 10.0 9.88 9.88 10.13 10.08 100.0 98.8 98.8 101.3 100.8

5.0 5.0 5.0 5.0 5.0 5.05 5.07 5.09 5.01 4.96 101.0 101.3 101.7 100.2 99.2

2.5 2.5 2.5 2.5 2.5 2.53 24.7 24.85 2.56 2.49 101.2 98.8 99.4 102.5 99.5

Mean recovery 100.3 99.8 100.4 100.6 99.6

R.S.E single (%) 1.17 1.75 1.18 0.78 0.66

R.S.Et (total) (%) 1.15

* Using standard addition method.

Table 5 Results of accuracy and recovery for DD-MCR method.

Level recovery Amount of pure added (mg) Amount of drug recovered (mg) Recovery (%)


80% 20.48 0.64 0.128 0.128 1.92 20.83 0.646 0.129 0.126 1.910 101.7 100.9 100.6 98.5 99.5

20.48 0.64 0.128 0.128 1.92 20.56 0.641 0.129 0.126 1.906 100.4 100.1 100.8 98.6 99.3

20.48 0.64 0.128 0.128 1.92 20.62 0.639 0.128 0.128 1.897 100.7 99.9 99.9 99.8 98.8

100% 25.60 0.8 0.16 0.16 2.4 25.47 0.811 0.162 0.160 2.390 99.5 101.4 101.6 100.2 99.6

25.60 0.8 0.16 0.16 2.4 25.28 0.796 0.162 0.160 2.369 98.7 99.5 101.3 100.1 98.7

25.60 0.8 0.16 0.16 2.4 25.42 0.806 0.160 0.160 2.40 99.3 100.8 100.1 99.9 100.0

120% 30.72 0.96 0.192 0.192 2.88 30.90 0.973 0.195 0.188 2.84 100.6 101.4 101.6 98.1 98.6

30.72 0.96 0.192 0.192 2.88 30.35 0.965 0.191 0.192 2.845 98.8 100.5 99.9 99.9 98.8

30.72 0.96 0.192 0.192 2.88 30.66 0.965 0.192 0.192 2.877 99.8 100.5 100.0 99.9 99.9

Mean recovery 99.9 100.5 100.6 99.4 99.2

R.S.D. 0.99 0.65 0.71 0.81 0.54


Please cite this article in press as: R.M. Nejem et al., Double divisor mean centering of ratio spectra as a developed spectrophotometric method forthe analysis of five-component mixture in drug analysis, Journal of Saudi Chemical Society (2014), http://dx.doi.org/10.1016/j.jscs.2014.03.001


Table 6 Analytical characteristics for analysis of PA, MP, PP, CH and PS by CLS method.

Drug Calibration equations R2 Linear range (lg ml�1) LOD (lg ml�1)

PA 11.7936A1 – 11.9448A2 + 6.3504A3 + 11.34A4

+ 13.0032A5 – 5.8968A6 – 10.8864A7 – 13,002A8 + 6.6528A9

=CPA 0.9998 0–30 0.09

MP �107.0496A1 + 1284.9256A2 – 473.1328A3 – 913.556A4 – 749.8428A5

+ 926.9372A6 + 1036.2996A7 + 578.8608A8 – 1968.358A9

=CPS 0.9999 0–100 0.05

PP �40.4995A1 + 114.9876A2 + 16.4268A3 – 11.5596A4 – 62.9694A5

+ 3.6504A6 + 13.3848A7 + 44.7174A8 – 21.5982A9

=CMP 0.9992 0–20 0.07

CH 99.1100A1 – 152.0888A2v15.8576A3 + 24.327A4

+ 85.7752A5 – 8.109A6 – 22.1646A7 – 56.5828A8 + 44.32.92A9

=CPP 0.9996 0–20 0.06

PS 25.0176A1 + 11.727A2 – 8.2089A3-17.9814A4 – 19.9359A5 – 3.909A6

+ 10.5543A7 + 19.9359A8 + 13.6815A9

=CCH 0.9997 0–45 0.05

8 R.M. Nejem et al.

mixtures was obtained as 1.77%, 1.15%, 1.98%, 1.55% and1.78%, respectively. The mean recoveries for simultaneous

determination were obtained as 100.33%, 99.84%, 100.43%,101.64% and 99.59% for PA, MP, PP, CH and PS,respectively.

The reproducibility of the method was determined byanalyzing the serum at different time intervals on the sameday (intra-day assay precision) and on three different days

(inter-day assay precision). Results of precision studies wereshown in Table 3. Percent RSD for intra-day and inter-day pre-cision studies for all drugs were well within the acceptable range(<2%) indicating that the method has good reproducibility.

11:7936 �11:9448 6:3504 11:3400 13:0032 �5:8968 �10:8864 �13:0032 6:6528

�107:0496 1284:9256 �473:1328 �913:5596 �749:8428 926:9372 1036:2996 578:8608 �1968:3580�40:4995 114:9876 16:4268 �11:5596 �62:9694 3:6504 13:3848 44:7174 �21:598299:1100 �152:0888 �15:8576 24:3270 85:7752 �8:1090 �22:1646 �56:5828 44:3292

25:0176 11:7270 �8:2089 �17:9814 �19:9359 �3:9090 10:5543 19:9359 13:6815

26666664

37777775

A230

A235

A240

A245

A250

A255

A260

A265

A270

266666666666666664

377777777777777775

¼

CPA

CPS

CMP

CPP

CCH

26666664

37777775

In order to obtain the accuracy and precision of the meth-od, several synthetic mixtures with different concentration ra-

tios of PA, MP, PP, CH and PS were analyzed using theproposed method. The results are given in Table 4. The predic-tion error of single component in the mixtures was calculated

as the relative standard error (R.S.E) of the prediction concen-tration [32].

R:S:Eð%Þ ¼PN

j¼1ðbC j � CjÞ2

PNj¼1ðCjÞ2

0@

1A

12

x100

where N is the number of samples, Cj the concentration ofcomponent in the mixture and bCj the estimated concentration.The total prediction error of N samples is calculated as

follows:

R:S:Etð%Þ ¼PM

i¼1PN

j¼1ðbCi j � Ci jÞ2

PMi¼1PN

j¼1ðCi jÞ2

0@

1A

12

x100


where Ci,j is the concentration of the component in the jth sam-ples and bCi j its estimation. Table 4 also shows the single andtotal relative errors for the five-component mixture.

4.2. Classical least squares method (CLS)

As explained in the previous section, the a-1 was calculated:

A9X1 ¼ a9X5 C5X1

a�15X9 A9X1 ¼ C5X1

Here, PA, MP, PP, CH and PS are the concentration (lg ml�1)of PA, MP, PP, CH and PS, respectively. The absorbance val-ues at nine points (230–270 nm) as shown in Fig. 1 for sampleswere introduced into the above equations. The concentration

of the five component mixtures in Decamol Flu syrup wascalculated.

Beer’s law was obeyed in the concentration 0–30 lg ml�1

for PA, 0–20 lg ml�1 for MP, 0–20 lg ml�1 for PP, 0–45 lg ml�1 for CH and 0–100 lg ml�1 PS. Table 6 shows thelinear regression parameters for calculation data for simulta-

neous determination of PA, MP, PP, CH and PS in theirmixtures.

To check the reproducibility of the method, the R.S.D for

five replicate determinations of 10 lg ml�1 each of PA, MP,PP, CH and PS, in the mixtures was obtained as 2.21%,1.39%, 1.62%, 1.69%, and 2.07%, respectively. The meanrecoveries where obtained as 99.60%, 100.19%, 100.78%,

100.34% and 99.50% for PA, MP, PP, CH and PSrespectively.



Table 8 Determination of PA, MP, PP, CH and PS in commercial syrup using the proposed methods.

Sample no. Concentration

(lg ml�1)

DD-MCR (recovery %) CLS (recovery %)


1 16.0 0.50 0.10 0.10 1.5 97.6 101.1 100.7 98.9 99.9 101.7 99.7 98.7 100.9 97.9

2 19.2 0.60 0.12 0.12 1.8 100.1 100.4 98.9 101.3 98.8 101.1 99.3 98.9 101.3 97.8

3 22.4 0.70 0.14 0.14 2.1 99.2 101.2 97.6 100.1 98.9 98.1 97.8 100.6 100.1 99.2

4 24.0 0.75 0.15 0.15 2.25 99.9 100.3 101.7 100.6 97.6 99.5 102.2 100.1 98.9 102.1

5 25.6 0.8 0.16 0.16 2.4 101.7 97.5 100.0 99.8 101.6 102.0 99.5 100.5 98.6 102.3

Mean recovery 99.7 100.3 99.8 100.1 99.4 100.4 99.7 99.7 100 99.9

S.D.a 1.48 1.56 1.59 1.10 1.49 1.56 1.60 0.90 1.19 2.21

tb 0.73 0.60 0.12 0.13 0.42

Fb 0.90 0.95 3.12 0.85 0.45

a Standard deviation.b Theoretical values for t and F at P= 0.05 are 2.31 and 6.39, respectively.

Table 7 Results of several experiments for Analysis of PA, MP, PP, CH and PS by CLS method.

Taken

(lg ml�1)Found (lg ml�1) Recovery (%)


20 0.8 0.16 5.0 2.4 20.21 0.79 0.156 5.10 2.36 101.1 98.80 97.50 102.0 98.30

15 2.0 4.0 2.0 5.0 15.13 1.96 3.92 1.96 4.90 100.9 98.00 98.00 98.00 98.00

20 1.0 2.0 0.16 5.0 20.05 0.99 2.01 0.164 5.00 100.3 99.00 100.5 102.5 100.0

25.6 1.0 2.0 5.0 2.4 25.40 0.98 2.08 5.12 2.38 99.20 98.00 104.0 102.4 99.20

15 15 15 15 15 14.90 15.30 15.30 15.18 14.8 99.30 101.3 102.0 101.2 98.70

10 10 10 10 10 9.80 10.30 10.30 9.92 9.98 98.00 102.0 103.0 99.20 99.80

5.0 5.0 5.0 5.0 5.0 4.90 4.96 4.96 4.93 4.94 98.00 102.0 99.20 98.60 98.80

2.5 2.5 2.5 2.5 2.5 2.50 2.55 2.55 2.47 2.58 100.0 102.4 102.0 98.8 103.2

Mean recovery 99.6 100.2 100.8 100.3 99.5

S.E.P 0.19 0.11 0.16 0.09 0.09

S.E.C 0.38 0.22 0.32 0.19 0.18


In order to obtain the accuracy and precision of the CLSmethod, several synthetic mixtures with different concentra-

tion rations of PA, MP, PP, CH and PS were analyzed usingthe proposed method. The results are given in Table 7. Thestandard error of prediction (S.E.P.) was calculated as [17]:

S:E:P: ¼PN


N

0@

1A

12

where N is the number of samples, Cj the concentration ofcomponent in jth mixture and bCj the estimated concentration.

The standard error of calibration denoted by S.E.C. iscalculated as follows:

S:E:C: ¼PN


N� P� 1

0@

1A

12

where P is the number of analytes in the samples. Table 7 alsoshows the standard error of precision and the standard error of

calibration.

4.3. Analysis of pharmaceutical syrup

The proposed DD-MCR and ILS methods were applied to

the simultaneous determinations of PA, MP, PP, CH andPS in commercial syrup. Five replicate determinations were


made. Satisfactory results were obtained for each compoundin good agreement with label claims (Table 8). No

published method has been reported for simultaneous deter-mination of the five components of this mixture. So the re-sults of the developed DD-MCR method were compared

with those of the CLS method. Statistical comparison be-tween the results was preformed with regard to accuracyand precision using student’s t-test and F-ratio at 95%

confidence limit (Table 8). There is no significant differencebetween the results.

5. Conclusion

A comparative study of the use of DD-MCR and CLS meth-ods for the resolution of five-component mixture of PA, MP,PP, CH and PS has been accomplished showing that the two

multivariate calibration methods provide, with adequate soft-ware support, a clear example of the high resolving power ofthis technique. These methods have the advantages of high

sensitivity, extremely low detection limit, good selectivity, ra-pid analysis and inexpensive instruments. Furthermore, whileworking with these methods one does not need to use toxic or-

ganic solvents. In other words, they belong to green chemistry.The developed DD-MCR and CLS methods were found to besuitable for the routine simultaneous determination of PA,

MP, PP, CH and PS in pharmaceutical syrup.



10 R.M. Nejem et al.

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