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The ionic product of water in highly concentrated sodium perchlorate solutions
Talanta 45 (1998) 931 – 934
The ionic product of water in highly concentrated sodium perchlorate solutions M.L. Turonek *, G.T. Hefter, P.M. May Department of Chemistry and Mineral Science, Murdoch Uni6ersity, Murdoch, WA 6150, Australia Received 15 April 1997; accepted 17 June 1997
Abstract The ionic product of water, pKw = −log[H + ][OH − ], has been determined in aqueous solutions of sodium perchlorate over the concentration range of 1.0 – 8.0 M at 25°C from high-precision potentiometric titrations carried out in cells with liquid junction using both glass and hydrogen electrodes. The glass electrode results are systematically lower probably as a result of interference by Na + ions. © 1998 Elsevier Science B.V. Keywords: Sodium perchlorate; High-precision potentiometric titrations; Glass electrode; Hydrogen electrode
1. Introduction The detailed study of thermodynamic parameters of highly concentrated mixed electrolyte solutions is of direct relevance to a wide variety of chemical systems of geochemical or industrial interest. Models for such systems aim to describe the change in chemical speciation over a wide range of temperature, pressure, concentration and composition. These models depend on equilibrium parameters extracted from simple systems. Sodium perchlorate is of special interest because of its high aqueous solubility and its broad use as an inert supporting electrolyte for maintaining ionic concentrations such that activity coefficients remain virtually constant.
* Corresponding author.
Accurate values of the ionic product of water, pKw: + − H2O X H(aq) + OH(aq) + − Kw = [H(aq) ][OH(aq) ]
are required for the estimation of activity coefficient changes, liquid junction potentials, and metalligand formation constants as part of our continuing thermodynamic investigations of chemical equilibria in concentrated electrolytes. In particular, we need systematic and internallyconsistent measurements of pKw for a wide range of ionic media. Data for the ionic product of water, pKw, in this medium [1–10] are scarce, however, above I= 4 M. Accordingly, new determinations of the ionic product of water at 25°C have been made in aqueous solutions of sodium perchlorate over the concentration range 1.0–8.0 M by application of glass- and hydrogen-electrode potentiometry.
0039-9140/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 9 - 9 1 4 0 ( 9 7 ) 0 0 1 9 9 - 9
932
M.L. Turonek et al. / Talanta 45 (1998) 931–934
2. Experimental
2.1. Materials Sodium perchlorate monohydrate, NaClO4.H2O, (BDH AnalaR, 99.0% purity) was used as received, with a water content determined by thermogravimetric analysis to be 11.99% (theor. 12.83%). The titrant was prepared from commercial volumetric ampoules of sodium hydroxide (BDH Convol) and the acid solutions were prepared from concentrated perchloric acid (70% w/w aqueous solution, analytical grade, Ajax Chemicals) and standardised volumetrically against NaOH (BDH Convol) using methyl orange indicator. All solutions were made up with Millipore Milli-Q water that had been boiled and purged with high purity nitrogen to remove oxygen and carbon dioxide. Gran analyses of the potentiometric titrations indicated that the solutions were essentially carbonate free (accounting for less than 0.2% of the total alkalinity).
2.2. Apparatus and procedure The ionic product of water was determined by potentiometric titration of HClO4 (0.020 M) dissolved in NaClO4 (c-0.020 M) with NaOH (0.1 M) in NaClO4 (c M). Measurements were carried out over the ionic strength range of 1.005 c5 8.00 M. All the titrations were performed using Ag/AgCl electrodes of in-house construction, together with either a glass electrode (Metrohm, model 6.0101.000) or a hydrogen electrode (prepared and used as described previously [11]) in a standard jacketed glass cell using the high precision automated titration system developed in our laboratories. Where glass electrode potentiometry was used the solutions were blanketed by high purity nitrogen delivered through a carbon dioxide trap and a pre-humidifier containing a solution of the sodium perchlorate at the concentration of interest. Where the hydrogen electrode was used ultra-high purity hydrogen gas (CIG) was delivered to the cell via thick-walled copper tubing to a pre-humidifier. The cell was tightly sealed to minimize contamination by atmospheric oxygen and carbon dioxide. The bu-
rettes were Metrohm 665 Dosimat (calibrated precision9 0.1%) driven by an IBM PC computer. All volumetric glassware was A-grade and calibrated. The cell emf was measured to90.1 mV by high impedance digital voltmeters of inhouse construction, interfaced with the computer. The temperature in the cells was maintained at 25.09 0.02°C by use of a circulator thermostat (Heto Birkerød Denmark, model 04 PT 623). Temperatures were monitored with a thermistor calibrated against a quartz crystal thermometer (Hewlett Packard, Model HP2804A). The cells used for the titrations may be represented schematically as: Ag AgCl(s) 5 M NaCl(aq) E 5 M NaCl(aq) j1
xHX,(c − x)MX HE E
(1)
j2
where HE represents a hydrogen ion-responsive glass (GE) or platinum (H2(g)/Pt) electrode, and Ej1 and Ej2 are liquid junction potentials. Ej1 is essentially constant and may be incorporated into the potential Eref of the silver-silver chloride reference electrode. The potential of the cell is then: Ecell = EHE − Eref − Ej2
(2)
If it is assumed that throughout the course of a titration that Eref, Ej2, the activity coefficients of the trace species of interest (H + and OH − ), and the hydrogen fugacity (pressure) are constant, then it is readily shown by the usual methods of electrochemical thermodynamics that, at 25°C, the relationship between the cell potential and the hydrogen ion concentration is: Ecell/mV= E 0%/mV+ 59.16 log([H + ]/M)
(3)
where E 0% is the ‘formal’ cell potential, which includes the standard cell potential, the liquid junction potential Ej2, and activity coefficient and hydrogen fugacity terms. The resulting emf data Eq. (3) were collected from 4–8 titrations for each sodium perchlorate concentration of interest and evaluated by leastsquares analysis with respect to either the values of the cell potential (to obtain an estimate of the formal potential) or of the concentration of H + ions (to obtain an estimate of pKw). The leastsquares optimizations were made using the ESTA
M.L. Turonek et al. / Talanta 45 (1998) 931–934
933
suite of computer programs [12 – 14]. Gran-plots were calculated for each titration to evaluate the degree of carbonate contamination and the general condition of the electrochemical cell.
3. Results and discussion Despite the high solubility of NaClO4 and its widespread use as a supporting electrolyte for equilibrium constant measurements, there is an absence of reliable literature data for pKw measured in the high background ionic strength range above 4.0 M. To our knowledge, this work is the first determination of the ionic product of water in sodium perchlorate in the ionic strength range above 5 M. The results of the least-squares analyses of the emf data are collected in Table 1. The stated precisions in parentheses refer to the internal consistency of the titration data; the real errors in the equilibrium constant (pKw) are generally an order of magnitude greater than the internal precision [14]. In Fig. 1, our experimental results for pKw in aqueous NaClO4 are plotted against ionic strength, together with selected data from the literature. It is noteworthy that the hydrogen electrode results of Carpe´ni et al. [10] and Fischer and Bye´ [6] lie reasonably close to the same curve as the present HE values, although the agreement is not as good as observed previously for NaCl solutions [11]. This may reflect the presence of minor impurities in the notoriously difficult to purify NaClO4. Similarly the glass Table 1 The ionic product of water, pKw, in aqueous sodium perchlorate at 298.15 K and 1 atma I (M)
pKw (HE)
OBJT/10−1 pKw (GE)
OBJT/10−8
1.0 2.0 4.0 6.0 8.0
13.7706 13.9597 14.5161 15.2234 15.9396
0.5 0.5 2.9 1.9 2.0
0.3 0.5 0.3 1.8 1.7
a
(7) (4) (8) (7) (8)
13.7709 13.9374 14.4465 15.1295 15.9653
(5) (4) (3) (6) (7)
HE, hydrogen electrode; GE, glass electrode; OBJT, objective function [12–14]. Numbers in parentheses indicate the standard deviation in the last decimal place quoted.
Fig. 1. Ionic product of water in sodium perchlorate at 25°C:
[6] (HE); [10] (HE); this work (GE); this work (HE).
electrode results of Na¨sa¨nen and Merila¨inen [5] match our own findings. It is apparent from Fig. 1 that there is a systematically increasing difference between the glass and hydrogen electrode results as the ionic strength increases up to 6.0 M. Although small, these differences are outside the experimental error (Table 1). Similar results were observed by us in NaCl media (up to I=5.0 M) and have been tentatively ascribed to interference of Na + with the glass membrane as no such effect is observed in KCl, at least up to the solubility limit. In 8.0 M NaClO4 the difference between the results obtained from the two electrodes virtually disappears. The reasons for this are unclear at present. Comparison of the slopes S (= DpKw/DI) of the GE and HE curves in Fig. 1 at first sight suggests this convergence may be due to a decline in the HE performance. Thus, SGE increases smoothly over the entire ionic strength range whereas SHE increases initially but eventually becomes constant (i.e. pKw become linearly dependent on I). However, a linear relationship (between log KHF and I) has also been observed for the similar equilibrium: + − HF(aq) X H(aq) + F(aq)
obtained from a fluoride ion-selective electrode measurements over the same concentration range in NaClO4 media [15]. It should also be noted
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M.L. Turonek et al. / Talanta 45 (1998) 931–934
Fig. 2. Performance of glass electrodes as measured by Gran plots (G =10E/59.16(V0 + V), where E is the cell potential (mV), V0 is the initial volume of the solution, and V is the volume of added titrant). (a) Electrode soaked in 0.02 M HClO4 and I = 8M (NaClO4) ( ); (b) electrode soaked in 0.02 M HClO4 and I = 1.0 M (NaClO4) for 36 h (); (c) electrode soaked in 1 mM HCl in I =1.0 M (NaClO4) (). Note: Gran plots refer to strong acid-strong base titrations in: (a,b) 8 M NaClO4; (c) 1 M NaClO4. The data points () and () are offset by 1 and 2 cm3, respectively for purposes of clarity.
that if the convergence of results at I = 8.0 M is due to a decline in performance of either or both electrodes, any such deterioration is not reflected in the objective function values or the standard deviations listed in Table 1. With respect to the glass electrode there is clear evidence of a degradation in performance at very high NaClO4 concentrations. Gran plots in the acidic region of the titration (Fig. 2, curve (a)) are clearly curved, which indicates that the glass electrode response is not Nernstian. This behaviour is in marked contrast to what we routinely observed in more dilute electrolte solutions (Fig. 2, curve (c)). Such behaviour first becomes apparent in 4.0 M NaClO4 solutions but is increasingly marked when c]6.0 M. Our customary protocol in using glass electrodes for equilibrium constant measurements in concentrated electrolyte solutions is to store the electrode between titrations in 1 mM H + and 1.0 M NaCl or in the medium of interest. Electrodes are always ‘rested’ in such solutions for at least 16 h before re-use. This minimises any ‘shock’ to the membrane when it is placed in a test solution and helps to shorten stabilisation times. It appears
that this protocol is unsatisfactory for very concentrated electrolyte solutions, at least in NaClO4, possibly due to the dehydration of the glass membrane induced by the very low water activity. The electrode response can be improved to a satisfactory level, as indicated by a return to linearity in the Gran plot, by allowing the glass electrode to soak in a solution of 0.02 M HClO4 and 1.0 M NaClO4 for 36 h before and after each titration to ‘recuperate’ (Fig. 2, curve (b)). Although some problems associated with loss of platinum black have occasionally been observed, especially in acid solution, the behaviour of carefully prepared hydrogen electrodes at these concentrations appears normal. For the present work, our hydrogen electrodes were always stored in 0.02 M HClO4 and 1.0 M NaClO4 for at least 24 h before re-use.
Acknowledgements This work was funded by the Australian alumina industry through the Australian Mineral Industry Research Association Project P380B and a collaborative grant from the Australian Research Council.
References ˚ gren, Acta Chem. Scand. 9 (1955) 39. [1] A. A [2] N. Ingri, G. Lagerstrom, M. Frydman, L.G. Sille´n, Acta Chem. Scand. 11 (1957) 1034. [3] G. Lagerstro¨m, Acta Chem. Scand. 13 (1959) 722. ˚ . Olin, Acta Chem. Scand. 14 (1960) 1999. [4] B. Carell, A [5] R. Na¨sa¨nen, P. Merila¨inen, Suom. Kem B33 (1960) 149. [6] R. Fischer, J. Bye´, Bull. Soc. Chim. Fr. (1964) 2920. [7] P.N. Kovalenko, K.N. Bagdasarov, Zh. Neorg. Khim. 10 (1965) 1624. [8] G. Anderegg, Helv. Chim. Acta 50 (1967) 2333. [9] H. Persson, Acta Chem. Scand. 25 (1971) 543. [10] G. Carpe´ni, E. Boitard, R. Pilard, S. Poize, N. Sabiani, J. Chim. Phys. 69 (1973) 1445. [11] I. Kron, S.L. Marshall, P.M. May, G.T. Hefter, E. Koenigsberger, Monatsh. Chem. 126 (1995) 819. [12] P.M. May, K. Murray, D.R. Williams, Talanta 35 (1988) 825. [13] P.M. May, K. Murray, Talanta 35 (1988) 927. [14] P.M. May, K. Murray, Talanta 35 (1988) 933. [15] G.T. Hefter, J. Solution Chem. 11 (1982) 45.
The ionic product of water in highly concentrated sodium perchlorate solutions M.L. Turonek *, G.T. Hefter, P.M. May Department of Chemistry and Mineral Science, Murdoch Uni6ersity, Murdoch, WA 6150, Australia Received 15 April 1997; accepted 17 June 1997
Abstract The ionic product of water, pKw = −log[H + ][OH − ], has been determined in aqueous solutions of sodium perchlorate over the concentration range of 1.0 – 8.0 M at 25°C from high-precision potentiometric titrations carried out in cells with liquid junction using both glass and hydrogen electrodes. The glass electrode results are systematically lower probably as a result of interference by Na + ions. © 1998 Elsevier Science B.V. Keywords: Sodium perchlorate; High-precision potentiometric titrations; Glass electrode; Hydrogen electrode
1. Introduction The detailed study of thermodynamic parameters of highly concentrated mixed electrolyte solutions is of direct relevance to a wide variety of chemical systems of geochemical or industrial interest. Models for such systems aim to describe the change in chemical speciation over a wide range of temperature, pressure, concentration and composition. These models depend on equilibrium parameters extracted from simple systems. Sodium perchlorate is of special interest because of its high aqueous solubility and its broad use as an inert supporting electrolyte for maintaining ionic concentrations such that activity coefficients remain virtually constant.
* Corresponding author.
Accurate values of the ionic product of water, pKw: + − H2O X H(aq) + OH(aq) + − Kw = [H(aq) ][OH(aq) ]
are required for the estimation of activity coefficient changes, liquid junction potentials, and metalligand formation constants as part of our continuing thermodynamic investigations of chemical equilibria in concentrated electrolytes. In particular, we need systematic and internallyconsistent measurements of pKw for a wide range of ionic media. Data for the ionic product of water, pKw, in this medium [1–10] are scarce, however, above I= 4 M. Accordingly, new determinations of the ionic product of water at 25°C have been made in aqueous solutions of sodium perchlorate over the concentration range 1.0–8.0 M by application of glass- and hydrogen-electrode potentiometry.
0039-9140/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 3 9 - 9 1 4 0 ( 9 7 ) 0 0 1 9 9 - 9
932
M.L. Turonek et al. / Talanta 45 (1998) 931–934
2. Experimental
2.1. Materials Sodium perchlorate monohydrate, NaClO4.H2O, (BDH AnalaR, 99.0% purity) was used as received, with a water content determined by thermogravimetric analysis to be 11.99% (theor. 12.83%). The titrant was prepared from commercial volumetric ampoules of sodium hydroxide (BDH Convol) and the acid solutions were prepared from concentrated perchloric acid (70% w/w aqueous solution, analytical grade, Ajax Chemicals) and standardised volumetrically against NaOH (BDH Convol) using methyl orange indicator. All solutions were made up with Millipore Milli-Q water that had been boiled and purged with high purity nitrogen to remove oxygen and carbon dioxide. Gran analyses of the potentiometric titrations indicated that the solutions were essentially carbonate free (accounting for less than 0.2% of the total alkalinity).
2.2. Apparatus and procedure The ionic product of water was determined by potentiometric titration of HClO4 (0.020 M) dissolved in NaClO4 (c-0.020 M) with NaOH (0.1 M) in NaClO4 (c M). Measurements were carried out over the ionic strength range of 1.005 c5 8.00 M. All the titrations were performed using Ag/AgCl electrodes of in-house construction, together with either a glass electrode (Metrohm, model 6.0101.000) or a hydrogen electrode (prepared and used as described previously [11]) in a standard jacketed glass cell using the high precision automated titration system developed in our laboratories. Where glass electrode potentiometry was used the solutions were blanketed by high purity nitrogen delivered through a carbon dioxide trap and a pre-humidifier containing a solution of the sodium perchlorate at the concentration of interest. Where the hydrogen electrode was used ultra-high purity hydrogen gas (CIG) was delivered to the cell via thick-walled copper tubing to a pre-humidifier. The cell was tightly sealed to minimize contamination by atmospheric oxygen and carbon dioxide. The bu-
rettes were Metrohm 665 Dosimat (calibrated precision9 0.1%) driven by an IBM PC computer. All volumetric glassware was A-grade and calibrated. The cell emf was measured to90.1 mV by high impedance digital voltmeters of inhouse construction, interfaced with the computer. The temperature in the cells was maintained at 25.09 0.02°C by use of a circulator thermostat (Heto Birkerød Denmark, model 04 PT 623). Temperatures were monitored with a thermistor calibrated against a quartz crystal thermometer (Hewlett Packard, Model HP2804A). The cells used for the titrations may be represented schematically as: Ag AgCl(s) 5 M NaCl(aq) E 5 M NaCl(aq) j1
xHX,(c − x)MX HE E
(1)
j2
where HE represents a hydrogen ion-responsive glass (GE) or platinum (H2(g)/Pt) electrode, and Ej1 and Ej2 are liquid junction potentials. Ej1 is essentially constant and may be incorporated into the potential Eref of the silver-silver chloride reference electrode. The potential of the cell is then: Ecell = EHE − Eref − Ej2
(2)
If it is assumed that throughout the course of a titration that Eref, Ej2, the activity coefficients of the trace species of interest (H + and OH − ), and the hydrogen fugacity (pressure) are constant, then it is readily shown by the usual methods of electrochemical thermodynamics that, at 25°C, the relationship between the cell potential and the hydrogen ion concentration is: Ecell/mV= E 0%/mV+ 59.16 log([H + ]/M)
(3)
where E 0% is the ‘formal’ cell potential, which includes the standard cell potential, the liquid junction potential Ej2, and activity coefficient and hydrogen fugacity terms. The resulting emf data Eq. (3) were collected from 4–8 titrations for each sodium perchlorate concentration of interest and evaluated by leastsquares analysis with respect to either the values of the cell potential (to obtain an estimate of the formal potential) or of the concentration of H + ions (to obtain an estimate of pKw). The leastsquares optimizations were made using the ESTA
M.L. Turonek et al. / Talanta 45 (1998) 931–934
933
suite of computer programs [12 – 14]. Gran-plots were calculated for each titration to evaluate the degree of carbonate contamination and the general condition of the electrochemical cell.
3. Results and discussion Despite the high solubility of NaClO4 and its widespread use as a supporting electrolyte for equilibrium constant measurements, there is an absence of reliable literature data for pKw measured in the high background ionic strength range above 4.0 M. To our knowledge, this work is the first determination of the ionic product of water in sodium perchlorate in the ionic strength range above 5 M. The results of the least-squares analyses of the emf data are collected in Table 1. The stated precisions in parentheses refer to the internal consistency of the titration data; the real errors in the equilibrium constant (pKw) are generally an order of magnitude greater than the internal precision [14]. In Fig. 1, our experimental results for pKw in aqueous NaClO4 are plotted against ionic strength, together with selected data from the literature. It is noteworthy that the hydrogen electrode results of Carpe´ni et al. [10] and Fischer and Bye´ [6] lie reasonably close to the same curve as the present HE values, although the agreement is not as good as observed previously for NaCl solutions [11]. This may reflect the presence of minor impurities in the notoriously difficult to purify NaClO4. Similarly the glass Table 1 The ionic product of water, pKw, in aqueous sodium perchlorate at 298.15 K and 1 atma I (M)
pKw (HE)
OBJT/10−1 pKw (GE)
OBJT/10−8
1.0 2.0 4.0 6.0 8.0
13.7706 13.9597 14.5161 15.2234 15.9396
0.5 0.5 2.9 1.9 2.0
0.3 0.5 0.3 1.8 1.7
a
(7) (4) (8) (7) (8)
13.7709 13.9374 14.4465 15.1295 15.9653
(5) (4) (3) (6) (7)
HE, hydrogen electrode; GE, glass electrode; OBJT, objective function [12–14]. Numbers in parentheses indicate the standard deviation in the last decimal place quoted.
Fig. 1. Ionic product of water in sodium perchlorate at 25°C:
[6] (HE); [10] (HE); this work (GE); this work (HE).
electrode results of Na¨sa¨nen and Merila¨inen [5] match our own findings. It is apparent from Fig. 1 that there is a systematically increasing difference between the glass and hydrogen electrode results as the ionic strength increases up to 6.0 M. Although small, these differences are outside the experimental error (Table 1). Similar results were observed by us in NaCl media (up to I=5.0 M) and have been tentatively ascribed to interference of Na + with the glass membrane as no such effect is observed in KCl, at least up to the solubility limit. In 8.0 M NaClO4 the difference between the results obtained from the two electrodes virtually disappears. The reasons for this are unclear at present. Comparison of the slopes S (= DpKw/DI) of the GE and HE curves in Fig. 1 at first sight suggests this convergence may be due to a decline in the HE performance. Thus, SGE increases smoothly over the entire ionic strength range whereas SHE increases initially but eventually becomes constant (i.e. pKw become linearly dependent on I). However, a linear relationship (between log KHF and I) has also been observed for the similar equilibrium: + − HF(aq) X H(aq) + F(aq)
obtained from a fluoride ion-selective electrode measurements over the same concentration range in NaClO4 media [15]. It should also be noted
934
M.L. Turonek et al. / Talanta 45 (1998) 931–934
Fig. 2. Performance of glass electrodes as measured by Gran plots (G =10E/59.16(V0 + V), where E is the cell potential (mV), V0 is the initial volume of the solution, and V is the volume of added titrant). (a) Electrode soaked in 0.02 M HClO4 and I = 8M (NaClO4) ( ); (b) electrode soaked in 0.02 M HClO4 and I = 1.0 M (NaClO4) for 36 h (); (c) electrode soaked in 1 mM HCl in I =1.0 M (NaClO4) (). Note: Gran plots refer to strong acid-strong base titrations in: (a,b) 8 M NaClO4; (c) 1 M NaClO4. The data points () and () are offset by 1 and 2 cm3, respectively for purposes of clarity.
that if the convergence of results at I = 8.0 M is due to a decline in performance of either or both electrodes, any such deterioration is not reflected in the objective function values or the standard deviations listed in Table 1. With respect to the glass electrode there is clear evidence of a degradation in performance at very high NaClO4 concentrations. Gran plots in the acidic region of the titration (Fig. 2, curve (a)) are clearly curved, which indicates that the glass electrode response is not Nernstian. This behaviour is in marked contrast to what we routinely observed in more dilute electrolte solutions (Fig. 2, curve (c)). Such behaviour first becomes apparent in 4.0 M NaClO4 solutions but is increasingly marked when c]6.0 M. Our customary protocol in using glass electrodes for equilibrium constant measurements in concentrated electrolyte solutions is to store the electrode between titrations in 1 mM H + and 1.0 M NaCl or in the medium of interest. Electrodes are always ‘rested’ in such solutions for at least 16 h before re-use. This minimises any ‘shock’ to the membrane when it is placed in a test solution and helps to shorten stabilisation times. It appears
that this protocol is unsatisfactory for very concentrated electrolyte solutions, at least in NaClO4, possibly due to the dehydration of the glass membrane induced by the very low water activity. The electrode response can be improved to a satisfactory level, as indicated by a return to linearity in the Gran plot, by allowing the glass electrode to soak in a solution of 0.02 M HClO4 and 1.0 M NaClO4 for 36 h before and after each titration to ‘recuperate’ (Fig. 2, curve (b)). Although some problems associated with loss of platinum black have occasionally been observed, especially in acid solution, the behaviour of carefully prepared hydrogen electrodes at these concentrations appears normal. For the present work, our hydrogen electrodes were always stored in 0.02 M HClO4 and 1.0 M NaClO4 for at least 24 h before re-use.
Acknowledgements This work was funded by the Australian alumina industry through the Australian Mineral Industry Research Association Project P380B and a collaborative grant from the Australian Research Council.
References ˚ gren, Acta Chem. Scand. 9 (1955) 39. [1] A. A [2] N. Ingri, G. Lagerstrom, M. Frydman, L.G. Sille´n, Acta Chem. Scand. 11 (1957) 1034. [3] G. Lagerstro¨m, Acta Chem. Scand. 13 (1959) 722. ˚ . Olin, Acta Chem. Scand. 14 (1960) 1999. [4] B. Carell, A [5] R. Na¨sa¨nen, P. Merila¨inen, Suom. Kem B33 (1960) 149. [6] R. Fischer, J. Bye´, Bull. Soc. Chim. Fr. (1964) 2920. [7] P.N. Kovalenko, K.N. Bagdasarov, Zh. Neorg. Khim. 10 (1965) 1624. [8] G. Anderegg, Helv. Chim. Acta 50 (1967) 2333. [9] H. Persson, Acta Chem. Scand. 25 (1971) 543. [10] G. Carpe´ni, E. Boitard, R. Pilard, S. Poize, N. Sabiani, J. Chim. Phys. 69 (1973) 1445. [11] I. Kron, S.L. Marshall, P.M. May, G.T. Hefter, E. Koenigsberger, Monatsh. Chem. 126 (1995) 819. [12] P.M. May, K. Murray, D.R. Williams, Talanta 35 (1988) 825. [13] P.M. May, K. Murray, Talanta 35 (1988) 927. [14] P.M. May, K. Murray, Talanta 35 (1988) 933. [15] G.T. Hefter, J. Solution Chem. 11 (1982) 45.