Criteria for Selecting Analytical Wavelengths for Multicomponent Mi

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Anal yt i ca Chimi ca Act a, 212

(1988)

145-153

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

145

CRITERIA FOR SELECTING ANALYTICAL WAVELENGTHS

FOR MULTICOMPONENT MIXTURES BY THE CPA MATRIX

METHOD AND SIMULTANEOUS SPECTROPHOTOMETRIC

DETERMINATION OF NIOBIUM AND TANTALUM

ZHENQING WANG, JIANJUN LI and HANXI SHEN*

Department of Chemi st ry, Nankai Uni versit y, Tianjcn China)

(Received 4th May 1987)

SUMMARY

The reversed matrix representation of the Lambert-Beer law (CPA matrix method) is applied

in simultaneous spectrophotometric determinations. Restrictions on the selection of analytical

wavelengths in applying the CPA matrix method are investigated experimentally and theoreti-

cally. Four criteria for selecting suitable wavelengths are described. A spectrophotometric proce-

dure for niobium and tantalum with salicylfluorone and cetyltrimethylammonium bromide in the

presence of tartaric acid was developed and used for the simultaneous determination of niobium

and tantalum by the CPA matrix method. The absorption maxima were at 520 and 513 nm, re-

spectively. Measurements at six wavelengths in the range 500-530 nm provided data from which

niobium (0.04-0.4 B ml-‘) and tantalum (0.08-0.8 pg ml-‘)

w ere

evaluated, with relative stan-

dard deviations of < 2%.

Spectrophotometric determinations of metal ions which have very similar

chemical properties always require preliminary separation procedures, which

are usually lengthy and inconvenient for routine analysis. In recent years, sev-

eral studies have been reported on rapid methods for the simultaneous analysis

of multicomponent mixtures [l-7]. Brown et al. [ 31 proposed the CPA matrix

method and applied it to the infrared spectrometric analysis of two-component

organic mixtures. Later, Wang and Yan [8] expanded part of the CPA matrix

method to give a procedure for the simultaneous determination of niobium and

tantalum but numerous experiments and calculations were needed to select

analytical wavelengths, and the relative errors were large (some > 10% ).

In order to broaden the range of applications of the CPA matrix method in

inorganic analysis, the key problem is the selection of suitable analytical wave-

lengths, which is discussed in some detail in this paper. Four criteria for se-

lecting the analytical w,avelengths are proposed and the concepts of “correlated

wavelengths” and “correlated components” are used. The analytical wave-

lengths could then be selected rapidly and precisely, and the error caused by

poor selection of analytical wavelengths could be minimized. The reaction be-

havior and spectrophotometric properties of niobium and tantalum with sali-

0003-2670/88/ 03.50

0 1988 Elsevier Science Publishers B.V.



46

cylfluorone in the presence of the cationic surfactant cetyltrimethylammonium

bromide, and the optimum reaction conditions for the simultaneous spectro-

photometric determination of niobium and tantalum are also described. After

the absorbances of the mixed ternary complex solutions of niobium and tan-

talum had been input to a computer, the amounts of niobium and tantalum

were obtained rapidly by calculations based on the CPA matrix method.

THEORY

Spectrophotometric determinations are based on the Lambert-Beer law

A

= abc where A is the absorbance, a the absorptivity, b the pathlength, and c

the concentration. For a multicomponent system, if the absorption spectra of

the components overlap and the absorbances of each of the components at each

of the analytical wavelengths are additive, the Lambert-Beer law can be ex-

pressed, assuming constant pathlength, as

A, = i K,C,

(i=1,2,. . . m)

1)

J=l

where A is the absorbance at the ith wavelength, K is the absorptivity of the

jth component at the ith wavelength, and C, is the concentration of the jth

component. This provides a matrix

A = KC [

31.

In spectrophotometry, the absorption spectra of a chromogenic reagent and

its metal complex usually overlap. Because the chromogenic reagent is usually

present in large excess, the absorbance provided by the reagent at the relevant

ith wavelength can usually be regarded as a constant.

Brown et al. [ 31 considered the absorbance as the independent variable and

reversed the usual Lambert-Beer equation to e = PA (in matrix notation);

here, C is the concentration of a component, P is the proportionality between

A and C and A is the absorbance, If there is a deviation from the Lambert-

Beer law, the curved relationship between absorbance and concentration can

be approximated to a straight line over a limited region of interest by adding a

non-zero intercept

[

31. The system c =

Pii

can be solved for

P

by the usual

least-squares procedure [31.

Criteria for selecting analytical wavelengths

The key problem in applying the CPA matrix method to the determination

of several components is the selection of a set of suitable analytical wave-

lengths. According to the theoretical analysis and experimental results, it was

concluded that four criteria can be used for this selection.

Criterion 1.

In a region in which the spectra of the components overlap, the

selected wavelengths should be distributed over the spectral range of larger

absorptivities for each of the components such that higher sensitivities are

obtained for each component at that wavelength. This will provide higher sen-

sitivities for each of the components.



47

Cri t eri on 2.

The absorptivities for each component at all the selected wave-

lengths should be neither equal nor proportional to one another; similarly, the

total absorptivities of the components at each selected wavelength should not

be the same. Obviously, the larger the better with regard to the difference be-

tween the ratios of the absorptivities of each of the components at each selected

wavelength.

The matrix representation of Eqn. 1 is as follows:

A,

AL?

.

.

.

A,

. I

i

Cl’

G?

.

.

.

G

. .

2)

To determine the concentrations of each of the components in a multicompo-

nent system, it is necessary to solve for column C when column A and the

proportionality

K

matrix are known. If

m = n,

then C =

K-‘A.

If

m > n, K

is

not square, hence c = PA, where P =

RET) -lRT.

Obviously, only if Rank

K ) = n

and the

K

matrix and RTii are non-sin-

gular, can their inverse be obtained. If Rank(K) <n, Eqn. 2 becomes indeter-

minant and column C cannot be solved. If some of the analytical wavelengths

selected are inappropriate, the rank of the

K

matrix may be decreased. This

decrease will happen in two cases. If the absorptivities of any two components

of the system at all the selected wavelengths are equal, or proportional, to each

other, two columns of the K matrix will be linearly correlated, so that Rank(K)

will decrease by one. Conversely, if the absorptivities of all the components at

any two selected wavelengths are equal, or proportional, to each other, two

rows of the K matrix will be linearly correlated, and if m= n, Rank(K) will

again decrease by one. In the first case, the two components are defined as

correlated components, in the second case, the two wavelengths are called cor-

related wavelengths.

Not all the correlated wavelengths will cause failure of the determination,

but if there are two correlated wavelengths, one of these wavelengths is actually

useless, which will introduce an error in the absorbance, and this error will be

transferred to the final results by the matrix calculations. If more correlated

wavelengths are used for the determination, Rank(K) may be decreased so

much as to cause failure of the determination. Therefore, the absorbances

should not be measured at correlated wavelengths.

Criterion 3. At the selected wavelengths, the relationship between the ab-

sorbances

A

and the concentration of each of the components must be linear

and the absorbances for each of the components must be additive, if the ab-

sorbance data are to be processed accurately with the present method.



48

Criterion 4. The number of the selected wavelengths must be larger than the

number of components. This is necessary because selecting more analytical

wavelengths can decrease the errors resulting from any careless selection of

correlated wavelengths. Experiments have shown that more than five analyt-

ical wavelengths should be selected for the determination of a two- or three-

component system.

For the simultaneous determination of niobium and tantalum by means of

the colored Nb (Ta) /salicylfluorone/cetyltrimethylammonium bromide com-

plex system and the CPA matrix method, six analytical wavelengths (505,510,

513,516,520,525 nm) were selected in the range 500-530 nm. Fifteen standard

mixtures of niobium and tantalum were used to solve for the P matrix, and

satisfactory results were obtained for synthetic solutions of niobium and

tantalum.

EXPERIMENTAL

Apparat us and reagent s

A Model UV-240 recording spectrophotometer (Shimadzu, Japan) and a

Model PC-1500 pocket computer (accessory CE-161, 16K RAM; Sharp, Ja-

pan) were used.

Standard solut i ons of niobium and t antal um A).

Transfer an accurately

weighed portion of Specpure Nb,O, (0.1430 g) or TazO, (0.1221 g) to a por-

celain crucible. Add 5 g of potassium pyrosulfate, heat gently to evaporate any

water and then heat more strongly for about 30 min, until the melt is clear.

After cooling, leach the solid cake with 1 M tartaric acid. Transfer the solution

to a l-l volumetric flask and dilute to the mark with 1 M tartaric acid. A stan-

dard solution with 0.100 mg ml-’ Nb (Ta) is obtained. Dilute suitable aliquots

of the Nb (Ta) solution with 0.5 M tartaric acid to give working solutions (2.0

pg ml-’ Nb or 4.0 pg ml-’ Ta).

St andard solut i ons of niobium and tant alum B).

Transfer accurately weighed

Specpure Nbz05 (0.1430 g) or Ta205 (0.1221 g) to a porcelain crucible con-

taining sodium carbonate (4.0 g) and heat at 950” C for 30 min. After cooling,

leach the solid cake with 0.5 M potassium hydroxide. Transfer to a l-l volu-

metric flask and dilute to 1 1 with the same solution. The solution contains

0.100 mg ml-l Nb (Ta). Dilute suitable aliquots with 0.5 M potassium hydrox-

ide to give working solutions (2.0 hg ml-l Nb or 4.0 ,ug ml-’ Ta).

Prepare an ethanolic 1

x

10B3 M salicylfluorone (SaF) solution [9,10] from

the pure reagent in ethanol containing 0.1 M hydrochloric acid. Cetyltrime-

thylammonium bromide (CTMAB) was dissolved in water. All other reagents

were prepared from analytical-grade reagents dissolved in distilled water.



149

Recommended procedure for the simultaneous determination of niobium and

tantalum

To a 25ml volumetric flask, transfer an aliquot of sample solution mixed by

standard solutions (A) containing niobium (O-10 pug) and tantalum (O-20

pg). Add 2 ml of 2 M hydrochloric acid, 2.5 ml of 1.0~ 10m3 M salicylfluorone

and 3.0 ml of 1.0 x lo-’ M CTMAB. Dilute to the mark with distilled water

and mix well. After about 30 min, measure the absorbances in a l-cm glass cell

against the reagent blank at the selected wavelengths of 505,510,513,516,520

and 525 nm. Input the absorbance data to the PC-1500; then the concentra-

tions of niobium and tantalum are calculated.

RESULTS AND DISCUSSION

Effects of auxiliary complexing agents and of mineral acid

In order to investigate the effect of auxiliary complexing agents on the

Nb (Ta) /SaF/CTMAB system, tartaric acid, citric acid, oxalic acid or sodium

fluoride was added to the standard KNb03 (KTa03) solution, and then the

recommended procedure was applied. The absorbance of the complex was mea-

sured at its absorption maximum (520 nm for Nb and 513 nm for Ta). The

results are shown in Fig. 1. As can be seen, in the absence of the auxiliary

complexing agent, the sensitivity for niobium or tantalum complex was low,

but changed significantly when the auxiliary complexing agent was added. Of

the four ligands tested, citric acid, oxalic acid and sodium fluoride had different

effects on the absorbances of the niobium and tantalum complexes, and so

could not be used as the auxiliary complexing agent for the simultaneous de-

termination. In contrast, tartaric acid provided similar moderate increases in

sensitivity for both the niobium and tantalum complexes, and could be used

over a wide range of concentration in which the absorbances remained con-

stant. Therefore, 0.08 M tartaric acid was chosen as the reaction medium for

further studies.

06

bl

” c 4 1” 12 14 0 2 4 6 8 10 12 14

Volume added ml 1

Volume added ml)

Fig. 1. Effect of auxiliary complexing agents on the absorbances of the niobium and tantalum

complexes: (a) niobium complex; (b

)

tantalum complex. Auxiliary complexing agent: ( 1) 0.1 M

oxalic acid, (2) 0.1 M sodium fluoride; (3) 0.1 M citric acid, (4) 0.1 M tartaric acid.



150

In the tartaric acid medium, Nb (Ta) /SaF/CTMAB systems provided higher

sensitivity in hydrochloric acid solution than in other acid solutions. The op-

timum acidities for the niobium and tantalum complexes were found to be

0.08-0.2 M and 0.08-0.5 M hydrochloric acid, respectively. For the simulta-

neous determivrition of niobium and tantalum, the acidity chosen was 0.16 M

hydrochloric acid.

Absorpt i on spect ra of he reagent and compl exes

The absorption spectra of the reagents and complexes of niobium and tan-

talum in the absence and in the presence of CTMAB are shown in Fig. 2. Niob-

ium and tantalum did not react with SaF in the absence of CTMAB (curves 1

and 2 coincided), but when CTMAB was added to the systems, niobium and

420 460 500

540 580 a

A rim)

08-

0.6 -

I-”

a

04

0.2

Fig 2. Absorption spectra: (1) 2.0 x 10e5 M SaF, (2) 2.0~ 10m5 M SaF with 4.0x 10e5 M Nb or

Ta; (3) 2.0x lOA M F/1.2x low3 M CTMAB; (4) 1.0x 10m4 M F/1.2x lop3 M CTMAB

with5.0x10-6MNb; (5) 1.Ox10-4MSaF/1.2x10-3MCTMABwith5.Ox10~sMTa.Spectra

l-3 measured vs. water blank; spectra 4 and 5 measured vs. reagent blank.

Fig. 3. Absorption spectra of different concentrations of the niobium and tantalum complexes:

(l-10) 1,2 ,... 9,lO pgNb/25 ml); l’-10’) 2,4 ,... l 20 ,ugTa/25ml.



5

tantalum reacted to form orange complexes. The maximum absorption wave-

lengths for Nb/SaF/CTMAB and Ta/SaF/CTMAB are at 520 and 513 nm,

respectively (curves 4 and 5). In the presence of CTMAB, the maximum ab-

sorption wavelengths of the reagent lies at 465 nm, so that ;1max or the niobium

and tantalum complexes are separated by 55 and 48 nm, respectively.

As calculated from the absorption spectra, the molar absorptivities for the

niobium and tantalum complexes were 2.0 x lo5 (513 nm) and 2.1 x lo5 1 mol-’

cm-’ (520 nm) respectively, and therefore provide very sensitive methods for

determining niobium and tantalum. From curves 4 and 5 (Fig. 2), it is evident

that the absorption spectra of the two complexes overlap, so that the mutual

interference will be severe. In order to determine the concentrations of niob-

ium and tantalum simultaneously in a solution by the CPA matrix method, it

is necessary to prove the linearity between the concentrations and the absor-

bances of the components and to select the proper analytical wavelengths. The

absorption spectra of different concentrations of Nb (Ta) complex are shown

in Fig. 3. From these spectra, it is clear that good sensitivity was provided over

the wavelength range 500-530 nm. Moreover, the relations between the absor-

bances and concentrations showed good linearity for the ranges 0.04-0.4 ,ug

ml-’ niobium and 0.08-0.8 lug ml-’ tantalum and the absorbance were strictly

additive. Therefore, the analytical wavelengths were selected over the range

500-530 nm.

Effects of reagent concentrations temperature and time

The absorbances of the niobium and tantalum complexes were found to reach

constant values when 1.5-3.0 ml of 1.0~ 10m3 M SaF was used, 2.5 ml was

chosen for the determination. With more than 1.0 and 2.0 ml of 1.0 x 10e2 M

CTMAB, respectively, the niobium and tantalum complexes reached constant

absorbance values, therefore, 3.0 ml of 1.0 x 10V2 M CTMAB was chosen for

the simultaneous determination of the two elements.

At room temperature, the Nb/SaF/CTMAB ternary complex formed slowly;

about 2 h was required to give a stable absorbance. In contrast, the Ta/SaF/

CTMAB complex developed very quickly, requiring only a few minutes. It was

found that when niobium and tantalum were present together, the color de-

velopment was fast; only 30 min was needed for the niobium and tantalum

complexes to exhibit their highest absorbances, i.e., the tantalum system

speeded up the formation of the niobium complex. The absorbances of both

complexes were stable for at least 4 h.

Calibration of the P matrix

Fifteen standard mixtures containing various proportions of niobium and

tantalum were used to calibrate the

P

matrix. The absorbances of the com-

plexes were measured by the recommended procedure and these data were used



52

TABLE 1

The P matrix

-0.101 41.712 - 19.030 61.263 - 158.988 55.514 44.737

4.099 - 103.509 93.405 - 135.336 303.684 - 106.035 - 80.177

TABLE 2

Amounts of niobium and tantalum added in the synthetic sample mixtures ( 25 ml)

Sample 1 2

3 4 5 6

7

8 9 10

Nb

9.0 8.5 7.0

6.0 5.5 4.5 3.0 2.0 2.5 0.5

Ta 1.0 2.0 6.0 8.0 9.0 11.0 14.0 16.0 18.0 19.0

TABLE 3

Amounts of niobium and tantalum found in the synthetic sample mixtures’

Sample 1

Sample 3

Absorb. data

Absorb. data

Sample 5

Absorb. data

Sample 7

Absorb. data

Sample 9

Absorb. data

Al 0.511

A2 0.618

A3 0.684

A4 0.738

A5 0.769

A6 0.723

Calc. cont.

Cl 9.058

c2 0.970

Al 0.575

A2 0.683

A3 0.735

A4 0.764

A5 0.759

A6 0.679

Calc. cont.

Cl 6.958

c2 5.999

Al 0.609

A2 0.712

A3 0.752

A4 0.766

A5 0.738

A6 0.636

Calc. cont.

Cl 5.458

c2 9.169

Al 0.638 Al 0.678

A2 0.738 A2 0.782

A3 0.762 A3 0.798

A4 0.754 A4 0.777

A5 0.693

A5 0.694

A6 0.564 A6 0.543

Calc. cont. Calc. cont.

Cl 2.974 Cl 1.470

c2 14.142 c2 17.802

Sample 2

Absorb. data

Sample 4

Absorb. data

Sample 6

Absorb. data

Sample 8

Absorb. data

Sample 10

Absorb. data

Al 0.525 A 1 0.587 A 1 0.610 A 1 0.636 A 1 0.675

A2 0.631 A 2 0.691

A

2 0.712

A

2 0.735

A

2 0.781

A3 0.695 A 3 0.736 A 3 0.745 A 3 0.754 A 3 0.796

A4 0.745

A

4 0.756

A

4 0.751 A4 0.739

A

4 0.770

A5 0.768 A 5 0.737 A 5 0.711 A5 0.668 A 5 0.679

A6 0.716 A6 0.645

A

6 0.601

A

6 0.530

A

6 0.520

Calc. cont. Calc. cont. Calc. cont. Calc. cont.

Calc. cont.

Cl 8.587 C 1 5.897 Cl 4.391 c 1 1.934 Cl 0.493

c2 2.040 C2 7.998 C2 11.127 C2 15.974 c 2 19.599

*AI- are the absorbances of the mixture solution measured at six analytical wavelengths; C, and

C, are the amounts of niobium and tantalum found in the synthetic sample mixture (pg/25 ml),

respectively.



153

for the calibration. Table 1 gives the solved

P

matrix as printed by the PC-

1500 computer.

Determination of niobium and tantalum in synthetic sample mixtures

Ten sample mixtures containing arbitrary proportions of niobium and tan-

talum (see Table 2 ) were used to examine the proposed method. The amounts

of niobium and tantalum found are presented in Table 3 (as printed out). The

results are in good agreement with the added amounts. Statistical analysis

showed that the mean relative standard deviations were 1.78% for niobium

and 1.66% for tantalum.

The standard deviations show clearly that the CPA matrix method with the

Nb(Ta)/SaF/CTMAB systems provides an effective method for the simul-

taneous determination of niobium and tantalum which should find many ap-

plications. Moreover, the CPA matrix method should be applicable to the

simultaneous determination of a larger number of components with very close

absorption maxima.

REFERENCES

1 B.E.H. Saxberg and B.R. Kowalski, Anal. Chem., 51 (1979) 1031.

2 C. Jochum, P. Jochum and B.R. Kowalski, Anal. Chem., 53 (1981)

85.

3 C.W. Brown, P.F. Lynch, R.J. Obremski andD.S. Lavery, Anal. Chem., 54 (1982) 1472.

4 M.A. Maris, C.W. Brown and D.S. Lavery, Anal. Chem., 55 (1983) 1694.

5 I.E. Frank, J.H. Kalivas and B.R. Kowalski, Anal. Chem., 55 (1983) 1800.

6 M.A. Korany, A.M. Wahbi, 5. Mandour and M.A. Elsayed, Anal. Lett., 18(Bl) (1985) 21.

7 G.R. Ramos, M.C.G. Alvarez-Coque, R.M.V. Camanas and C.M. Fernandez, Spectrochim.

Acta, Part A, 42 (1986) 771.

8 B. Wang and T. Yan, Fenxi Huaxue, 14 (1986) 182.

9 G.S. Petrova, D.M. Lukin andE.E. Balkevich, Zh. Prikl. Khim. (Leningrad), 43 (1970) 1644.

10 H. Sano, Bull. Chem. Sot. Jpn., 31 (1958) 974.

Documents

Criteria for Selecting Analytical Wavelengths for Multicomponent Mi