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Determination of sulphate by pH titration
0039-9140/87s3.00 + 0.00 Copyright 0 1987Pcrgsmon Journals Ltd
Talanfa, Vol. 34, No. 4, pp. 397-400, 1987 Printed in Grest Britain. All rights re~rved
DETERMINATION
OF SULPHATE
BY pH TITRATION
B&A No!&L and m Jux-&z Department of Inorganic and Analytical base, L. E&v& University, 1088 Sudapest, Miueum krt. 4/B, Hungary (Received 20 August 1985. Revised 28 July 1986. Accepted 15 November 1986)
Smnmary-A simple and inexpensive method has been developed for the determination of sulphate and other very weak bases and acids. It utilizes the partial protonation of the weak base or the partial dissociation of the weak acid, which has not been exploited for analytical purposes thus far. The procedure consists of three pH titrations: one with a test solution of known sulphate content, the second with the sulphate sample, and the third with a blank. This method can be used in the presence of several inorganic ions and organic matrices, including non-aqueous solvents. In aqueous medium sulphate contents above 10m3Mcan be determined. The use of solvent mixtures may increase the sensitivity of the method by two orders of magnitude.
Most analytical methods for the determination of sulphate (gravimetry, chelatometry, potentiometry, cqnductometry, amperometry etc.) are based on the foliation of its barium or lead salts.’ Besides these, several classical or instrumental analytical methods have been developed in which organic reagents are used to form a sulphate precipitate. However, there is no report on the analytical exploitation of the equilibrium interaction between the sulphate and hydrogen ions. The obvious reason is the low basicity of sulphate, which does not allow its dete~ination by normal direct acidimetric tit~tion. Here a method, and its application to sulphate, will be introduced, which utilizes the partial protonation of very weak bases (or dissociation of fairly strong acids). The best known method for evaluating potentiometric titrations of weak bases and acids is the classical Gran plot.* Preconditions for its use are knowledge of the equilibrium constant valid under the given circumstances, and of the pH and the titrant concentration. The procedure of Ivaska and Nagyp;;i13 needs considerable mathematical apparatus, but can be used even for analysis of mixtures. The recent method by Burger et at.,’ based on measurement of the amount of bound reagent, applies when protonation or deprotonation is practically complete. The present method does not require knowledge of the equilibrium constant, the pH or the titrant concentration, and furthermore is satisfactory even if the reaction takes place only to the extent of 20-30%; thus it is suitable for the determination of very weak acids and bases.
co-ordination
chemistry?
The formation constant (B) for BH+ is:
Combining
(1) and (2) gives:
The equivalent relation for a polyacidic base (yielding BH;+ on complete protonation) is:
c &W+l’
i-0
Dissociation of acidr
The extent of dissociation of an acid HA is given by the function:
R=
M-1 IA- I + IHAl
which can be expressed in terms of [H+ ] and protonation constant of A-: Ram
l
1 + /3[H+l’
For a polybasic acid (H,A): m-1
m + C (m - i)B,[H+]
Protonation of bases
The proportion of the conjugated acid (HB+) formed in the protonation ~~lib~~ B f H+ *BH’ of a monoacidic base (B) can be calculated from the formation function well known in
It is a common property of (3) and (4) as well as of (6) and (7), that n’ and R depend only on the
397
398
BELA NOSZAL and M.&~A Jutisz
equilibrium constant and the hydrogen-ion activity, and are independent of the total (analytical) concentrations. Accordingly, 6 and R are intensive attributes of the material (acid or base) in question. Their actual value at a given pH are as characteristic of them in pH titrations as the molar absorption coefficient at a given wavelength is in spectrophotometry. Nevertheless, it does not make sense to introduce the term “molar protonation coefficients”, since the term A has long been familiar in equilibrium chemistry. Experimental determination of ii and
A
number of extra moles of acid number of moles of weak base ’
13 -
111*L(*
xi
12 -
5s I I I ;x + x
11 10 9-
; ? t :
",6 76-
d
xx x x x x x
*\ 0, .\
5-
::
43-
From (3), (4), (6) and (7), A and Rcan be calculated from the equilibrium constants and hydrogen-ion activities. However, the equilibrium constants are only valid for the ionic strength, temperature, medium and circumstances under which they were determined. Furthermore, they are subject to the experimental error of their determination, which is especially significant, when the glass electrode is used, at the pH values at which the weakest bases or acids are protonated or deprotonated (as the case may be). Moreover, there are several substances for which the protonation constants are not known (e.g., polypeptides, proteins, nucleic acids, compounds of unknown structure), or cannot even be determined unambiguously (for example in non-aqueous medium). Consequently their fi or R values cannot be calculated. More reliable and strictly valid fi or R values can be obtained by determinations made with a known amount of pure test substance. This can be done by two potentiometric titrations. In a blank titration sodium hydroxide (or simply water) is titrated potentiometrically with an acid titrant, and in the second titration an identical amount of hydroxide (or water) plus a known amount of weak base is titrated under the same conditions, to the same pH value. In this way the number of extra moles of titrant needed in the presence of the weak base, divided by the number of moles of weak base present, yields the g value: <=
14 _LL
(8)
Figure 1 shows three titration curves, where in each case sodium hydroxide was accompanied by a weak base, the bases differing in strength. It is remarkable that the strongest of these bases, cyanide, can be well determined, whereas the less basic acetate, even in high concentration, can only be determined with much ambiguity by traditional evaluation methods, owing to its incomplete protonation during the second pH “break”. The very weak base sulphate cannot be determined at all by simple evaluation methods, because it is only partially protonated, even at the lowest pH which can be reached by using 1M strong acid as the titrant. Nevertheless, from (8) and a third titration the number of moles of sulphate can be obtained from the measured extra number of moles
2l1IlIIIIIIII 0
12
3
45
6
7
691011
Fig. 1. Calculated titration curves for 5.0 of solution titrated with l.OM HCI. a. l.OM NaOH alone: b. l.OM NaOH +OSM K,SO,i c, l.OM NaOH +d.SM CH,COONa; d, l.OM NaOH + OSM KCN. The basicities of cyanide,6 acetate’ and sulphate* were taken from the literature values recommended by Martell and Smith.s
of titrant needed and previously determined fi data as a function of pH. It is recommended to use a high ionic strength medium (e.g., 2M sodium perchlorate) for all three titrations, to eliminate matrix effects. Determination of very weak acids can be done in an analogous manner by titrations with a base. EXPERIMENTAL We have developed a microtitration technique with a combined microelectrode suitable for pH determination in
an initial volume of 0.6-l .Oml. Accordingly, with 2.OM acid @-INOr, HCl, HClO,) as titrant, as little as 0.02 g of sodium sulphate can be determined. If the amount of sulphate in the sample is approximately known, it is recommended to use as similar an amount of reference material as possible for the A determination. Since different pH regions of the titration curves do not provide equally undistorted data, it is also advisable to check these A values against known amounts of sulphate in one or two preliminary experiments. Normally the best parts of the titration curves to use for the analysis are those where the protonation of sulphate is already significant (10% or more), but the titration curves have not yet become horizontal. The amount of analyte can be calculated most conveniently by means of the equation
4
MT=-mS
4
where mr and ms are the numbers of moles of sulphate in the test sample and the reference standard respectively, and DT and D, are the corresponding distances of their titration curves from the sulphate-free titration curve at a given pH. DT and D, can be measured in the same arbitrary units (ml or mm on a graph) since only their ratio is significant. Since the ratio D,/m, is a form of A, equation (9) is also a simple, practical derivative of equation (8). It can be seen that by means of this equation the determination of sulphate is reduced to measurement of the titrant volumes. For accurate measurements of small volumes and their differences a Radiometer ABU 12 automatic burette was used. All the potentiometric titrations were done by with use of an Orion Research 801-2 pH-meter with Ingold 104053059
Determination
399
of sulphate
Table 1. Experimental results for sulphate determinations under different conditions. A, B and C refer to the blank, standard and sample titration curves, respectively Number of titration
Sulphate taken, g/100 ml
Number of different pH values
Standard
Samule
Found,* g/100 ml
A
B
C
7.1021 7.1021 7.1021 2.8400 8.5700
8.5221 8.5221 7.8122 8.5206 11.6680
8.6, 8.3, 7.8, f 0.0, 8.4, f 0.2, 11.7,*0.1,
1
1 1
1 1 1
4.3760
8.5742
8.6, + 0.2,
1
1
1
10
1.2-1.55
4.3500 3.1188 4.9900
2.7250
2.6, + 0.1,
1
1
1
10
0.07-0.92
NaCl, 2M NaCl, 2M NaCl, 2M NaCIO,, 2M NaNO,, 2M NaOGCCH,, 0.12M > NaNO,, 2M NaNO,, 2M
3.7425
3.7, f 0.09
1
2
1
15
0.74-0.96
NaNO,, 2.63.1M
curves
1 1 1 1
1 1 1
1 9
1
10 10
1
Medium
PH 0.4 0.65 0.47-1.10 161.9 1.7-2.1
*Mean f 95% confidence limits.
combined electrode. The method requires neither temperature-control nor calibration of the cell, but the A determination and the analytical measurements have to be made under strictly identical conditions. For approximate pH standardization, Radiometer pH 7.0 buffer was used. All the chemicals were of analytical-reagent grade (Reanal, Hungary) and used without further purification. RESULTS AND DISCUSSION
It can be seen in Fig. 1, that the sulphate and blank titration curves are identical above pH 3, owing to the negligible protonation of the sulphate, so this part of the titration is of no value for our purpose. Table 1 shows experimental results for determination of sulphate in the presence of accompanying electrolytes at high concentrations. It can be seen that the sulphate determination is feasible in solutions of not only the less basic chloride, nitrate and perchlorate ions, but also in the presence of the significantly more basic acetate (and of course hydroxide) ions. Since the acetate protonation is more than 99% complete below pH 2.7, this effect can be quantitatively taken into account at pH 0. l-l .9, where the evaluation of the sulphate content is best. The use of two standards, at greater and lower sulphate concentration than that of the sample, is recommended when the ionic strength is unknown or cannot be kept constant. It is obvious from theoretical considerations that sulphate can be determined by this simple method without interference in the presence of all the halides and perhalates, carbonate, permanganate, sulphide and so on. Of the other common inorganic anions, phosphate, chromate and thiosulphate definitely interfere. In general, those bases with protonation constants (log K) outside the range log KS%- + 3 do not interfere, the others do. Ions with log K > 4.5 are protonated practically completely by the acid titrant before the sulphate is protonated, and nitrate and the other anions of very low basicity do not even begin to be protonated. Since SO:-, SrO:- and H,PO; are all protonated in a similar pH range, !I,@- and
seriously interfere. However, sulphate can still bc determined in the presence of ions of similar basicity by potentiometric mixture analysis, which is an improved version of this evaluation method.” Table 1 shows that even a single determination at one pH value (arbitrarily chosen) gives satisfactory results. Interfering ions can be detected by the use of the titration data for several pH-values. Accurate measurements in the absence of interferents give the same, pH-independent, analytical results from different points over a wide pH range. If the protonation properties of the interfering ions are not identical to those of sulphate, they will cause a definite pHdependence of the analytical data. The protonation constant of sulphate decreases with increase in ionic strength.* Accordingly, the lower the salt concentration in the titrated solution, the lower the concentration of sulphate that can be determined. Similarly, if the protonation of sulphate is promoted by a decrease in the dielectric constant of the medium (e.g., by use of a non-aqueous or partly aqueous solvent), the sensitivity of the method can be increased, by as much as two orders of magnitude. The classical gravimetric methods for sulphate determination are certainly more accurate and precise, but simplicity, cheapness and rapidity are advantageous characteristics of this titrimetric type of determination of sulphate (and other very weak bases and acids). H,PO;
REFERENCES 1.
W. J. Williams, Handbook of Anion Determination,
Butterworths, London, 1979. 2. G. Gran, Analyst, 1952, 77, 661. 3. A. Ivaska and I. Nagypal, Magy. Kern. Foly., 1980,&j, 84. 4. K. Burger, G. Pethis and B. No&l, Anal. Chim. Acta, 1980, 118, 93. 5. N. Bjerrum, Z. Anorg. Chem., 1921, 119, 179; J. Bjerrum, Metal Ammine Formation in Aqueous Solution, Haase, Copenhagen, 1941.
400
BELANam4~ and M~A
6. K. P. Ang, J. Chem. Sot., 1959, 3822. 7. I. Feldman and L. Koval, Inorg. Chem., 1963, 2, 145. 8. C. W. Davies, H. W. Jones and C. B. Monk, Trans. Faraaky Sot., 1952, 40, 921.
Jtiz
9. R. M. Smith and A. E. Martell, Critical Stability Const~fs, Vol. 4, Plenum Press, New York, London, 1977. 10. B. Nosti and M. Juhbz, in preparation.
Talanfa, Vol. 34, No. 4, pp. 397-400, 1987 Printed in Grest Britain. All rights re~rved
DETERMINATION
OF SULPHATE
BY pH TITRATION
B&A No!&L and m Jux-&z Department of Inorganic and Analytical base, L. E&v& University, 1088 Sudapest, Miueum krt. 4/B, Hungary (Received 20 August 1985. Revised 28 July 1986. Accepted 15 November 1986)
Smnmary-A simple and inexpensive method has been developed for the determination of sulphate and other very weak bases and acids. It utilizes the partial protonation of the weak base or the partial dissociation of the weak acid, which has not been exploited for analytical purposes thus far. The procedure consists of three pH titrations: one with a test solution of known sulphate content, the second with the sulphate sample, and the third with a blank. This method can be used in the presence of several inorganic ions and organic matrices, including non-aqueous solvents. In aqueous medium sulphate contents above 10m3Mcan be determined. The use of solvent mixtures may increase the sensitivity of the method by two orders of magnitude.
Most analytical methods for the determination of sulphate (gravimetry, chelatometry, potentiometry, cqnductometry, amperometry etc.) are based on the foliation of its barium or lead salts.’ Besides these, several classical or instrumental analytical methods have been developed in which organic reagents are used to form a sulphate precipitate. However, there is no report on the analytical exploitation of the equilibrium interaction between the sulphate and hydrogen ions. The obvious reason is the low basicity of sulphate, which does not allow its dete~ination by normal direct acidimetric tit~tion. Here a method, and its application to sulphate, will be introduced, which utilizes the partial protonation of very weak bases (or dissociation of fairly strong acids). The best known method for evaluating potentiometric titrations of weak bases and acids is the classical Gran plot.* Preconditions for its use are knowledge of the equilibrium constant valid under the given circumstances, and of the pH and the titrant concentration. The procedure of Ivaska and Nagyp;;i13 needs considerable mathematical apparatus, but can be used even for analysis of mixtures. The recent method by Burger et at.,’ based on measurement of the amount of bound reagent, applies when protonation or deprotonation is practically complete. The present method does not require knowledge of the equilibrium constant, the pH or the titrant concentration, and furthermore is satisfactory even if the reaction takes place only to the extent of 20-30%; thus it is suitable for the determination of very weak acids and bases.
co-ordination
chemistry?
The formation constant (B) for BH+ is:
Combining
(1) and (2) gives:
The equivalent relation for a polyacidic base (yielding BH;+ on complete protonation) is:
c &W+l’
i-0
Dissociation of acidr
The extent of dissociation of an acid HA is given by the function:
R=
M-1 IA- I + IHAl
which can be expressed in terms of [H+ ] and protonation constant of A-: Ram
l
1 + /3[H+l’
For a polybasic acid (H,A): m-1
m + C (m - i)B,[H+]
Protonation of bases
The proportion of the conjugated acid (HB+) formed in the protonation ~~lib~~ B f H+ *BH’ of a monoacidic base (B) can be calculated from the formation function well known in
It is a common property of (3) and (4) as well as of (6) and (7), that n’ and R depend only on the
397
398
BELA NOSZAL and M.&~A Jutisz
equilibrium constant and the hydrogen-ion activity, and are independent of the total (analytical) concentrations. Accordingly, 6 and R are intensive attributes of the material (acid or base) in question. Their actual value at a given pH are as characteristic of them in pH titrations as the molar absorption coefficient at a given wavelength is in spectrophotometry. Nevertheless, it does not make sense to introduce the term “molar protonation coefficients”, since the term A has long been familiar in equilibrium chemistry. Experimental determination of ii and
A
number of extra moles of acid number of moles of weak base ’
13 -
111*L(*
xi
12 -
5s I I I ;x + x
11 10 9-
; ? t :
",6 76-
d
xx x x x x x
*\ 0, .\
5-
::
43-
From (3), (4), (6) and (7), A and Rcan be calculated from the equilibrium constants and hydrogen-ion activities. However, the equilibrium constants are only valid for the ionic strength, temperature, medium and circumstances under which they were determined. Furthermore, they are subject to the experimental error of their determination, which is especially significant, when the glass electrode is used, at the pH values at which the weakest bases or acids are protonated or deprotonated (as the case may be). Moreover, there are several substances for which the protonation constants are not known (e.g., polypeptides, proteins, nucleic acids, compounds of unknown structure), or cannot even be determined unambiguously (for example in non-aqueous medium). Consequently their fi or R values cannot be calculated. More reliable and strictly valid fi or R values can be obtained by determinations made with a known amount of pure test substance. This can be done by two potentiometric titrations. In a blank titration sodium hydroxide (or simply water) is titrated potentiometrically with an acid titrant, and in the second titration an identical amount of hydroxide (or water) plus a known amount of weak base is titrated under the same conditions, to the same pH value. In this way the number of extra moles of titrant needed in the presence of the weak base, divided by the number of moles of weak base present, yields the g value: <=
14 _LL
(8)
Figure 1 shows three titration curves, where in each case sodium hydroxide was accompanied by a weak base, the bases differing in strength. It is remarkable that the strongest of these bases, cyanide, can be well determined, whereas the less basic acetate, even in high concentration, can only be determined with much ambiguity by traditional evaluation methods, owing to its incomplete protonation during the second pH “break”. The very weak base sulphate cannot be determined at all by simple evaluation methods, because it is only partially protonated, even at the lowest pH which can be reached by using 1M strong acid as the titrant. Nevertheless, from (8) and a third titration the number of moles of sulphate can be obtained from the measured extra number of moles
2l1IlIIIIIIII 0
12
3
45
6
7
691011
Fig. 1. Calculated titration curves for 5.0 of solution titrated with l.OM HCI. a. l.OM NaOH alone: b. l.OM NaOH +OSM K,SO,i c, l.OM NaOH +d.SM CH,COONa; d, l.OM NaOH + OSM KCN. The basicities of cyanide,6 acetate’ and sulphate* were taken from the literature values recommended by Martell and Smith.s
of titrant needed and previously determined fi data as a function of pH. It is recommended to use a high ionic strength medium (e.g., 2M sodium perchlorate) for all three titrations, to eliminate matrix effects. Determination of very weak acids can be done in an analogous manner by titrations with a base. EXPERIMENTAL We have developed a microtitration technique with a combined microelectrode suitable for pH determination in
an initial volume of 0.6-l .Oml. Accordingly, with 2.OM acid @-INOr, HCl, HClO,) as titrant, as little as 0.02 g of sodium sulphate can be determined. If the amount of sulphate in the sample is approximately known, it is recommended to use as similar an amount of reference material as possible for the A determination. Since different pH regions of the titration curves do not provide equally undistorted data, it is also advisable to check these A values against known amounts of sulphate in one or two preliminary experiments. Normally the best parts of the titration curves to use for the analysis are those where the protonation of sulphate is already significant (10% or more), but the titration curves have not yet become horizontal. The amount of analyte can be calculated most conveniently by means of the equation
4
MT=-mS
4
where mr and ms are the numbers of moles of sulphate in the test sample and the reference standard respectively, and DT and D, are the corresponding distances of their titration curves from the sulphate-free titration curve at a given pH. DT and D, can be measured in the same arbitrary units (ml or mm on a graph) since only their ratio is significant. Since the ratio D,/m, is a form of A, equation (9) is also a simple, practical derivative of equation (8). It can be seen that by means of this equation the determination of sulphate is reduced to measurement of the titrant volumes. For accurate measurements of small volumes and their differences a Radiometer ABU 12 automatic burette was used. All the potentiometric titrations were done by with use of an Orion Research 801-2 pH-meter with Ingold 104053059
Determination
399
of sulphate
Table 1. Experimental results for sulphate determinations under different conditions. A, B and C refer to the blank, standard and sample titration curves, respectively Number of titration
Sulphate taken, g/100 ml
Number of different pH values
Standard
Samule
Found,* g/100 ml
A
B
C
7.1021 7.1021 7.1021 2.8400 8.5700
8.5221 8.5221 7.8122 8.5206 11.6680
8.6, 8.3, 7.8, f 0.0, 8.4, f 0.2, 11.7,*0.1,
1
1 1
1 1 1
4.3760
8.5742
8.6, + 0.2,
1
1
1
10
1.2-1.55
4.3500 3.1188 4.9900
2.7250
2.6, + 0.1,
1
1
1
10
0.07-0.92
NaCl, 2M NaCl, 2M NaCl, 2M NaCIO,, 2M NaNO,, 2M NaOGCCH,, 0.12M > NaNO,, 2M NaNO,, 2M
3.7425
3.7, f 0.09
1
2
1
15
0.74-0.96
NaNO,, 2.63.1M
curves
1 1 1 1
1 1 1
1 9
1
10 10
1
Medium
PH 0.4 0.65 0.47-1.10 161.9 1.7-2.1
*Mean f 95% confidence limits.
combined electrode. The method requires neither temperature-control nor calibration of the cell, but the A determination and the analytical measurements have to be made under strictly identical conditions. For approximate pH standardization, Radiometer pH 7.0 buffer was used. All the chemicals were of analytical-reagent grade (Reanal, Hungary) and used without further purification. RESULTS AND DISCUSSION
It can be seen in Fig. 1, that the sulphate and blank titration curves are identical above pH 3, owing to the negligible protonation of the sulphate, so this part of the titration is of no value for our purpose. Table 1 shows experimental results for determination of sulphate in the presence of accompanying electrolytes at high concentrations. It can be seen that the sulphate determination is feasible in solutions of not only the less basic chloride, nitrate and perchlorate ions, but also in the presence of the significantly more basic acetate (and of course hydroxide) ions. Since the acetate protonation is more than 99% complete below pH 2.7, this effect can be quantitatively taken into account at pH 0. l-l .9, where the evaluation of the sulphate content is best. The use of two standards, at greater and lower sulphate concentration than that of the sample, is recommended when the ionic strength is unknown or cannot be kept constant. It is obvious from theoretical considerations that sulphate can be determined by this simple method without interference in the presence of all the halides and perhalates, carbonate, permanganate, sulphide and so on. Of the other common inorganic anions, phosphate, chromate and thiosulphate definitely interfere. In general, those bases with protonation constants (log K) outside the range log KS%- + 3 do not interfere, the others do. Ions with log K > 4.5 are protonated practically completely by the acid titrant before the sulphate is protonated, and nitrate and the other anions of very low basicity do not even begin to be protonated. Since SO:-, SrO:- and H,PO; are all protonated in a similar pH range, !I,@- and
seriously interfere. However, sulphate can still bc determined in the presence of ions of similar basicity by potentiometric mixture analysis, which is an improved version of this evaluation method.” Table 1 shows that even a single determination at one pH value (arbitrarily chosen) gives satisfactory results. Interfering ions can be detected by the use of the titration data for several pH-values. Accurate measurements in the absence of interferents give the same, pH-independent, analytical results from different points over a wide pH range. If the protonation properties of the interfering ions are not identical to those of sulphate, they will cause a definite pHdependence of the analytical data. The protonation constant of sulphate decreases with increase in ionic strength.* Accordingly, the lower the salt concentration in the titrated solution, the lower the concentration of sulphate that can be determined. Similarly, if the protonation of sulphate is promoted by a decrease in the dielectric constant of the medium (e.g., by use of a non-aqueous or partly aqueous solvent), the sensitivity of the method can be increased, by as much as two orders of magnitude. The classical gravimetric methods for sulphate determination are certainly more accurate and precise, but simplicity, cheapness and rapidity are advantageous characteristics of this titrimetric type of determination of sulphate (and other very weak bases and acids). H,PO;
REFERENCES 1.
W. J. Williams, Handbook of Anion Determination,
Butterworths, London, 1979. 2. G. Gran, Analyst, 1952, 77, 661. 3. A. Ivaska and I. Nagypal, Magy. Kern. Foly., 1980,&j, 84. 4. K. Burger, G. Pethis and B. No&l, Anal. Chim. Acta, 1980, 118, 93. 5. N. Bjerrum, Z. Anorg. Chem., 1921, 119, 179; J. Bjerrum, Metal Ammine Formation in Aqueous Solution, Haase, Copenhagen, 1941.
400
BELANam4~ and M~A
6. K. P. Ang, J. Chem. Sot., 1959, 3822. 7. I. Feldman and L. Koval, Inorg. Chem., 1963, 2, 145. 8. C. W. Davies, H. W. Jones and C. B. Monk, Trans. Faraaky Sot., 1952, 40, 921.
Jtiz
9. R. M. Smith and A. E. Martell, Critical Stability Const~fs, Vol. 4, Plenum Press, New York, London, 1977. 10. B. Nosti and M. Juhbz, in preparation.