Calculating the Equilibrium Constants for All Monoazide Lanthanide Complexes in Aqueous Solution Based on the Formation of Eu(III)/N –3

Interest in lanthanide (Ln)/azide (N –3 ) chemical interactions, especially those involving Eu(III), has recently increased because N –3 quenches the luminescence of some lanthanides. Consequently, accurate equilibrium constant values for Ln/N –3 complexes are useful thermodynamic data. Herein, potentiometrically determined equilibrium constant data for the Eu(N 3 ) 2+ complex in aqueous solution at constant ionic strength (2.0molL − 1 , with NaClO 4 ) and temperature (25 . 0 ± 0 . 1°C) are reported. Data for the average number of ligands (¯ n ) were obtained by measuring the pH of the Eu(III)/N –3 /HN 3 system. The relationship between the integrated ¯ n versus [N – 3 ] curve, built by consecutively incrementing [N –3 ], provided the Fronaeus function, F 0 (L). This relationship (in the 0.010–0.10molL − 1 [N –3 ] range) at four different Eu(III) concentrations (28.6–45.2mmolL − 1 ) revealed a single mononuclear complex ( β 1 = 4 . 51mol − 1 L). This β 1 value was used in a mathematical approach to calculate the β 1 values of all other lan-thanides.


Introduction
Studies into lanthanide (Ln) azides have their origins in the last years of the nineteenth century. In 1896, Dennis was the first researcher to mention interactions between inorganic azides and lanthanides, describing the use of potassium azide (KN 3 ) as a precipitating agent for the quantitative separation of Th(IV) from other rare earths present in monazite, a mineral found in Brazil [1]. In 1931, Ant-Wuorinen used a sodium azide (NaN 3 ) solution to fractionally precipitate rare earths [2], and ten years later he separated rare earth alkalis by the electrolysis of their respective azides [3]. La(III) and Ce(III) were the first lanthanides to be evaluated separately in aqueous solution, and equilibrium constants of their complexes with N -3 were determined by potentiometry [4]. Soon after, equilibrium constants for complexes formed between N -3 and other Ln(III) ions in aqueous solution were determined. In 1975, Ezaby and Abdel-Aziz were the first to publish spectrophotometrically determined data for the azide complexes of Pr(III), Nd(III), and Sm(III) [5].
In 1977, Cuillerdier et al. determined values for Nd(III) and Er(III) complexes by spectrophotometric and potentiometric methods [6]. In the same year, Godinho et al. determined equilibrium constants for the monoazide complexes of La(III), Nd(III), and Er(III) by spectrophotometry, and reported values that were of the same order of magnitude [7]. A decade later, Choppin and Barber studied the complexations of N -3 with lanthanide (Ln 3+ ) and actinide (An 3+ ) ions using solvent extraction and radioanalysis, and showed that Ln 3+ monoazide complexes, particularly those of Pm(III), Eu(III), and Tm(III), are slightly less stable than the An 3+ monoazide complexes of Am(III), Cm(III), and Cf(III) [8].
Musikas et al. evaluated the formation of some Ln/N -3 complexes by solvent extraction with thenoyltrifluoroacetone and spectroscopic techniques (specifically UV, Raman, and NMR), and reported that monoazide complexes of Nd(III), Eu(III), and Yb(III) have the same equilibrium constant values. They also mentioned the formation of azido complexes containing higher numbers of N -3 groups for the same lanthanides, namely, Nd(III), Eu(III), and Yb(III), and two actinides, namely, Am(III) and Cm(III), in highly concentrated N -3 solutions [9]. Despite the above-mentioned studies, interactions between N -3 and all 4f block elements in an aqueous solution have not been extensively studied to date. The currently available data are also not completely conclusive, which is ascribable to the high oxophilicity of lanthanides, resulting in an unfavourable competition between the azide ion and water, with Ln(III) ions preferring oxygen donor ligands; hence, methods using different analytical techniques are required for determining these equilibrium constant values.
Interest in chemical interactions between N -3 and Ln(III) ions, especially Eu(III), has increased over the past few decades because N -3 is able to quench the luminescence of some Ln(III) ions in aqueous [10,11] and nonaqueous [12] solutions. Therefore, the value of the equilibrium constant of the complex formed between Eu(III) and N -3 obtained under careful experimental conditions and high precision is very useful thermodynamic information.
In the present study, we carefully determined the value of the formation constant, β 1 , for the Eu(N 3 ) 2+ monoazide complex in aqueous solution using a calibrated glass electrode, constant ionic strength, and temperature control. In addition, this β 1 value was then used in a mathematical procedure to calculate the equilibrium constants of the monoazide complexes of all other 4f block elements. This approach provides a reasonable alternative method for determining values that have not yet been obtained experimentally.

Materials
A Metrohm 654 pH meter and glass electrode (Metrohm AG, Herisau) combined with a Ag/AgCl reference electrode (6.0210.100) filled with 3.0 mol L −1 NaCl, was used at 25.0 ± 0.1°C in the pH experiments in this study.

Chemicals
All reagents were of analytical-grade and were obtained from Merck, Sigma-Aldrich or Fluka Chemie A. G. Deionised water was used to prepare all solutions.
solution was prepared by directly reacting Eu(III) oxide (Eu 2 O 3 , 351.93 g mol −1 , 99.9%, Sigma-Aldrich) with HClO 4 . Eu 2 O 3 (∼ 3.5 g) was transferred to a 1.0 L beaker containing 500 mL water and then perchloric acid (HClO 4 , 100.46 g mol −1 , d = 1.67 g mL −1 , 70-72%, Merck) was slowly added in excess [17]. Mild heating was required to dissolve the Eu 2 O 3 . After filtering off the excess unreacted Eu 2 O 3 , the obtained solution was 10-fold concentrated by controlled evaporation (∼ 50 mL), after which a 1.0 mol L −1 HClO 4 solution was used to adjust the pH to 2.0 in order to prevent hydrolysis [18]. Standardisation was carried out by complexometric titration with EDTA [19]. Briefly, 1.00 mL of the Eu(ClO 4 ) 3 solution was transferred to a 25-mL conical flask and hexamethylenetetramine powder was added until pH 6.0 was achieved, after which 100 mg of a xylenol orange:KNO 3 mixture (1:90 w/w) was added and the solution was titrated with a 0.01 mol L −1 EDTA solution until the colour changed from purplish red to yellow. Four amounts (0.900-1.500 μL) of 0.3482 mol L −1 Eu(ClO 4 ) 3 solution were added to separate samples of each N -3 /HN 3 buffer working solution such that the Eu(III) concentrations in the final solutions ranged from 28.6 mmol L −1 to 45.2 mmol L −1 . Changes in pH were measured from the initial (pH 1 ) to the final (pH 2 ) value after adding the Eu(III) solution to the N -3 /HN 3 buffers, and followed potentiometrically using a calibrated glass electrode.

Potentiometric measurements and data treatment
In order to measure the hydrogen ion concentration, a 0.05 mol L −1 potassium phthalate buffer solution (conditional pH = 3.812) with the same ionic strength as the working solutions (2.00 mol L −1 , NaClO 4 ) was used to calibrate the glass electrode [13,14,15]. This potassium phthalate solution had been previously calibrated with a 0.0100 mol L −1 HClO 4 solution at the same ionic strength (2.00 mol L −1 ; NaClO 4 ).

Results and discussion
The mass balances and the Henderson-Hasselbalch equation (1) for buffer solutions were applied to the N -3 /HN 3 system in which N -3 acts as both a ligand for Eu(III) and as a component of the buffer solution [13,14,15,20].
A conditional pKa for HN 3 at an ionic strength of 2.00 mol L −1 (NaClO 4 ) and a temperature (T) of 25.0 ± 0.1°C were determined for each pH experiment. Determining the pKa values in different experiments has been found to be a reliable procedure as it corrects for any drift in junction potential, small losses of volatile HN 3 , and even possible slope deviations of the glass electrode. The mean pKa value for HN 3 was determined to be 4.626 ± 0.028 under these experimental conditions.
Because the formation and stability of the Eu(III)/N -3 complex is pH-dependent and hydrolytic species, such as Eu(OH) + 2 , may be present in solutions at pH > 6.0 [21], the experimental approach used in the present potentiometric study is advantageous since the pH of the N -3 /HN 3 buffer solution lies in the 4.4-4.7 range (Table 1) and such hydrolytic species are unlikely to be present.
A computer program elaborated in QuickBasic 4.50 (Microsoft) [13,14,15,23] was used to integrate then All studies were performed at T = 25°C [5,9] and there is no mention of temperature control; "a" and "b" are the parameters of (4) developed by Kumok and Serebrennikov [24]. "Mathematical" means obtained using (4) developed by Kumok and Serebrennikov [24]. (c) Calculated value in the present work using (4 Treatment of the F 0 (L) data using a computer method for determining equilibrium constants [13,14,15] revealed solely the formation of the Eu(III) monoazide complex (Eu(N 3 ) 2+ ) under these experimental conditions, with a β 1 value of 4.51 ± 0.11 mol −1 L. Table 2 lists a selection of literature-reported equilibrium constant data for monoazide lanthanide complexes, Ln(N 3 ) 2+ . Most of these values were determined by spectrophotometry or potentiometry, which are very useful techniques for this purpose. Table 2 reveals that most equilibrium constants are of the same order of magnitude. The equilibrium constants for Pr(III), Nd(III), and Sm(III) with N -3 obtained using the Scott and dilution methods [5] are in good agreement; however, these low values do not agree with those obtained by other authors, and these differences cannot be attributed solely to the absence of temperature control in these experiments. In the study reported by El Ezaby and Abdel-Aziz [5], two absorbent species were found in solution; one was assumed to be Ln(III), with the other the corresponding azide complex. These two species were determined only by graphical methods, and the calculational methods (Scott's equation and dilution) were used with some modifications to suit conditions under which Ln(III) ions and their complexes absorb at the same wavelength, which may provide reasons for the low equilibrium constant values obtained.
Kumok and Serebrennikov [24] statistically evaluated the global equilibrium constants, β 1 , of rare-earth, except Pm(III), monocomplexes with 55 different ligands, and found that the logarithms of the β 1 values were linearly correlated. According to these authors, the β 1 value of any lanthanide monocomplex (LnL) is related to that of the lanthanum monocomplex (LaL) through (4). In this equation, a and b are constants obtained by statistically treating each trivalent Ln cation, and log β 1 (LnL) and log β 1 (LaL) refer to the monocomplexes of the lanthanide (Ln) and lanthanum (La), respectively, The a and b values for Eu(III) are 1.1367 and 0.009, respectively [24]. With this in mind, we applied (4) to the β 1 value found in the present study for Eu(N 3 ) 2+ (i.e., 4.51 mol −1 L), which provided 3.70 mol −1 L as the β 1 value for La(N 3 ) 2+ . Since the values of a and b for trivalent Ln cations have been reported [24], the β 1 values were calculated for the monoazide complexes of all lanthanides, the results of which are listed in Table 2.
As expected, these complexes are very weakly bound since trivalent lanthanides are hard cations [25] and prefer to form complexes with oxygen or mixed oxygennitrogen donor ligands rather than nitrogen donors such as N -3 . Despite being weak, the equilibrium constants calculated using only the equation developed by Kumok and Serebrennikov [24] for the Ln monocomplexes with N -3 also need to be determined experimentally. The values obtained experimentally will facilitate a more realistic interpretation of the calculational methodology used in the present study for determining these same values mathematically.

Conclusions
Potentiometric measurements using a calibrated glass electrode at constant ionic strength (2.0 mol L −1 ; NaClO 4 ) and controlled temperature (T = 25.0°C) enabled the accurate determination of the formation constant for the Eu(N 3 ) 2+ complex in aqueous solution (β 1 = 4.51 ± 0.11 mol −1 L). No polynuclear complex is formed in the Eu(III) concentration range used in this study (28.60-45.18 mmol L −1 ). The β 1 value found for the Eu(N 3 ) 2+ complex was used in a mathematical approach to calculate the β 1 values for the monoazide complexes of all other 4f block elements, which provides a reasonable alternative procedure for determining values that have not yet been obtained experimentally.