a new derivatization procedure for the determination of cephalexin with 1,2-naphthoquinone...

A new derivatization procedure for the determination of cephalexinwith 1,2-naphthoquinone 4-sulphonate in pharmaceutical and

urine samples using solid-phase extraction cartridges andUV±visible detection

Luisa Gallo-Martinez, Adela Sevillano-Cabeza, Pilar CampõÂns-FalcoÂ*, Francisco Bosch-Reig

Departamento de QuõÂmica AnalõÂtica, Facultad de QuõÂmica, Universidad de Valencia, Doctor Moliner, 50, 46100-Burjassot, Valencia, Spain

Received 16 December 1997; received in revised form 16 April 1998; accepted 22 April 1998

Abstract

The present report shows how to derivatize cephalexin with 1,2-naphthoquinone-4-sulphonate (NQS) into solid-phase extraction

cartridges (C18) using UV±visible detection. Optimum conditions for this new procedure are: hydrogen carbonate/carbonate buffer

pH�10.5, 5 min reaction time at 258C and NQS concentration of 7.1�10ÿ3 mol lÿ1. The accuracy and the precision of the method

were tested. The procedure was used to measure cephalexin in pharmaceutical and urine samples. The results obtained were

contrasted with those reported by UV-spectrophotometric and HPLC methods for pharmaceutical samples and with HPLC method

for urine samples. The H-point standard additions method was used to measure cephalexin in pharmaceutical samples, and the

generalized H-point standard additions method was used to measure cephalexin in urine samples.# 1998 Elsevier Science B.V. All

rights reserved.

Keywords: Cephalexin; Derivatization; Solid-phase extraction; UV±visible detection; Pharmaceuticals; Urine; H-point standard additions

method; Generalized H-point standard additions method

1. Introduction

Semi-synthetic cephalosporin antibiotics have been

used since the mid 1960s. Cephalexin, 7-(D-a-amino-

a-phenylacetamido)-3-methyl-3-cephem-4-carboxylic

acid is a second-generation cephalosporin and

one of the most commonly used cephalosporin

antibiotics.

Several methods for cephalexin determination in

pharmaceutical preparations have been reported. The

1988 British Pharmacopoeia [1] recommends the iodo-

metric method, while the 1985 US Pharmacopeia [2]

selected the UV-spectrophotometric method and the

1990 US Pharmacopeia [3] the microbial assay and the

HPLCmethod.Mostof thespectrophotometricmethods

reviewed require long reaction times (25±55 min), and

for one of them high temperatures (60±98.518C) are

needed. Spectrophotometric methods for cephalexin

determination using nickel(II)-hydroxylamine [4],

methylene blue [5], mercury(II)-imidazole [6,7],

ammonium paramolybdate [8], molybdophosphoric

acid [9], copper(II) acetate [10], iron(III)-o-phenan-

throline [11], iron(III)-NN'-diethyl-p-phenylenedi-

Analytica Chimica Acta 370 (1998) 115±123

*Corresponding author. Tel.: 0034-9-6-3983002; fax: 34-9-6-

3864322; e-mail: [email protected]

0003-2670/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved.

P I I S 0 0 0 3 - 2 6 7 0 ( 9 8 ) 0 0 2 7 6 - 1

amine sulphate [12], formaldehyde [13] and cobalt

nitrate[14] have been proposed.

Folin [15] described ®rstly a method for determin-

ing amino acids that depends on the combination of

the amino groups with sodium 1,2-naphthoquinone 4-

sulphonate (NQS) in an alkaline solution to form

highly coloured compounds. Other authors have used

NQS to determine amines, and reddish dyes were

extracted into chloroform [16±18]. In previous reports

we described the extractive-spectrophotometric deter-

mination of ephedrine [19], amphetamine [20], metha-

mphetamine [21] and furosemide [22] with NQS.

We have demonstrated the possibility of performing

off-line and on-line derivatization with different

reagents (NQS, o-phthaldialdehyde, 9-¯uorenylmethyl

chloroformate) into C18 solid packings (cartridges or

primary columns, respectively) for determination of

amines like amphetamine in liquid chromatography

[23,24]. Also we have shown that this methodology

can be applied for determining amines spectrophoto-

metrically [25]. Commercial C18 packing materials

were used instead of polymeric reagents specially

prepared for solid-phase reactions.

In the present report we extend our methodology to

cephalexin. A very simple continuous liquid±solid

procedure for the derivatization of cephalexin on

solid-phase cartridges with NQS reagent is proposed.

It can simultaneously serve to carry out the sample

clean-up and derivatization steps. The method was

applied to the analysis of pharmaceutical and urine

samples by UV±visible detection using the H-point

standard additions method (HPSAM) and the general-

ized H-point standard additions method (GHPSAM),

respectively. The results obtained were contrasted

with those provided by UV-spectrophotometric

method [2,26] and HPLC method [3,27] for pharma-

ceutical samples and with HPLC method [3,27] for

urine sample.

2. Experimental

2.1. Apparatus

All spectrophotometric measurements were done

on a Hewlett-Packard (Avondale, PA, USA) HP 8452.

A diode-array spectrophotometer furnished with

quartz cuvettes with 1 cm pathlength.

A Hewlett-Packard 1014 A liquid chromatograph,

equipped with a diode array detector linked to a data

system (Hewlett-Packard HPLC Chem Station, Palo

Alto, CA, USA) was used for data acquisition and

storage. The system was coupled to a quaternary pump

(Hewlett-Packard, 1050 Series) and an automatic

sample injector (Hewlett-Packard, 1050 Series). The

column was a Hypersil ODS-C18, 5 mm (125�4 mm

ID) (Hewlett-Packard, Germany). The detector was set

to collect a spectrum every 640 ms (over the range

220±600 nm) and all the assays were carried out at

ambient temperature.

2.2. Reagents

Stock solutions of cephalexin hydrate (Sigma, St.

Louis, USA) were prepared by dissolving 0.2000 g of

the solid in 100 ml of water. Working solutions

between 19.8 and 86.85 mg lÿ1 of cephalexin were

prepared. The 1,2-naphthoquinone-4-sulphonate stock

solutions were prepared by dissolving the sodium salt

(Sigma, St. Louis, MO, USA) in water. This solution

was prepared fresh for each experiment and was stored

in the dark at room temperature. Acetonitrile was of

HPLC grade from Scharlau (Barcelona, Spain). C18

(200 mg mlÿ1) Bond Elut columns were obtained

from Varian (Harbor, USA).

The NaH2PO4 solution was prepared by dissolving

3.5 g of sodium dihydrogen phosphate (Probus) in

500 ml of distilled water. The pH was adjusted to 3

by adding a minimum amount of H3PO4 50%.

2.3. Columns and mobile-phases

A gradient of acetonitrile, NaH2PO4 5�10ÿ2 M

(pH�3), with an acetonitrile content that increased

from 10% at zero time to 20% at 2 min, 20% at 6 min

and 50% at 8 min was used. The solution was prepared

daily, ®ltered through a nylon membrane, 0.45 mm

(Teknokroma, Barcelona, Spain) and degassed with

helium before use. The ¯ow-rate was 0.75 ml minÿ1

and 10 ml of each sample was injected.

2.3.1. Dosage forms

The dosages were obtained from local sources and

several formulations were used.

Ke¯oridina forte, 500 mgofcephalexinmonohydrate

per capsule (Lilly SA, Alcobendas, Madrid, Spain).

116 L. Gallo-Martinez et al. / Analytica Chimica Acta 370 (1998) 115±123

Ke¯oridina suspension, 250 mg of cephalexin

monohydrate per packet (Lilly SA).

Ke¯oridina mucolitico, 500 mg of cephalexin

monohydrate and 8 mg of bromhexine clorhydrate

per capsule (Lilly SA).

Ke¯oridina mucolitico suspension, 250 mg of

cephalexin monohydrate and 4 mg of bromhexine

chlorhydrate per packet (Lilly SA).

All solutions were made in distilled water and all

reagents used were of analytical-grade chemicals.

2.4. Derivatization into the solid-phase extraction

columns

C18 extraction columns were previously condi-

tioned by drawing with 1 ml of methanol, followed

by 1 ml of buffer, pH 3 (NaH2PO4 5�10ÿ2 mol lÿ1).

Then 1 ml of H3PO4:H2O (1:8) (v/v) and 1 ml of

sample solution containing different cephalexin con-

centrations (19.8±86.85 mg lÿ1 or 5.7�10ÿ5±

2.5�10ÿ4 mol lÿ1) were transferred to the column.

When the cephalosporin was retained in the column,

0.25 ml of NQS reagent (1.5% (w/v)) and 1 ml of

hydrogen carbonate±carbonate solution 8% (w/v) at

pH 10.5, previously mixed, were added. After 5 min at

a temperature of 258C, the columns were washed with

5 ml of distilled water. The reaction products (cepha-

lexin-NQS) were eluted from the columns with 2 ml of

acetonitrile:water (1:1). The absorbance between 190

and 820 nm was registered. Absorbance was measured

against acetonitrile:water (1:1) at 258C. Three or more

replicates were processed in all cases. The analytical

signal was measured at 442 nm.

2.5. Determination in dosage forms

2.5.1. Capsules

The contents of ®ve capsules were thoroughly

mixed and weighed. An accurately weighed quantity

of powder equivalent to 183 mg of cephalexin was

transferred to a 100 ml volumetric ¯ask, and dissolved

in and diluted to volume with water. The mixture was

then shaken and ®ltered through Whatman no. 42

paper. The ®rst portion of ®ltrate was discarded.

The clear solution obtained was used as stock solution

(0.005 mol lÿ1). Different volumes of this sample

solution were taken following the procedure of the

standard samples.

2.5.2. Oral suspensions

A quantity of powder equivalent to 183 mg of

cephalexin was accurately weighed, and treated as

described in Section 2.5.1.

2.6. Standard additions methods (urine samples)

For the standard additions method (MOSA) [28],

aliquots of urine samples (25 ml) with 19.8 mg lÿ1 of

cephalexin were spiked at different cephalexin con-

centration levels (10±86.85 mg lÿ1). Then 1 ml of

these samples was processed according to the proce-

dure described for standard solutions.

3. Results and discussion

3.1. Optimization of the working conditions

We have observed that the amine-NQS derivatiza-

tion reaction takes place at lower temperatures and in a

shorter time when the pH is high [21,25]. We therefore

selected pH 10.5 in order to increase the reaction rate

and perform the derivatization procedure at room

temperature (258C). The signal corresponding to the

NQS-cephalexin was approximately constant up to

5 min decreasing slowly up to 15 min.

The effect of the NQS concentration was evaluated

in the 1.2�10ÿ3±1.2�10ÿ2 mol lÿ1 range, with the

cephalexin concentration of 14.15�10ÿ5 mol lÿ1. The

analytical signal increased linearly up to an NQS

concentration of 5.7�10ÿ3 mol lÿ1. The signal of

the blank reagent increased with the concentration.

In order to have low blank interference, the reagent

concentration chosen was 7.1�10ÿ3 mol lÿ1. Differ-

ent water volumes were passed through the column to

eliminate the excess reagent and a water volume of

5 ml was selected as optimum.

Acetonitrile was selected as the elution solvent

because it provides good sensitivity and a low analyti-

cal signal for the NQS reagent. Although 1 ml of

solvent was enough to elute all the reaction product

formed, we eluted with 2 ml acetonitrile: water (1:1) to

obtain enough volume to measure the analytical signal.

Using the optimum parameters described above, the

regression equation, calculated from the calibration

graph correlating the absorbance, at 442 nm, versus

the cephalexin concentration (mol lÿ1) was:

L. Gallo-Martinez et al. / Analytica Chimica Acta 370 (1998) 115±123 117

A�(a�sa)�(b�sb) C�(0.27�0.03)�(3100�200)

where sa and sb are the standard deviations of the

intercept and the slope, respectively. The dynamic

range of concentration was 5.7�10ÿ5±2.5�10ÿ4 mol lÿ1 of cephalexin. The quanti®cation limit

was 5.5�10ÿ5 mol lÿ1, calculated as (10 SB/b) [29],

where SB�0.017 is the standard deviation of the NQS

blank and b is the slope of the calibration graph. The

limit of detection was 1.6�10ÿ5 mol lÿ1 calculated as

(3 SB/b) [30].

3.2. Determination of cephalexin in pharmaceutical

samples

The cephalexin contents of capsules and oral sus-

pension (both singly and in combination with brom-

hexine) were determined.

The concentrations of cephalexin in the dosage

forms were determined using the calibration graphs

and the HPSAM [31±34] calibration method

(Table 1). The HPSAM is described in Appendix A.

The analytical signal processed was absorbance incre-

ment because only the cephalexin concentration is

needed. The pairs of wavelengths used were chosen to

give the same absorbance for NQS but a different

absorbance for cephalexin. There are different pairs of

wavelengths, as can be deduced from spectrum 1 or

spectrum 2 in Fig. 1. The pairs of wavelengths used

were: 435±510, 440±505, 440±500 and 436±519. As

can be seen in Table 1, the relative errors obtained

using both methods are acceptable in all instances.

The mean recovery (n�8) obtained for the four

pharmaceutical formulations assayed were: cepha-

lexin capsules 95�2, cephalexin�bromhexine cap-

sules 112�6, cephalexin oral suspension 100�2 and

cephalexin�bromhexine oral suspension 100�2 (see

Table 1). When UV-spectrophotometric methods

[2,26] were used the absorbance was measured at

262 nm. The mean recovery (n�3) obtained for the

four pharmaceutical formulations assayed were:

cephalexin capsules 99�8, cephalexin�bromhexine

capsules 107�2, cephalexin oral suspension 98�7 and

cephalexin�bromhexine oral suspension 106�4. The

mean recovery (n�3) obtained for the four pharma-

ceutical formulations assayed using the HPLC method

[3,27] were: cephalexin capsules 98�5, cephalex-

in�bromhexine capsules 100�3, cephalexin oral sus-

pension 100�2 and cephalexin�bromhexine oral

suspension 107�4. From this study, it can be con-

cluded that the results obtained using the proposed

method agree with those obtained using the reference

methods.

The impurity 7-aminocephalosporanic acid (7-

ACA), which can be present in the trade product

did not react with NQS. The 7-ACA is an interferent

species in the determination of cephalexin using UV-

method because it shows an absorption band at

262 nm due to the b-lactam ring. For the dosage forms

assayed, the HLPC method showed that 7-ACA was

absent.

3.3. Urine samples

When MOSA was applied to three forti®ed urine

samples corresponding to a healthy adult volunteer,

the slopes�sb obtained were: b1�sb�3900�200;

Table 1

Assay of cephalexin in commercial preparations (conditions: NQS 7.1�10ÿ3 mol lÿ1; pH 10.5; temperature 258C; and eluent, acetonitrile±

water (1:1))

Sample Drug Concentration

added

(mol�lÿ1)�105

Concentration found (M�105); (%) recovery

Calibration HPSAMa

Cephalexin Relative

error (%)

Cephalexin RSD

(%)

Relative

error (%)

Capsule Cephalexin 10.58 11.19; 106 5.8 10.1�0.2; 95�2 1.98 ÿ4.53

Cephalexin � Bromhexine 10.52 11.09; 105 5.4 11.8�0.6; 112�6 5.08 12.17

Oral suspension Cephalexin 10.46 10.07; 96 ÿ3.7 10.5�0.2; 100�2 1.90 0.38

Cephalexin � Bromhexine 10.38 9.23; 89 ÿ11.1 10.4�0.2; 100�2 1.92 0.19

aMean�s.d. (n�8).


b2�sb�3500�100; b3�sb�3300�100. These values

were similar to those obtained for standard samples

in the calibration graph with standards (b�3100�200), which indicates that matrix effects were not

present.

The blanks for three urine samples are given in

Fig. 2. As can be seen, the NQS-urine blanks are

different from the NQS blank. This situation was

similar to that reported for amphetamines-NQS pro-

cedure [20]. In order to correct this bias error, the

Fig. 1. Absorption spectra for NQS (1) and NQS-cephalexin (Kefloridina suspension) derivative (2). Conditions: NQS 7.1�10ÿ3 mol lÿ1;

cephalexin 10.5�10ÿ5 mol lÿ1; pH 10.5; temperature 258C; and eluent, acetonitrile±water (1:1).

Fig. 2. Graph of absorbance, recorded against an acetonitrile-water (1:1) blank at 442 nm, versus � for NQS reagent and for three different

urines samples. (1) NQS reagent; (2±4) urine samples. Conditions: NQS 7.1�10ÿ3 mol lÿ1; pH 10.5; temperature 258C; and eluent,

acetonitrile-water (1:1).


generalized H-point standard addition method

(GHPSAM) was proposed by CampõÂns et al. [35].

The GHPSAM can be used instead of the Youden

method [36]. Due to the fact that the matrix effect is

absent the GHPSAM can work with standard solutions

instead of standard addition solutions. This method is

described in Appendix A. Fig. 3 is an example of

A00s;l="00x;l versus �j plots, which were used to identify

the interval at which this quotient was constant and the

interferent, therefore, linear. This corresponds to a

constant value for C8. The selected intervals for the

28 spiked urine samples appear in Table 2. These

values are not de®nitive, but they enabled us to choose

the linear interval in which the spectral interference

(endogenous compounds of urine sample) behaviour

is almost linear (see Figs. 2 and 3).

When the linear limits for the interference were

evaluated, the GHPSAM calculated the analyte con-

centration free of bias error (Eq. (A.7)). In this equa-

tion the M value corresponds to standard solutions.

The results appear in Table 3. The relative error was

acceptable in all instances.

The mean recoveries found using HPLC method

[3,27] for the urine sample no. 2 was 101�6 (n�5).

From this study, it can be concluded that the results

obtained using both methods agree.

4. Conclusions

This study shows that cephalexin using NQS, as the

derivatization reagent, previously retained in C18

columns, can be determined spectrophotometrically.

The procedure used optimizes the reaction conditions

in the C18 cartridges and is applied in this study to

determine cephalexin in pharmaceuticals and urine

samples. The generalized H-point standard addition

method was used to measure cephalexin in urine

samples. This is a simple procedure, which allows

cephalosporins to be measured in a short analysis time.

The volume of solvent employed is smaller than that

required in HPLC method. It permits to carry out

sample clean up and derivatization in the same sup-

port.

Acknowledgements

The authors are grateful to the CICYT for ®nancial

support (Project no. SAF95-0586).

Fig. 3. A00s;l="00x;l versus �j plots for urine sample no. 4 according to

Table 2. Conditions: NQS 7.1�10ÿ3 mol lÿ1; cephalexin

1.7�10ÿ4 mol lÿ1; pH 10.5; temperature 258C; and eluent,

acetonitrile±water (1:1).

Table 2

C8 results obtained for the A00S;j versus �j plots for the nineteen

samples assayed (conditions: NQS 7.1�10ÿ3 mol lÿ1; pH 10.5;

temperature 258C; and eluent, acetonitrile±water (1:1))

Urine

samples

Cephalexin

(mol�lÿ1)

�105

Wavelength

selected

intervals

(C0 � S0C) found

mean value�105

(%) Recovery

Urine 1

1 8.49 430±470 8.9�0.3; 105�3

2 11.3 430±470 11.7�0.2; 103�2

3 17.0 430±470 15.0�0.2; 88�2

4 19.8 430±470 18.5�0.2; 93�2

5 22.6 430±470 21.8�0.3; 96�3

6 25.5 430±470 25.8�0.3; 101�3

Urine 2

7 5.66 425±470 5.1�0.2; 90�2

8 8.49 425±470 8.3�0.2; 98�2

9 11.3 425±470 11.2�0.2; 99�2

10 19.8 425±470 19.2�0.2; 97�2

11 22.6 425±470 21.9�0.2; 97�2

12 25.5 425±470 25.6�0.2; 100�2

Urine 3

13 5.66 425±475 5.6�0.2; 99�2

14 8.49 425±475 8.4�0.2; 99�2

15 11.3 425±475 11.0�0.2; 97�2

16 17.0 425±475 16.7�0.2; 98�2

17 19.8 425±475 19.9�0.2; 100�2

18 22.6 425±475 21.8�0.2; 96�2

19 25.5 425±475 25.7�0.3; 101�3


Appendix A

A.1 H-point standard additions method [31±34]

HPSAM develops a procedure for measuring binary

mixtures that can be employed to quantify an analyte

in the presence of known [31,32] or unknown [33,34]

interferences. Two standard additions plots, with

M(�1) and M(�2) slopes at two previously selected

wavelengths, �1 and �2, are constructed, which inter-

sect at the H-point, with (±CH, AH) coordinates. The

H-point is a function of the analyte concentration (CX)

expressed in the following equation:

CH � A��1� ÿ A��2�M��1� ÿM��2� �

�A0 ÿ b0� � �A0 ÿ b�M��1� ÿM��2� ;

(A.1)

where A(�1) and A(�2) are the sample absorbance

values at �1 and �2, respectively; b0 and A0 the

absorbance values for the analyte and b and A0 the

interferent values in the sample problem, at �1 and �2,

respectively.

If �1 and �2 are selected in such a way that

the interferent absorbances are equal to A0�b, the

abscise of the H-point will be the analyte concentra-

tion, ÿCH:

ÿCH � �A0 ÿ b0�M��1� ÿM��2� � ÿCX : (A.2)

The interferent concentration is calculated by inter-

polation of the AH value in a conventional calibration

graph.

When the matrix effect is absent, the resolution of

binary mixtures can be done using molar absorption

coef®cients of pure analyte as M values following

Eq. (A.2). In this case it is not necessary to use

standard additions.

The method can generally be performed with more

than one pair of wavelengths (�1, �2), in which case it

can be considered a multivariate method.

Table 3

Results obtained applying the generalized H-point standard additions method for the 19 samples assayed (the number of �m for the three

wavelength selected intervals was 18, 21 and 21, respectively)

Urine

samples

Concentration

added�105 (mol�lÿ1)

Concentration found�s�105

(mol�lÿ1) (%) Recovery

RSD

(%)

Relative

error (%)

Urine 1

1 8.49 8.9�0.3; 105�3 3.18 5.1

2 11.3 11.7�0.2; 103�2 2.02 4.0

3 17.0 15.0�0.2; 88�2 1.31 ÿ11.8

4 19.8 18.5�0.2; 93�2 0.97 ÿ6.4

5 22.6 21.8�0.3; 96�3 1.16 ÿ3.3

6 25.5 25.8�0.3; 101�3 1.26 1.5

Urine 2

7 5.66 5.1�0.2; 90�2 4.26 ÿ9.1

8 8.49 8.3�0.2; 98�2 2.45 ÿ1.6

9 11.3 11.2�0.2; 99�2 1.52 ÿ0.7

10 19.8 19.2�0.2; 97�2 0.99 ÿ2.8

11 22.6 21.9�0.2; 97�2 0.68 ÿ3.2

12 25.5 25.6�0.3; 100�2 1.09 0.4

Urine 3

13 5.66 5.6�0.2; 99�2 3.67 ÿ1.2

14 8.49 8.4�0.2; 99�2 2.51 ÿ1.1

15 11.3 11.0�0.2; 97�2 1.70 ÿ2.3

16 17.0 16.7�0.2; 98�2 0.93 ÿ1.8

17 19.8 19.9�0.2; 100�2 0.93 0.8

18 22.6 21.8�0.2; 96�2 0.72 ÿ3.5

19 25.5 25.7�0.3; 101�3 1.10 1.1


A.2 Generalized H-point standard additions

method [35]

We consider that the spectral behaviour for analyte

X in the sample, at concentration C0X , can be described

as

A0X;1 � C0

X � "X;1; 1 2 ��1; �k�: (A.3)

If the spectral behaviour of the unknown interferent

Y can be described as a straight line in the spectral

region selected, the resulting equation is:

AY ;1 � a� b� �1; 1 2 ��1; �k�: (A.4)

For sample S, addition of analyte X at concentration

C0X and interferent Y, the next expressions for absor-

bance is:

AS;1 � A0X;1 � AY ;1 � C0

X � "X;1 � a� b� �1:

(A.5)

From Eq. (A.5) we can deduce that:

A00S;1"00X;1� C0

X: (A.6)

Thus, the quotient of the second derivative spectrum

of sample A00S;l and "00X;l (calculated from the slopes of

the calibration lines obtained from the second deri-

vative spectra of the calibration or standard additions

solutions) is a constant if the spectral behaviour of the

unknown interferent Y is linear. The intervals at which

this value could be considered constant were selected

from plots of Eq. (A.6).

Let us suppose that using the procedure described

above we have selected the wavelength interval

[�1, �k] in which the spectral behaviour for the

interferent can be considered linear. First of all, we

must select a third wavelength, �m, belonging to the

previously selected wavelength interval. This will

allow us to correctly locate the H-point. The

GHPSAM works with trios of wavelengths. We de®ne

two parameters, p and q, as

p � �m ÿ �1

�k ÿ �1

; (A.7)

q � �k ÿ �m

�k ÿ �1

: (A.8)

The unbiased analyte concentration is calculated

from the GHPSAM expression:

where �AS,(1,m) and �AS,(m,k) are the absorbance

increments of the sample at �1, �m and �m, �k,

respectively. The other symbols have the meaning

de®ned in the text.

From these expressions we can optimize the values

for �1, �m and �k to make the denominator in Eq. (A.9)

larger, and obtain the most precise results. In addition,

Eq. (A.9) can be used with M-values obtained from

standard addition line at �1, �m and �k or calibration

graphs for pure analyte if matrix effects are known not

to be present.

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ÿCH �q��AS;�1;m�ÿp��AS;�m;k�

p��MkÿMm�ÿq��MmÿM1� �q��A0

X;mÿA0X;1�ÿp��A0

X;kÿA0X;m�

p��MkÿMm�ÿq��MmÿM1� �A0

X;mÿq�A0X;1ÿp�A0

X;k

q�M1�p�MkÿMm

; (A.9)


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