Non-linearity with metal-metal indicator complex reactions in flow-injection analysis

Talanta ELSEVIER

Talanta

43 (1996)

881-888

Non-linearity with metal-metal indicator complex reactions in flow-injection analysis ’ J.F. van Staden *, D. Malan Received

I? August

1995:

revised

71 November

1095: accepted

21 November

1995

Abstract The linearity of the standard calibration curve in a flow-injection system involving a calcium~cresolphthalein complexone reaction was improved by replacing the organic base, 2-amino-2-methylpropanI-01, with the weak inorganic acid-conjugate base, boric acid&borate system as buffer. This was done after a theoretical study done on the relationship between the amount of coloured complex, Ca,(CPC)‘~ . as major chromophore formed and the total amount of calcium added at different pH values. and employing the knowledge obtained via proton side-reactions. It was shown that a linear calibration curve between I50 and 1000 mg I ’ of standard Ca”+ solutions was obtained with a buffer solution containing 0.05 mol I ’ boric acid. 0.05 mol I ’ KC1 and 35 g 1 ’ sodium acetate at a pH of 8.5. Kq~~dr:

Calcium-

cresolphthalein

complexone

reaction:

Flow-injection:

1. Introduction Non-linear calibration curves are sometimes obtained in flow-injection systems. These curves are either non-linear over the whole concentration range or only linear over a limited concentration range and furthermore tend to flatten when an element is determined over a wide concentration range. This has an influence on the accuracy and * Corresponding ’ Presented at Flow USA.

InjectIon August

OO3Y-9140

SSDl

author. Fax: ( + 27) 12432863. the Seventh International Conference

Analysis (ICFIA l3- 17. 1995.

96 Sli.00

r

0039.9130(95)01827-I

lYY6

Elsevier

‘95).

held

Science

in Seattle,

B.V.

All

on WA.

rights

reserved

Non-linearity:

Standard

calibration

curve

precision of results obtained. Although this is not such a big problem with modern technology involving computers and chemometrics, many routine laboratories do not have these facilities or access to these facilities and therefore have problems in reporting the correct results. There are two main

factors

that

may

contribute

to

this

phe-

nomenon. i.e. the physical and chemical parameters involved in the optimisation of a flowinjection system. Physical parameters such as sample volume. line length, tube diameter, etc. are usually easily optimised in order to obtain linear calibration curves in the working concentration range of a specific element. With chemical parame-

ters. the reaction involved governs the optimisation process and therefore optimisation in this regard is not always such an easy process. In flow-injection systems where spectrophotometry is used as the detection method, the intensity measured at a certain wavelength of the coloured complex formed is directly proportional to the amount of the metal ion present in a sample if only one complex is formed [l]. The reaction must however fulfill all the requirements needed for flow-injection spectrophotometry. Although the reaction may not reach completion in the flow-injection system, each standard and sample is treated in exactly the same way due to the hydrodynamic nature of the system. This normally results in a linear calibration curve. Complexation reactions between metals and ligands often result in the formation of more than one product [2-81. An in-depth discussion on this phenomenon formed the subject of many papers from a number of authors including a recent valuable detailed publication by Budesinsky [8] on the optimal acidity of complexes by solution of polynomials and by iteration. If a metal ion M with analytical concentration (total metal ion concentration) C, reacts with a ligand L to form a number of complexes as illustrated above, the mass balance (material balance) [3,6,7] on the metal ion is given by C, = [M] + [ML] + [MLJ + [ML,] +. . + [ML,,]

= WI + BOWI + PdW[Ll*+ B,ML13 + + PnPWl” where n is the maximum coordination number of the complexes, [ ] are the concentrations of the different substances, K,, K2, K,...K,, are the formation constants for each step in the overall reaction process, and /?n is the overall formation constant with P,=K,, P2=K,K2, /I3 =K,K,K,, etc. The extent to which a complexation reaction proceeds to form any of these complexes is determined by the experimental conditions and the formation constants for each step in the overall reaction process. In order to quantify the concentration of each complex in solution, the degree of formation [6] (complex formation fractions), 2, is given by the general equation

;(,i =

zML,,

where

n=O, 1, 2. 3.

X()= XM --P=(l

. and

+~,[L]+~*[L]‘+~,[L]‘+~~~

M

+ P,z[W ~ ’ The r values represent the ratios of the concentrations of the individual metal-containing species to the analytical concentration of the metal C,. It can however be seen from the expressions that the x values are functions of the equilibrium constants and the free (i.e. not bound to M) ligand concentration. Hence it is possible to plot a series of component distribution curves [6] (n + 1 of them) of SL,,vs. [L]. The r,, function is used as an atlas of metal-ligand equilibria in aqueous solution to show at a glance the relative proportions of each of the species in solution [9]. In order to visualize how these quantities of different complexes vary with the addition of a ligand to a metal, it is useful to employ graphs, called logarithmic concentration diagrams, having log concentration along the vertical ~1axis vs. log [L] or pL along the horizontal x axis. It is further possible to construct a complexometric titration curve by transforming the results in a logarithmic concentration diagram into a titration curve, where a metal ion is titrated with a ligand. The pattern obtained with this titration curve resembles the calibration curve actually obtained when the intensity of a coloured complex product at a certain wavelength is measured in a flow-injection spectrophotometric system. It is clear from this information that due to the formation of a number of complexes the calibration curve is only linear over a limited concentration range and that a non-linear calibration curve is obtained when extended to a full concentration range. It is possible to extend the linearity of the calibration curve to the full concentration range by manipulation of the reaction conditions through side-reactions [2,4,5,7] of the ligands or metal ions in the complexes. When another metal ion. N, or proton, H+, is added to the complex, ML,,, there is a competition between the other metal, N, or proton H+, for the ligand, L, and the ligand. L, is ‘withdrawn’ from the complex,

ML,,. The dissociation of ML,, is enhanced and the concentrations of these complexes are decreased by the amount bound in the side-reaction complexes. To evaluate the extent of the side-reaction quantitatively in order to control the side-reaction, a side-reaction coefficient (2) is introduced which for the addition of a proton is given by

&‘I aL(H)= [Ll [L] + [HL] + [H&l

+ [H,L] + .‘. + [H,,,L]

Ll = 1 +~;‘+[H+]+p~+[H+]‘+~~+[H+]3 +.

.+/Y;-[H+]“’

where [L’] is the conditional free ligand concentration. This clearly shows that the side-reaction coefficient is only dependent on the concentration of the proton added and if this is carefully controlled then the dissociation of the original complex can be controlled. The complexometric reaction between calcium as metal ion and cresolphthalein complexone (CPC) as metallochromic indicator was chosen as a scale model to illustrate this concept. In flow-injection analysis the standard curve is non-linear when calcium is determined over a wide concentration range measuring the calcium-CPC complex. At high calcium concentrations the calibration curve tended to flatten. The reasons for the non-linearity of the standard curve have been investigated and this paper gives an account of the results obtained. This paper also describes conditions used with side-reactions to extend the linearity of the calibration curve and the results obtained in this regard.

measurements with a vacuum pump system. The main solutions were prepared as follows.

2.2. Standard calcium solution A calcium stock solution was prepared by dissolving 24.9800 g of analytical-reagent grade calcium carbonate carefully in approximately 0.5 mol 1 ’ hydrochloric acid which was added dropwise until all of the calcium had just dissolved. The solution was boiled for a few minutes in order to remove carbon dioxide. The calcium solution was then neutralised with approximately 0.1 mol 1 ’ sodium hydroxide solution, adjusting the pH to 3 9, whereafter it was diluted to 1 1 with distilled water in order to obtain a stock solution containing 10 g 1 ’ of calcium. Standard working solutions containing 1, 4, 8, 15, 40, 100, 150, 250, 500, 750 and 1000 mg 1~ ’ of calcium were prepared by suitable dilution of the stock solution.

2.i. CPC rragmt The solution was prepared by dissolving 50 mg of CPC, obtained from BDH, and 1.0 g of quinolin-8-01 in distilled water to which a few drops of concentrated hydrochloric acid were added. The pH of the solution was adjusted to z 4 with sodium hydroxide, whereafter it was quantitatively diluted to 2 1 with distilled water.

2.4. Base solution Four bufler solutions were prepared by taking 50 ml of stock solution containing 0.1 mol l- ’ boric acid and 0.1 mol 1 ’ KC1 for each buffer solution and adding amounts of sodium acetate to

2. Experimental

Table Buffer

2.1. Reagents and solutions

Butler

PH

[Sodium

All reagents were prepared from analyticalreagent grade chemicals unless specified otherwise. Doubly-distilled, deionised water was used throughout. All solutions were degassed before

t

8.5

35 10

c D

1 solutions:

experimental

design

8.5 9.5

35

9.5

IO

acetate]

(g IF’)

884

J. F. can SIU&I,

mUmin

D. Mulurr

S

Water

CPC

Buffer

Fig. I. A schematic diagram of the Row system sample: M. mixing coil; D. detector: W, waste: Ml M7 = 405 cm: tube i.d. = 0.76 mm.

used. S. = 30 cm;

each as indicated in Table 1. The pH of each buffer solution was adjusted with 0.1 mol 1 ’ NaOH to the pH values given in Table 1. The final buffer solutions were each quantitatively diluted to 100 ml with distilled water.

A schematic diagram of the flow system used is outlined in Fig. 1. The manifold consisted of Tygon tubing (0.76 mm i.d.) cut to the required lengths and wound around glass tubes with an o.d. of 10 mm. The following equipment also formed part of the flow-injection analysis (FIA) system: a Gilson minipuls peristaltic pump (operating at 10 rev min ‘) was used to supply the different streams and a VICI Valco IO-port multifunctional valve was used for injection of 25 ltl samples. A Unicam 8625 UV’Vis spectrophotometer equipped with a 10 mm Hellma-type flowthrough cell (volume: 80 ltl) was used as the detector. The whole FIA system was controlled from a computer with a FLOWTEK program [lo] and the signal output of the detector was fed to the same program for data processing.

3. Results and

discussion

CPC is a metallochromic indicator that has been used successfully for a long period for the

Tularlrcl

43 (I 996) 881

888

determination of metal ions such as calcium, strontium and barium. The indicator was originally introduced by Anderegg et al. [1 ,l I] as a complexometric reagent for the determination of calcium in complexometric titrations with EDTA. Under these circumstances there is a reasonably well-defined colour change with a small change in metal ion concentration at the endpoint of the titration. The value of CPC as an indicator for the direct spectrophotometric determination of the alkaline earth metals was soon realised [12] and it was adapted for the calorimetric estimation of calcium in serum [13]. Many variants of the method have been used. Most continuous-flow analytical procedures involve the use of a procedure similar to that used by Kessler and Wolfman [14] for the determination of calcium with CPC and diethylamine -sodium acetate as a base component. The absorbance of the calcium-CPC complex is measured at 580 nm and pH 12.0. Working at this pH and wavelength gave less interference from magnesium. Gitelman [15] improved this method by introducing quinolin-8-01 to eliminate interference from magnesium and by measuring the absorbance of the complex at 570 nm. Some methods also incorporated cyanide as stabiliser and to complex other potentially interfering metals. Moorehead and Biggs [16] modified this method by replacing the toxic and volatile diethylamine (pK, 11.0) with the more stable 2amino-2-methylpropan-l-01 (AMP) (pK, 9.6) as a base solution. The CPC reagent is almost colourless at pH 10, but highly coloured at pH 12; therefore, the blank was reduced and the sensitivity increased. Moorehead and Biggs reported that as the interference from magnesium was eliminated by using quinolin-S-01, it was not necessary to work at higher pH. Basson and van Staden [17] found that AMP as a base gave a sufficiently stable solution for the FI determination of calcium in animal feeds, which obviates the use of toxic potassium cyanide as stabiliser. An organic base is used to provide the necessary alkaline conditions, inorganic alkalis tending to cause high blanks [ 181. Although the sensitivity of the method was excellent, a major problem was the narrow linear range of the calibration curve. CPC does not only

J.F.

un

Studen.

D. Ma/m

function as a metallochromic indicator, but also at the same time acts as an acid-base indicator. A fully protonated CPC indicator in acidic conditions can be represented as HJCPC). H,(CPC) is deprotonated under alkaline conditions to various ionic forms of CPC. The actual amount and z values of each ionic form at different pH values can be calculated from the pK, values for the dissociation of CPC given by Anderegg et al. [2,1 l] and these are outlined in a r distribution diagram of a vs. pH in a simple graphical form in Fig. 2. The spectrophotometric method for the determination of free calcium is based on the reaction between the metallochromic CPC indicator and calcium using the correct pH conditions. However, with CPC indicator, the equilibrium situation is rather involved, and the choice of the best experimental conditions is not quite simple. CPC forms Ca(CPC)4p, CaH(CPC)’ - and Ca,(CPC)‘~ complexes with Ca’ + (or MgZ + ). A weak absorbing complex H,(CPC)“is also formed [l I]. The concentration of these species is a function of pH, metal ion concentration and ionic surroundings. The colour formation is enchanced by bivalent metals and an increase in pH. A graphical presentation [2] of the equilibrium. based on the values of the stability constants determined by Anderegg et al. [ 1I], offers a guide to choosing the most favourable conditions. Corns and Ludman [19] postulated the type of equilibrium involved as H&PC)

H,(CPC)’

H,(CPC)’

(CPC)”

100

80

60

00

40

x 8

20

0

H,(CPC)

H(CPC)’

H,(CPC)’

-20 0

4

6

8

IO

12

I“

PH

Fig. 2. An r distribution ionic forms of CPC.

diagram

of I vs. pH for the ditferent

16

Tulunra

41 (1996)

881

Ca’ + + H,(CPC)4 with the ionisation CaH,(CPC)’

885

888

z$ CaH,(CPC)’

-

of the complex so formed:

+ CaH(CPC)‘~

+ H+

According to these authors further reaction could then occur between this complex and a second calcium ion Ca’ + + CaH(CPC)’

~ z$ Ca,H(CPC) ~

with subsequent ionisation

to

Ca2H(CPC) - c$ Ca,(CPC)’ - + H + Anderegg et al. [l l] postulated that the formation of the coloured complex only occurred on binding of the second calcium ion, in the same way that full colour development of phenolphthalein only occurs on ionisation of the second phenolic hydrogen atom, and formation of a quinoid structure. However, the H(CPCY ion is pale pink in colour [ 1 I], which implies that the CaH(CPC)3 ion may also be coloured, although the Ca,(CPC): ion would be exected to be the major chromophore. Corns and Ludman [19] studied the reasons for the non-linearity of the standard curve for the CPC reaction. They found that calcium forms both 1:l and 2: 1 complexes with CPC; at low calcium concentrations the 1: 1 complex predominates and caused non-linearity. At high concentrations the CPC concentration becomes limiting, resulting in flattening of the calibration curve. Cowley et al. [20] improved the linearity of the calibration curve to a certain extent in the physiological range 20--200 mg 1. ’ with the addition of sodium acetate to the AMP buffer solution. The option was investigated for FIA with the addition of various amounts of sodium acetate (15-35 g 1 ‘) to various amounts of AMP (15535 g 1-l) in different combinations using the FI system in Fig. 1, but with the pH of the CPC indicator solution at 1.5 as previously described. Calibration curves in the range O-1000 mg 1~ ’ of standard free calcium solutions were recorded and the final pH measured. The following conclusions were drawn from the results obtained. Addition of various amounts of sodium acetate to the buffer stream had only a minor effect on the calibration curve if

886

J.F.

wn

St&w,

D. Malatr

the addition was done to a buffer with a high concentration of AMP. However, with smaller amounts of AMP in the buffer the amount of sodium acetate added had an influence on the calibration curve. The disappointment was that all efforts tried did not give a linear calibration curve. It seemed that the acetate anion as ligand was a minor role player in the reaction and that it was not possible to use manipulation of reaction conditions through the side-reaction of acetate as ligand in order to get a linear calibration curve. It was, however, observed that the final pH of the different experiments above varied considerably for the different solutions, depending on reaction conditions. It followed from the results that pH played a bigger role in the linearisation of the calibration curve than the acetate anion. A theoretical study was done on the relationship between the amount of coloured complex Ca,(CPC)’ -, as major chromophore formed and the total amount of calcium added at different pH values. Calculations were done using a Lotus-123 spreadsheet. The overall constants, log /I,, = 7.8, log pz, = 12.8, the conditional formation constants corresponding to the proton side-reaction, log K,, = 11.6, log KZH = 7.6, and the pK, values of the CPC indicator (pK,, = 2.2, pK,, = 2.9, pK,, = 7.0, PK.+ = 7.8, pK,, = 11.4 and PK.+ = 12.0) given by Bishop [4] were used. The results for number of pH values are outlined in Fig. 3. It is clear from the results that the best chance for linearity was at a pH of 8-9. Although a beautiful titration curve was obtained at a pH of 10, linearity over a wide range was not possible. The results also showed that the possibility of linearity decreased drastically with an increase in pH above 11 and that the flattening of the calibration curve as experienced by various authors came into operation. The method was then modified by replacing the organic base, AMP (pK, 9.6) with the weak inorganic acid-conjugated base, boric aciddborate system as buffer. Boric acid with the lower pK, value of 9.23 was chosen as it tended to keep the pH value of the buffer to 9 easier than AMP. This was nearer to the linear goal as illustrated in Fig. 3. Various concentrations and buffer systems of the boric acid-borate buffer without the addition

Tulmta

43 (1996)

M-888

of sodium acetate were studied. but without success. Results were not repeatable which showed that the formation of the major chromophore was not consistent. This was confirmed by the instability of the final pH measured in the Fl system. The preparation of the CPC reagent solution was changed to the preparation described in Section 2 where the pH of the final CPC reagent solution was changed from 1.5 to 4. This resulted in a more stable final pH measured in the Fl system. The calibration curve was, however, still not linear. A factorial experiment was used to investigate the influence of the amount of sodium acetate added and the pH of the buffer solutions at the same time. The following four buffer solutions were prepared by taking 50 ml of stock solution containing 0.1 mol 1- ’ boric acid and 0.1 mol 1~ ’ KC1 for each buffer solution and adding amounts of 0.1 mol 1-I NaOH and 250 g 1-I sodium acetate as indicated in Table 2. The final buffer solutions were each quantitatively diluted to 100 ml with distilled water. The calibration curves obtained using these buffer solutions in the Fl system are given in Fig. 4. It is clear from these results that both the proton and acetate ligand side-reations as well as interaction between the two had an influence on the linearity of the calibration curve. An amount of 35 g l- ’ (14 ml of 250 g l- ’ sodium acetate added) gave a sufficient side-reaction with the calcium to decompose the major chromophore to such an extent that the calibration curve A became linear. The proton side-reaction at pH 8.5 was sufficient to enhance this tendency. The final pH of the Fl system was measured as 8.1. It is, however, also clear from the response that the sensitivity of the method decreased due to the decomposition of the major chromophore under the influence of proton and ligand side-reactions. The reaction capability of the H,(CPC)4m species at pH 8.5 is also not fully utilised as seen from the x distribution diagram in Fig. 2. Enlargement of calibration curve A (in Fig. 4) showed that the calibration curve is actually linear between 150 mg 1~ ’ and 1000 mg 1~ ’ of standard Ca2 + solutions as illustrated in Fig. 5. It is possible to increase the sensitivity of the method by increas-

pH9

PHI

(4

[Cal as molh

(b) pH 10

pH 11

; iCa]

ai

moli

20 30 [Cal as mol/l

Cd)

4c

50

[Cal as mol/l

Fig. 3. Graphical presentations of a theoretical study on the relationship between the amount of coloured complex, Ca,(CPC)‘-, and the total amount of calcium added at diRerent pH values: (A) pH 8; (B) pH 9; (C) pH IO: (D) pH II: (E) pH I?.

Table 2 Preparation Butfer

15

of buffer pH

solutions

Volume

ing the concentration solution.

14

NaOH

(ml)

Volume acetate

r

13

sodium (ml)

12

of CPC in the CPC reagent

4. Conclusion The linearity of the standard calibration curve in a FI system involving a calcium-CPC reaction was improved by replacing the organic base AMP with the weak inorganic acid-conjugate base, boric acid-borate system as buffer. This was done after a theoretical study done on the relationship between the amount of coloured complex, Ca,(CPC)‘~ , as major chromophore formed and the total amount of calcium added at different pH values and employing the knowledge obtained via proton side-reactions. It was shown that a linear calibration curve between 150 and 1000 mg 1~ ’ of standard Ca2 + solutions was obtained with a buffer solution containing 0.05 mol 1 ’ boric acid, 0.05 mol 1~ ’ KC1 and 35 g 1 ’ sodium acetate at a pH of 8.5.

Fig.

[I] [2] [3] [4] [5] [6] [7]

[IO] [I I]

C

[I31 [I31 [I41 [I51 [16]

.’

B

[17] [I81 [I91 Fig. 4. Calibration curves of four evaluated in the FIA system.

different

buffer

solutions

of calibration

curve

A in Fig. 4.

References

[8] [9]

D

5. Enlargement

[20]

J. Ruzicka and E.H. Hansen, Flow Injection Analysis, 2nd edn., John Wiley, New York, 1988. A. Ringbom. Complexation in Analytical Chemistry. Interscience Publishers. New York, 1963. W.B. Gunther, Chemical Equilibrium. Plenum Press, New York. 1975. E. Bishop. Indicators. Pergamon Press. Oxford, 1972. 0. Budetsky. Foundations of Chemical Analysis. John Wiley, New York. 1979. F R. Hartleyt, C. Burgess and R.M. Alcock, Solution Equilibria, Ellis-HorwJood. Chichester. UK, 1980. H. Fretser. Concepts and Solutions in Analytical Chemistry. A Spreadsheet Approach, CRC Press, Boca Raton, FL, 1992. B.W. Budesinsky, Talanta, 42 (1995) 423. J. Kragten, Atlas of Metal-L&and Equilibria in Aqueous Solution. Ellis-Hotwood. Chichester. UK, 1978. G.D. Marshall and J.F. van Staden, Anal. Instrum., 20 (1992) 79. G. Anderegg, H. Flaschka. R. Sallman and G. Schwarzenback. Hely. Chim. Acta, 37 (1954) 113. F.H. Pollard and J.V. Martin. Analyst. 81 (1956) 348. J. Stern and W.H.P. Lewis. Chn. Chim. Acta, 2 (1957) 576. G. Kessler and M. Wolfman, Chn. Chem., IO (1964) 686. H.J. Gitelman, Anal. Biochem., I8 (1967) 521. W.R. Moorehead and H.G. Biggs, Clin. Chem.. 20 (1974) 1458. W.D. Basson and J.F. van Staden, Analyst., 103 (1978) 296. H. Dtehl, Anal. Chem.. 39 (1967) 30A. C.M. Corns and C.J. Ludman. Ann. Clin. Biochem.. 24 (1987) 345. D.M. Cowley, B.M. Mottram, N.B. Hahng and T.J. Sinton, Clin. Chem., 32 (1986) 894