Spectrophotometric determination of the stability constant of the Eu(III)—murexide complex

Talma, Vol. 39, No. 12, pp. 1647-1652, 1992 Printed in Great Britain. All rights rcscrvcd

0039-9140/92 s5.00 + 0.00 Copyright 0 1992 Pcrgamon Press pk

ANALYTICAL DATA

SPECTROPHOTOMETRIC DETERMINATION OF THE STABILITY CONSTANT OF THE Eu(III)--MUREXIDE

COMPLEX *

SHASHJ JAIN and PINAKI GUPTA-BHAYA*

Department of Chemistry, Indian Institute of Technology, Kanpur, Kanpur 208 016 (UP), India

(Received 24 September 1988. Revised 16 December 1991. Accepted 24 December 1991)

!&mmmry-The values of the stability constants of the Ca(I1) and lanthanide(II1) complexes of murexide reported in the literature were. determined without proper correction for binding of buffer ions to the metal ion. The constants are best determined without a buffer present. Accurate values of conditional stability constants for the Eu(III)-murexide complex (relative standard deviation better than 3%), of the differential molar absorptivity of the Eu(III)-murexide complex with respect to murexide at 480 nm (relative standard deviation better than 0.5%) and of the molar absorptivity of murexide at 520 and at 506 nm (precision better than 0.4%) at pH 5.0 and 6.5 at 15, 25 and 35” are reported. The accuracy and precision of the concentration of metal ion in solution determined by using these conditional stability constants are discussed.

The stability constants of metal-dyestufF complexes are important for the detection and determination of low concentrations of metal ions. Besides their analytical use, metallochromic indicators are used to determine concentrations of free metal ion in a mixture of metal ion and ligand for determination of stability constants and rate constants of metal-ligand systems. Murexide has been used in this way for various metal ions, in particular calcium(I1) and lanthanide(III), but accurate values of metal-murexide (MMu) stability constants are not always available.

In earlier determinations of metal-murexide stability constants,‘-3 buffers were used to keep the pH constant when the absorbances of mixtures of metal ions at different concentrations with murexide at fixed concentration were measured against murexide at the same total concentration, but side-reactions of the metal ion with the buffer or other background anions (from electrolytes added to keep the ionic strength constant) were ignored. The stability constants thus obtainedlm3 were therefore conditional constants. The free metal ion concentrations in solution calculated by using these conditional constants are incorrect. Balaji

*Author for correspondence.

et al.’ pointed out that the true stability constants (K) can be obtained from the conditional values K’ (calculated by ignoring metal-binding by the buffer) by means of the relation

K = iql + CK~~,[M][B]:) = KIa, I

where the &a, values are the metal-buffer stability constants and [B], is the total concentration of buffer. It is assumed that the free buffer concentration [B], is approximated by [B], since [B], >> [Ml,. If a is incorrectly determined, Kmay have high precision, but will have low accuracy. The authors used literature values (corrected for changes in experimental conditions) of & to calculate cc. These KMB values had been obtained from pH titrations, and had good precision, but also a large systematic error arising from lanthanide hydrolysis.4 Also, they were based on use of high concentrations of buffers (acetate and phosphate) that bind certain metal ions fairly strongly, making a B 1. Even a small error in the values of &,s, makes a inaccurate to a significant extent. This could be ignored for

[M]r is calculated from

[Mlf = Mt - [MMuI - CM&I* , 1647

1648 SHASHI JAIN and PINAKI GUPTA-BHAYA

In the experiments of Balaji et al.’ the minimum error in the values of KMB used is lo%.’ Since [B], is large, the error in

~[MBiI

is of the order of [MIF. This leads to a very large relative error in [Ml, and therefore in KMMU. The effect of metal ion-chloride association was not considered.

The ideal buffer would have a small but accurately and precisely known stability constant for its metal-complex, and a pK value close to the desired pH, so that its concentration can be kept low. The pH values used here were 5.0 and 6.5. Some good buifers for these values weakly bind metal ions.6 Many nitrogenous heterocycle buffers, e.g., Pipes [piperazine- di(ethanesulfonic acid)] react with murexide, and Tes [N-tris(hydroxymethyl)methyl-2- aminoethanesulfonic acid], pK 7.5, seems the only choice for use at pH 6.5, but is poor because a high Tes concentration is necessitated by its low buffer capacity at this pH. The binding constant of Tes and Eu(II1) is not known, but its effect cannot be ignored even if it is small, because of the high Tes concentration needed. If [Tes] is -1OOmM and KMB is -10, then if [B],= [B],, [MB] is -7% of [MMu] (assuming use of typical concentrations). At pH 5.0, Bistris [bis(2-hydroxyethyl)imino-tris(hydroxymethyl)methane] or acetate buffer can be used, but Bistris binds several metal ions strongly.’ A preliminary experiment (with murexide to indicate the free metal concentration) showed that the stability constant of the Eu(III)-Bistris complex is N 10’. The stability constant of the Eu(III)-acetate complex is large,5 with an error of 10% as estimated by the authors. The effect of lanthanide hydrolysis introduces an additional unestimated error.4 An accurate value of the Eu(III)-acetate equilibrium constant is thus not available.

In view of all this, the Eu(III)-murexide equilibrium is best examined in the absence of a buffer. The accuracy depends on having the same pH and total murexide concentration in both cuvettes, one containing Eu(II1) and the other not, since otherwise AA = AE[MMu] will not hold for the difference in absorbance (AA); AC is the difference between the molar absorptiv- ities of murexide and the complex. Addition of a metal solution to unbuffered murexide solution will change the pH, and restoration of this to the original value while keeping the total

murexide concentrations equal must be done directly in the cuvette. The error in so doing is insignificant and less than that due to the uncertainty in KMB. The values of KMMU however, should be determined at a definite ionic strength maintained by a sufficiently high inert electrolyte concentration (O.lOOM KC1 is recommended by IUPAC and IUPAB8). The values of KMMu reported in this paper can only be used in calculating the free metal ion concentration in metal-ligand titration experiments aimed at determination of metal-ligand stability constants if these are conducted at a sufficiently high ionic strength. This is because in such titrations the concentrations of metal and ligand are varied over as wide a range as possible, and in the absence of an ionic-strength adjuster the ionic strength of the metal-ligand mixture will change considerably, since the metal ion and quite often the ligand will be charged. Such an adjustment, however, introduces the risk of side-reactions of the cation and anion of the “inert” electrolyte with the ligand and the test metal ion, respectively.

EXPERIMENTAL

Reagents

Eu,03 (purity 99.9%, Sigma); murexide (analytical grade, Koch-Light) with purity checked by C,H,N analysis (Ca*+ was found to be absent). Other chemicals were analytical grade. All the reagent solutions were prepared in the appropriate buffer (acetate for pH 5, Tes for pH 6.5) and adjusted to ionic strength O.lOOM with potassium chloride.

Europium solution. EuZOs was dissolved in hydrochloric acid and the solution evaporated to dryness. This step was repeated 3 or 4 times and the EuCl, obtained was dissolved in the buffer. The solution was standardized by weight titration of 100 ~1 with EDTA at pH 5.0, with Xylenol Orange as indicator.g The [EDTA]/[Eu] ratio was about 0.25, and the standardization error was about 0.5%.

In this and all the other experimental work, high precision was achieved by weighing to find the volumes of reagents dispensed, with careful adjustment to the desired values by dispensing from pl-pipettes. The maximum error was -1 hl.

Murexide solution. A freshly prepared solution of murexide (in demineralized water) was filtered, then lyophilized. Thermogravimetry showed that the product contained no water of

Stability constant of the Eu(III)-murexide complex 1649

hydration. A buffered solution in O.lM potassium chloride at 25” deteriorated in N 1.5 hr at pH 5 and -3.5 hr at pH 6.5. Calculation of the concentration requires the molar absorptivity (c) to be known. Schwarzenbach and Gysling’ reported its value at 520 nm, pH 8.53 and an unspecified temperature. It is expected to be dependent on pH and may depend on temperature owing to a change in solvation. We have redetermined 6 under the experimental conditions of interest, by dissolving a weighed quantity of lyophilized murexide in 1000 ml of buffer solution (15mM acetate buffer at pH 5.0 and 1OOmM Tes buffer at pH 6.5) of ionic strength 0.100 (adjusted with potassium chloride) and measuring the absorbance at 520 and 506 nm against the corresponding buffer blank. The molecular weight of non-hydrated murexide was used to calculate the concentration. Two independent measurements agreed within -0.1%.

Determination of AC

Identical volumes of murexide solution in the acetate or Tes buffers just mentioned, of ionic strength adjusted to O.lOOM @Cl), were added to the reference and sample cuvettes. A preliminary experiment was used to find what concentration of europium chloride solution would be needed for 100 ,~l of it to convert all the murexide into its europium complex, and 100 ~1 of the appropriate solution (in the correct buffer) was added to the murexide solution in the sample cell. An identical volume of buffer/KC1 solution was added to the murexide solution in the reference cell. The absorbance of the sample solution was measured (AA) and divided by the total murexide concentration (which was equal to the concentration of the europium complex) to give AL The value was checked by making further lOO+l additions of europium solution to the sample cell and buffer/KC1 solution to the reference cell and redetermining AA.

The following considerations show that AC values reported here can be used at a given pH even when the bufIer and KC1 are absent. (a) We have found that the molar absorptivity of murexide at 480 nm is 2% higher in IOOmM potassium chloride than in Tes buffer alone. The same is true for the europium complex. Thus AC (EuMu - Mu) at 480 nm is not affected significantly by the presence of potassium chloride. (b) The Eu(III)-Tes complex, free Eu(II1) and Eu(III)-Cl- complex absorb negligibly at 480

nm. The buffer contributes very little sodium ion compared to the amount of potassium present. Thus the presence of buffer also does not affect AC at 480 nm. (c) [K+], nearly equals [K+], in both cuvettes. The value of [Mu],, however, is nearly zero in one cuvette and is non-zero in the other. Thus [KMu] is different in the two ceils, but this is of negligible consequence since 480 nm is at the tail end of the difference spectrum of murexide in the presence and absence of 1OOmM potassium chloride (the difference is only N 2%). The maximum of the difference spectrum is at 518 nm, where the difference is N 8%). Values of A6 determined in the absence of buffer agreed with those reported in Table 2, within experimental error.

Metal-murexide stability constant

Identical volumes of murexide solution were added to the two cuvettes, the concentration of murexide being such that the absorbance at 520 nm was between 0.65 and 1.05. Metal solution was then added to the sample cell and an identical volume of water to the reference cuvette, followed by enough potassium chloride solution to make the ionic strength O.lOOM in both cuvettes. The concentration of metal was chosen so that [MMu] and [Mu], were similar.

The pH of the test solution was adjusted by addition of dilute sodium hydroxide solution

(PH -8), the approximate volume of base needed having already been estimated in a separate experiment. The solution was mixed and the final pH checked with a microelectrode inserted into the cuvette. The pH was almost always within 0.05 of the pH of the murexide solution in the reference cuvette. If it was slightly outside this range, a measured small volume (l-2 ~1) of base or acid was added by pl-pipette to bring the pH closer to the desired value, and an identical volume of potassium chloride solution @ = 0. IOOM, pH equal to that of the solution in the reference cuvette) was added to the reference cuvette. The liquid lost when the microelectrode is removed after the pH measurement does not affect the accuracy, because it does not alter the concentration. In spite of a small difference in pH (~0.05) between the two cuvettes the reproducibility is l-3%. The analysis of errors given later shows that inaccurate adjustment of pH does not significantly contribute to the error.

The Hellma ceils have small openings and were kept tightly stoppered during spectral

1650 SIWW JAIN and FINAKI GUPTA-BHAYA

measurements and weighings. The loss by evaporation was negligible.

The absorbance of the test solution (AA ) was measured against the murexide reference solution at the desired temperature (thermostat- ically controlled cell compartment) at 480 run (the wavelength of the maximum in the difference spectrum) in a Cary 17D spectropho- tometer. The mean absorbance and its standard deviation were noted from the digital read-out. The reagent concentrations were chosen to make AA high (>OS) so that its standard deviation of 0.002 was insignificant.

RESULTS AND DISCUSSION

Trends and comparison with literature values

The values of L, AC and KlvIMu are given in Tables 1, 2 and 3 respectively. The values of c at pH 5.0 and 6.5 are equal within experimental error, as expected in view of the pK value of murexide. There is a small but significant decrease in 6 with increasing temperature at both 520 and 506 nm. The ratio of the two values of 6 can be used as an indicator of the quality of the murexide sample. Schwarzenbach and Gysling* reported a value of 1.35 x lo4 l.mole-‘.cm-’ for 6 at 520 nm in Verona1 buffer (pH 8.53) at an unspecified temperature. This value lies between the values determined by us at 15” and 25”. Schwarzenbachl” has published the spectra of murexide at pH 7 and 13, without giving numerical values of the absorbance. An approximate estimate made from the plot shows that the difference in L is N 5% at J_. At pH 13 two protons (p& = 9.2, pK, = 10.5) are completely dissociated; at pH 8.53 the first dissociation is only about 17% complete, so a difference of only N l% is expected between the spectrum at pH 8.53 and that at pH s 7.0. The difference between the 6 values determined by us and those reported by Schwarzenbach and Gysling* is of that order. The values of AC decrease with increase in temperature or pH,

Table 1. Molar absorptivity of mm&de

L+, IO’ Lmole-‘.cm-’ Temperature, “C At 506 mn At 520 mn

15 1.260 f 0.0005 1.365 f 0.002 25 1.247 f 0.001 1.341 f 0.002 35 1.233 f 0.001 1.323 f 0.002

*Range of two independent measurements, one for 7.672 x lo-‘M mumxide and the other for 7.995 x lo-SM.

Table 2. Differential molar absorptivity (&)

Temperature, AC f s,* PD “C lo’ Lmole - ‘.cm - ’

6.5 15 1.312 f 0.003 25 1.289 f 0.005 35 1.264 f 0.005

5.0 15 1.385 f 0.006 25 1.351 f 0.006 35 1.325 f 0.004

*Average of six independent measurements. Concentration of mm&de being saturated is in the range 3.39-6.7 x IO-‘M. The & values are independent of the absolute value of the concentration of murexide and the presence of KC1 and buffer salts.

whereas the values of KMMu decrease with decrease in pH or increase in temperature. The values differ significantly from those determined by Balaji et al.,’ who took into account the effect of metal-buffer interaction incorrectly. For 25”, pH 5.0 and p= O.lOOM, they reported lo@ = 5.42. The value reported here is lo@ = 4.20. The value reported by Geie? for 12”, pH 4.0, p = O.lOOM, without consideration of metal-buffer interaction (the chemical nature of the buffer was not specified) was 1ogK = 4.18. At 15”, pH 5.0, p = O.lOOA4, we found 1ogK = 4.28. As 1ogK decreases with decrease in pH our result seems in good accord with Geier’s.

Nature of the constants and their range of validity

In the calculation of K, we consider Mu and MMu as single species without regard to proto- nation. These constants are thus conditional constants dependent on pH. As is shown below, binding of K+ to Mu and metal ion to Cl- causes further complications. The values of K are calculated assuming that a 1: 1 complex is

Table 3. LogK of Eu(III)-murexide association eouilibria

PH 5.0

6.5

Temperature, “C 1ogK*s*

15 5.278, f 0.006, 25 5.205, f 0.007, 35 5.143, f 0.004, 15 5.525 f 0.013 25 5.435 f 0.011 35 5.365 -t 0.012

*Average of 6 or 7 measurements; titration points for EMU] = 60% of [Mu], or [Ml, are omit- ted. Inclusion of these points increases the value of s. These values do not include the effect of binding of K+ to murexide and that of Eu(II1) to Cl-, but these conditional stability constants yield correct values of free Eu(II1) in solution (see Results and Discussion).

Stability constant of the Eu(III)-murexide complex 1651

formed, which appears to be valid over the range of concentrations explored (3-4 x 10e5M [MMu], 2.5-5 x lo-‘M [Ml,, 3-5 x 10-5M wu],) because the KMMu values obtained are the same within l-3% at a given temperature and PH.

Estimate of precision

The maximum error of the volume measurements made by weighing was 5 x lo-’ ml (maximum weighing error 0.05 mg) and is negligible. The error in absorbance measurement was estimated from the fluctuation in the digital read-out, and an absorbance of 0.6 or above had a maximum error of m 0.3%, equivalent to a relative standard deviation (s) of -0.1% (99% confidence). The europium concentration has a relative standard deviation of -0.5%, which is wholly due to the end-point error and the burette reading error. The EDTA concentration has a maximum error of -0.5%, arising from the purity of the EDTA used, the weighing error and the error in making up the solution to standard volume. This error does not affect the precision but alters the accuracy since only one EDTA solution is made. The error in the volume of europium solution taken for titration is negligible because the volume is measured by weighing. The error in measuring the molar absorptivity depends on the absorbance (maximum error ~0.3%) and the murexide concentration error (weighing error -0.2%, volume error in dilution to 1000 ml ~0.04%), and thus is -0.3% maximum, equivalent to a relative standard deviation of w 0.1% (the value observed, Table 1).

From these values it can be calculated that the relative standard deviation of KMMU is about 1.2%, in agreement with the precision found experimentally. We conclude that adjustment of the pH directly in the cuvette does not lead to any additional error. The maximum error in the pH was f0.05, the reading error of the pH- meter.

The values of log&,, in Table 3 are quoted to four (pH 5.0) and three @H 6.5) decimal places even though the third (pH 5.0) and the second (pH 6.5) places respectively are in error. This is done to avoid truncation errors. The quantity of eventual interest to us is [Ml,, which is calculated from w], = Pf MWPWdGmu and has a calculated error of w 1.6%. Any truncation should be done at this stage.

E$ect of binding of potassium by murexide

Potassium chloride at O.lM concentration was used to maintain the ionic strength constant. Though the afSnity of murexide for potassium is less than that for Eu(III), it cannot be ignored. The difference [Mu], - EMU] gives only the apparent concentration of free murexide, [Mu];. The true value is MU]~= [Mu]; - [KMu]. [KMu] is given by KKMU[K+]r[Mu]r; since pC+] N lO’Q4u], [K+],- [K+], and [Muir= l?W;/(l + Kc~.[K+lt) = DW;hu(~+p As the value of KKMu in aqueous medium is not known, [Mu’k of necessity remains a conditional concentration. However, a crude value for the constant might be estimated from the reported values for non-aqueous media” and the difference in dielectric constant, and appears likely to be in the range l-25. If so, aMfl+) would be in the range 0.1-2.5 and would change [Mu], by a factor of between -0.3 and 0.9.

Inability to calculate a prevents us from calculating the true value of KEuMUS but does not affect the value of free Eu(II1) ion concentration determined in a solution by use of mu&de as indicator. It can be readily shown, using FluI; = &,,Nkt,[Mu] that the measured values of AE (Table 2) equal {+uMu - [Et&l/a) - 6,&l - I/a)]), where a =ayugc+), and that M = A@uMu] holds, even if cMu # cm”. At 480 nm, however, L,,,” differs negligibly from Lo”. Therefore [EuMu] calculated as (M/AC) is correct and is unalfected by aMa+). The conditional KEuMu reported in Table 3 uses Flu]; for calculation. If [Mu], were used instead, we would obtain &,&corrected) = akINk+ )KEUMu (conditional). Then [Mu];&UMU(conditional) = [Mu]&&corrected). We conclude that [Et& calculated as [EuMu]/([Mu]~&,,,(conditional)} is unaffected by the factor aMa+).

E$ct of side-reactions of Eu(III)

The value of the free europium concentration used in calculating KMMu obtained by subtract- ing [MMu] from lM], is not its true value, but is a conditional quantity m’]r, because of side- reactions with chloride. w’]r = a,(,,[Mlr where aM(ci) = (1 +81VWt+~2[Cl-13 (B, and I% a= the stability constants for EuCP+ and EuCI:+). The reported values i2-i8 of /3, and f12 were determined at high ionic strengths, and after being corrected to p = O.lM yield a temperature- independent mean value of a = 1.088 f 0.01 for p = O.lM (KC]).

1652 SHASHI JAIN and PINAKI GUPTA-BHAYA

In contrast t0 the effect Of aMu( that Of aMcc,) can be corrected for, but since inability to calculate aMW+) already prevents us from calculating the true KEuMu, we do not apply the correction due to aMCcr). It turns out once again, that the value of [Eu], in a solution, determined by use of murexide as indicator, is not seriously a&ted by aM(o). If we use the conditional &MU value reported in Table 3 in calculating the ratio [EuMu]/{[Mu];K,,~,} we obtain [Eu];. The desired quantity [Eu], can then be calculated from [Eu]; by using the value of ay(c]). The precision of [Eu]; is only slightly worse than that

Of &Mu (the worst is -3%, Table 3). The precision of aM{cr) as calculated from the mean values of fi,,r for the Eu(III)-Cl- association given in 16 reports is w 1%. Twelve of these values differ from the mean value by N 1 %, 3 by -3%, and only one ‘* differs from it significantly (N 7%), but that work perhaps detected only one of several Eu(III)-Cl- complexes. The precision of & in the individual reports varies, the best being +4%.14 The accuracy and precision of [Eu], is thus slightly inferior to that of

[EuX -

Potential use of KMMu

In metal-ligand mixtures of various concentrations of metal and ligand, values of [Ml; and [Ml, can be calculated from &Mu. The titration data can then be analysed by a computer program to obtain the best values of the stability constants of the metal-ligand complexes. In our laboratory, we have successfully used this technique to determine the /I -values for Eu(III)- amino-acid complexes. I9 Determination of [Ml, by use of murexide as a metallochromic indicator is also useful in stopped-flow or temperature-jump relaxation experiments aimed

at the determination of the rate constants of metal-ligand interaction.

Acknowledgemenr-The authors express their gratitude to the referees and Dr. R. A. Chalmers, whose criticism and suggestions have added to the value of the paper.

REFERENCES

1. K. S. Balaji, S. D. Kumar and P. Gupta-Bhaya, Anal. Chem., 1978, SO, 1972.

2. G. Schwarxenbach and H. Gysling, He/v. Chim. Actu, 1949, 32, 1314.

3. G. Geier, Ber. Bunsenges., 1965, 69, 617. 4. R. Prados, L. G. Stadtherr, H. Donato, Jr and R. B.

Martin, J. Inorg. Nucl. Chem., 1974, 36, 689. 5. R. S. Kolat and J. E. Powell, Inorg. Chem., 1%2,1,293. 6. D. E. Gueffroy (ed.), A Guide for the Preparation and

Use of Buffers in Biological Systems. Calbiochem, California, 1975.

7. K. H. Scheller, T. H. J. Abel, P. E. Polanyi, P. K. Wenk, B. E. Fischer and H. Sigcl, Eur. J. Biochem., 1980,107, 455.

8. Interunion Commission on Biothermodynamics, J. Biol. Chem., 1976, 251, 6879.

9. I. M. Koltboff and P. J. A. Elving (eds.), Treatise on Analytical Chemistry, Part II, p. 57. Interscience, New York, 1963.

10. G. Schwarxenbach, Complexometric Titrations, p. 36. Methuen, London and Interscience, New York, 1960.

11. M. Shamsipur, S. Madaeni and S. Kashanian, T&nta, 1989, 36, 773.

12. G. R. Choppin and P. J. Unrein, J. Inorg. Nucl. Chem., 1963, 25, 387.

13. H. M. N. H. Irving and P. K. Khopkar, ibid., 1964.26, 1561.

14. P. K. Khopkar and P. Narayanankutty, ibid., 1971,X$ 495.

15. T. Sekine, ibid., 1964, 26, 1463. 16. D. F. Peppard, G. W. Mason and I. Hucher, ibid., 1962,

u, 881. 17. B. M. L. Bansal, S. K. Patil, H. D. Shanna, ibid., 1964,

26,993. 18. P. J. Breen and W. Dew. Horrocks, Jr., Inorg. C/rem.,

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Spectrophotometric determination of the stability constant of the Eu(III)—murexide complex

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Transcript of Spectrophotometric determination of the stability constant of the Eu(III)—murexide complex