- Email: [email protected]
Hydroxide complexes of cerium(III)
Talente, Vol. 25, pp 147-150.Pergamon Prss, 1978.Prmtedin GreatBritain
HYDROXIDE
COMPLEXES J.
OF CERIUM(II1)
KRAGTEN
Physical Laboratory, Valckeniersstraat 65, University of Amsterdam, Amsterdam, The Netherlands and L. G. DECNOP-WEEVER Laboratory for Analytical Chemistry, Nieuwe Achtergracht 166, University of Amsterdam, Amsterdam, The Netherlands (Received 20 June 1977. Revised 3 October 1977. Accepted 18 October 1977)
Summary-From the experimentally determined borderline of precipitation in the phi-pH diagram, the stability constants of the mononuclear and polynuclear species of cerium hydroxide have been determined graphically. The stability constants found are log*b, = - 8.1, log*/?, = - 16.3, log*& = -26.0, log*/&, = -32.8 and log*& = 20.1. These values refer to freshly prepared precipitates, at room temperature and an ionic strength of 1, and are precise to about 0.2 log units.
The behaviour of Ce3+ ions in aqueous solution is of increasing interest because cerium(II1) is an excellent back-titrant in complexometry, with Xylenol Orange as indicator, especially for titrations at low concentration levels. For selection of optimum conditions for these titrations insight into cerium-hydroxide complex formation is necessary. Limited reliable information about the hydrolysis of Ce3+ ions and precipitation of cerium hydroxide is available. Moeller’ investigated the composition and stability of the hydroxide complexes in 0.01-0.3&f cerous sulphate. He supposed CeOH’+ to be formed, the stability constant being log*B, = -9.0. Biedermann and Newman’ measured the pH change in a series of cerous perchlorate solutions (concentration range 0.05-1M; medium 3M perchlorate) when the hydrogen ions were reduced electrochemically by constant-current coulometry. They found strong evidence for the formation of Ce,(OH}z+ with stability constant log*/?,,, = - 35.7 at the pH just before the start of precipitation. Stepanov and Shvedov3 investigated the hydrolysis of cerous nitrate solutions at low concentrations (10-4-10-6M) by studying the electromigration of radioactive tracers. From the dependence of the migration on pH in the range 2-5 it was deduced that mononuclear hydroxide complexes predominate in acid solutions at pCe > 5. Although it was suggested that at low pH polynuclear complexes are formed at slightly higher concentrations, definite conclusions cannot be drawn from their experiments. Buchenko et ~1.~ studied the hydrolysis of cerous sulphate solutions (3.7 x 10e4 and 9.75 x 10w4M) by means of an oscillopolarographic method. Cerium(II1) hydroxide was precipitated in the pH range 6-7.6; a value of 19.1 was obtained for log*& (extrapolated to I = 0). The identity of the soluble hydroxide complexes was not investigated. 147
Kumok and Serebrennikov’ proposed the relationship log*K,,, = a log*&, + b, and tabulated a and b for the lanthanide cations. Baes and Mesmer’j applied this relationship to Ce(II1) and calculated log*K, = -8.3 (I = 0), - 8.6 (I = 0.05) and -9.7 (I = 3). The solubility product of Ce(II1) hydroxide is also given as log*K,e = 19.9 (I = 0). Up till now there is no information about the stability of Ce(OH): and higher hydroxides and the solubility of Ce(OH),(s) over the pH range 6-14 has not been determined. Kragten7 showed that the borderline of precipitation in a pM’-pH diagram can be considered as composed of separate straight-line segments, each holding for a distinct pH region in which a specific hydroxide species predominates. When this theory is applied to an experimentally determined borderline, in principle the identity and stability constants of the various hydroxide species can be determined. In this paper the application to the precipitation of cerium(II1) hydroxide will be described. THEORY
The stability constant of the complex M,(OH), be defined according to IUPAC notation as
can
(note the reversal of p and q). If this complex predominates, the following equation can be derived for the a-coefficient for the side-reaction of the metal ion with hydroxide:‘,s
1%%(OH)=
108*/t&p + 108P
0 I ;
pH+
P
J.
148
KRAGTEN
and L. G.
DECNOP-WEEVER
Table 1. Initial Ce(II1) concentration
where [M’] is the total concentration of the metal present in solution. For a given [M’] every complex Cp,q)gives rise to a straight line on the log CIvs. pH diagram. The maximum solubility of M(OH),(aq) in equilibrium with its precipitate may be expressed as
CWOW,l,,, = *Km= *Bn~*Kso.
(2)
Final pCe’
Initial pCe’
O-O.4 0.4-0.75 0.75-2.0 1.0-3.0 2.1-6.0 >5.0
0 0.3 0.7 1.0 2.0 3.0
Combined with
*B = CMWMCHI” n CM”‘1
and -CM’1 = [M”+] %(OH)
this leads to the following formula for the borderline of the precipitation region: pM&
= -log*&
+ npH -
logcc,,,)
(3)
Substitution of (1) in (3) finally gives the general formula for the straight-line approximation to the borderline of precipitation: PM;,, = (np-q)pH - (P log*&
+ log*&,, + log P) (4)
The different (p,q) combinations lead to a set of straight lines in the pM’-pH diagram. The true curve is the envelope of the line segments corresponding to the lowest pM’ values. When the precipitation region in the pM’-pH diagram has been experimentally established, the straight-line segments, each with its distinct slope (nq - q), can be shifted so that the envelope curve fits the experimental points. From the final position of the lines the stability constants and probable composition of the hydroxide complexes can be deduced. EXPERIMENTAL
The experiments were done with cerous nitrate in 1M perchlorate as indifferent medium under constant ionic strength conditions. The tervalent form is the stable oxidation state of cerium in solution. A cerous hydroxide precipitate, once formed, becomes easily oxidized to the yellowish CeO,.nH,O when exposed to the air. This process lowers the pH, as-it gives rise-to the formation of hydrogen ions. There is also evidence that the solution absorbs COs, with further release of HsO+ ions. In order to prevent these phenomena all experiments were performed under nitrogen. It is difficult to define a state of equilibrium adequate for practical applications where formation of a metal hydroxide precipitate in contact with solution is concerned. Typical phenomena obscuring the equilibrium are supersaturation, dependence of the solubility on particle size, slow reactions in dilute solution and recrystallization. The first two phenomena are especially important in studies of the lanthanides. Our experiments were done with unbuffered solutions and although only very small amounts of HsO’ ions were released in comparison with the amount of precipitate present, the phenomena mentioned could cause a shift of several pH units because the system was near neutrality (pH 7), resulting in a non-equilibrium situation. The reaction proceeds to equilibrium very slowly or not at all. It was found that reproducibility of the results improved remarkably when they were obtained under “fresh precipitate” conditions. To what extent we were then dealing with equilibrium conditions is of minor importance.
Reproducible and comparable circumstances for precipitation over the whole pH region of interest (pH 612) were achieved in the following way. 1. The ionic strength was kept constant at 1 (within a few per cent). 2. The initial Ce(II1) concentration was matched to the final pCe’ values to limit the amount of precipitate formed (see Table 1). 3. The precipitate was removed from solution after about 30 min by filtration (Schleicher and Schiill, Blue-Band paper no. 589/3). The adsorption of Ce(II1) on this paper has been tested and found to be less than 5 x lo-‘M. Apparatus
Precipitation and filtration were done in a glove-box flushed with nitrogen at a rate of 0.2-0.5 l./sec, starting at least 1 hr beforehand. Procedure
A 50% sodium hydroxide solution was added dropwise to 200-300 ml of cerous nitrate solution (in 1M perchloric acid) with vigorous stirring, until a pH of 1 was reached. Then dilute alkali was added carefully until precipitation just began. About 25 ml of the solution were removed and dilute alkali was added to the remaining solution until the pH had increased by about 0.2. This step was then repeated until the desired pH range had been covered. After being aged for about 30 min all the fractions were filtered and the pH of the filtrates was determined. Finally the pH of the filtrates was adjusted to 1 with 5M perchloric acid. pCe’ was determined by complexometric titration, with Xylenol Orange as indicator. Filtrates with cerium concentrations >10W4M were diluted (with O.OlM perchloric acid), so that the metal ion concentration was 10-4-10-5M. Then 5-ml portions of the solution were placed in the titration cell, 1 ml of the indicator solution (10m4M, pH 2) and 5 ml of the buffer solution (0.5M hexamine, pH 5.8) were added, and the solution was titrated with 10m4M EDTA at a wavelength of 575 mn.
RESULTS AND CONCLUSIONS
The experimental results are presented as points in Fig. 1. The slope of the nearly straight part in the region pH 7.12-7.75 and pCe’ 0.74-3.11 has been determined by regression analysis; a value of 4.0 (kO.2) was found. The theoretical value of the slope being (npq), it can be concluded that either Ce,(OH)$+ or Ce,(OH)i+ predominates in this region. The formation of higher complexes such as Ce,(OH)i+ and Ce,(OH):: is most unlikely.* If only Ce,(OH), and/or Ce,(OH)‘:+ are present, the following system of linear equations, representing a set of lines in the pM’-pH diagram, can be introduced (Table 2).
149
Hydroxide complexes of cerium(II1)
6 5 P$
10 11 12 13 PH Fig. 1. The region of Ce(OH), precipitation (solid curve), the region for the Ce,(OH)t+ complex (dashed curve) and the experimentally determined points. The curves are constants constructed with the 1og*p, = -8.1; log*p, = - 16.3; log*/& = -26.0; log */I4 = -38.0; log*&, = -32.8; log*& = 20.1. The straight lines 0, 1, 2, 3 and 4 relate to the approximation of the borderline of precipitation [equations (4f), (4e), (4d), (4c), (4b) respectively]. The numbering gives the slope of the lines. 5
6
7
6
9
The experimental points in Fig. 1 corresponding to concentrations below pCe’ = 0.74 obviously deviate from the best fit with slope 4. This is evidently caused by the high ionic strengths (I = 47), at which precipitate formation necessarily has to take place. These points are not taken into consideration, as theoretical corrections can only be made qualitatively. From our experimental results it directly follows that
(1) the extrapolated steep part of the precipitation borderline intersects the pH axis at pH = 7.0; substitution of this value in the straight-line formulae (4b) and (4a) gives: 3 log*Z& + log*/?,,3 = 27.5
(5)
2log*&
(6)
and + log*&,
= 27.7
(2) from the horizontal part of the precipitation curve in the pH region 10.2-11.5 a mean value of pCe’ = 5.9 + 0.15 can be estimated. Substitution in equation (4f) leads to: log*K,, = 1og*Z& + log*/& = -5.9
It will be clear that the lines with slopes of 0 and 4 certainly contribute to the envelope. As a first approximation, straight lines with definite slopes of 1,2 and 3 can be drawn as tangents to the experimental curve. The line with slope 1 definitely contributes to the envelope. This line intersects the horizontal line at pM’ = 5.9 [equation (7)]. Substituting the pH value of this point of intersection in equation (4e) and using (7) gives the value for log*K, (=log*/3, - 1og*fi.J. In principle, from the points of intersection of the other lines-l and 2, 2 and 3, respectively-we can obtain values for log*Kz and log*Kr. In this area the points of intersection are close together; the different mono-complexes all contribute to the envelope. The straight lines must be shifted upwards+compared with the true tangents-about 0.25 units, as otherwise the exactly calculated envelope will lie too low. The line with slope 2 contributes in a small region (see Fig. 1) and log*K2 (=log*& - log*/?,) can be deduced from equations (4d) and (4e) by substitution of the pH value of the point of intersection. The line with slope 3 may also contribute to the envelope and must be placed to the left of the point of intersection of the lines with slopes 2 and 1, corresponding to equations (4d) and (4e). If the line with slope 3 is placed to the right of the position indicated in Fig. 1, it will certainly contribute to the envelope, which will then change its shape and no longer give the best fit to the experimental points. If the line is chosen left of the position indicated in Fig. 1, it does not contribute to the envelope. The position in Fig. 1 can be regarded as an extreme position. It suggests that a minimum value of -8.1 for log*/I, is reasonable. It is generally agreed by Biedermann and Newman’ and many others that polycomplexes of Ce(II1) are formed only in a small re&on just before precipitation starts. Support for fixing log*/Z,, at -8.1 is given by the fact that this value minimizes the area of polycomplex formation. We introduce the 1% polycomplex borderline’ as a measure for defining the extent of the polycomplex region. The following equations can be derived for the straight-line approximation to the steep left-handside of this region, concerning the two possible Ce(II1) polycomplexes: PM;J = 2pH + log*&,
(7)
+ 2.3
Table 2. Equation
p
4
4a 4b 4c 4d 4e 4f
2 3 1 1 1 1
2 5 0 1 2 3
Slope Wq) 4 4 3 2 1
0
PM’ = 4 pH - (2 log*&, + log*/?,,, + 0.3) PM’ = 4 pH - (3 log*& + log*& + 0.5) pM’ pM’ PM’ PM’
= = = =
3 pH - log*&,, 2 pH - (log*& + log*&) pH - (log*& -I- log*/?,) -log*& = -(log*& + log*&)
(8)
J. KRAGTEN and L. G. DECNOP-WEEVER
150
and pM;,s = 2.5 pH + 3 (log*/!?,,, + 2.5)
(9)
When log*p, is assumed to be less negative it can be proved easily, by using equations (5x7), that log*/& and log*&3 become less negative, which according to equations (8) and (9) shifts the corresponding polycomplex borderlines to lower pH values, thus increasing the polycomplex region. This is not consistent with a minimum region of polycomplexation, so again we may assume log*j, = -8.1. From the graphically estimated values the envelope has been calculated by a computer program. Some minor adjustments turned out to be necessary. (This program is available on request.) The following values can be regarded as giving the best fit: log*,!l, = -8.1 log*/& = -16.3
log*/_?,= -26.0 log*& = 20.1
and log*/&, = - 12.4 or log*fl,,, = - 32.8, depending on which species prevails. Substitution of the appropriate values in (8) and (9) gives two borderlines, of which that for Ce,(OH)i+ leads to the smallest polycomplex region. It makes Ce,(OH):+ the more likely of the two to be present in solution, in agreement with the evidence of Biedermann and Newman.’ Baes and Mesmer6 reported the possibility of the formation of M(OH); hydroxides when various lanthanide hydroxides dissolve in concentrated sodium hydroxide solution. In the case of Ce(II1) no data have been reported for *p4, As we did not observe an increase in solubility below pH = 12, we can only state that log *K4 < - 12. DISCUSSION
The accuracy of the calculated constants can be assessed only qualitatively. The error in log*Ks3 (7) may be taken as equal to the standard deviation of the horizontal part of the approximated precipitation curve: S,, = 0.15. When all the approximated straight lines are shifted by such a distance, the points of intersection also shift. The resulting uncertainty in the constants can be estimated to be about kO.2 units in this way, except for logfi,,, for which the uncertainty is about +l unit. Another approach to the determination of the stability constants uses matrix calculus. Formulae (4d), (4e), (4f) and (4b) can be written as a system of four linear equations with */?r, */12, *p3 and *&3 as the unknown variables and *KS0 as the independent variable. This system has also been solved by standard numerical methods. In this way we found for the best fit: log*K,e = 20.1; log*/?, = -8.2; log*/?, = - 16.4; log*/?, = -26.3 and log*/?,,, = -32.8, in good agreement with the values found graphically. When the pCe’ values of the experimental points are changed by kO.15, the logarithms of the constants
vary by up to 50.2, which agrees with the graphically estimated uncertainty. For a comparison of our constants with values reported by other investigators, the constants should be referred to the same ionic strength. This can be done in principle by using the equations of Pitzer and Brewer.’ However, as the values for the interaction coefficient Bc,x (X = anion) are not available, only approximate corrections can be calculated. Moeller’ neglected the interaction of Ce(III) ions with sulphate and his value of log*/I, may be regarded as too low for this reason. Stepanov and Shvedov3 reported log*fl, = -4.3 (I = 0.005) a value much higher than those found by other investigators for lanthanide hydroxides. The statistical method of Kumok and Serebrennikov’ used by Baes and Mesmer6 results in values for log*p,, which are in agreement with those of Moeller. The statistical method is based on the use of log*/I, values of lanthanides with a great variety of ligands other than OH-; the compilation by Baes and Mesmer seems reliable. Our values for log*b, = 8.1 (I = 1) and log*b,,, = -32.8 f 1 (I = 1) fit very well in this compi1ation.2~6 Small differences can be attributed to different working conditions; the determinations by Biedermann and Newman took 12-15 hr, for instance. Correcting our value for log*KsO by using the formulae of Pitzer and Brewer’ we obtain log*KsO = 21.0 (I = 0). This value does not agree well with that obtained by Buchenko et a1.,4 but these authors kept the heterogeneous system for 24 hr at room temperature, before the filtration. The higher value found by us is in agreement with the fact that fresh precipitates consist of relatively fine particles, for which log*KsO will be higher, compared with aged precipitates. Finally we conclude that, in so far as our constants were comparable to those found in the literature, the agreement is sufficiently good. The method described in this paper seems very promising for the determination of the hydrolysis constants of lanthanides under “freshly precipitated” conditions. Further experiments are in preparation for the other lanthanides. REFERENCES 1. T. Moeller, J. Phys. Cheat., 1946, 50, 242. 2. G. Biedermann and L. Newman, Arkiu Kemi, 1964, 22, 303. and V. P. Shvedov, Russ. J. Inorg. 3. A. V. Stepanov Chem., 1965, 10,541. and M. M. Evstifeev, 4. L. I. Buchenko. P. N. Kovalenko ibid., 1970, 15, 1666. ibid., 1965. 5. V. N. Kumok and V. V. Serebrennikov. 10, 1095. The Hydrolysis of 6. C. F. Baes and R. E. Mesmer, Cations. Wilev-Interscience, New York, 1976. I. J. Kragten, Z%anta 1977, 24, 483. in AnalyticaI Chemistry, In8. A. Ringbom, Complexation terscience, New York, 1963. 9. K. S. Pitzer and L. Brewer, Thermodynamics, (G. N. Lewis and M. Randall revised edition), McGraw-Hill, New York, 1961.
HYDROXIDE
COMPLEXES J.
OF CERIUM(II1)
KRAGTEN
Physical Laboratory, Valckeniersstraat 65, University of Amsterdam, Amsterdam, The Netherlands and L. G. DECNOP-WEEVER Laboratory for Analytical Chemistry, Nieuwe Achtergracht 166, University of Amsterdam, Amsterdam, The Netherlands (Received 20 June 1977. Revised 3 October 1977. Accepted 18 October 1977)
Summary-From the experimentally determined borderline of precipitation in the phi-pH diagram, the stability constants of the mononuclear and polynuclear species of cerium hydroxide have been determined graphically. The stability constants found are log*b, = - 8.1, log*/?, = - 16.3, log*& = -26.0, log*/&, = -32.8 and log*& = 20.1. These values refer to freshly prepared precipitates, at room temperature and an ionic strength of 1, and are precise to about 0.2 log units.
The behaviour of Ce3+ ions in aqueous solution is of increasing interest because cerium(II1) is an excellent back-titrant in complexometry, with Xylenol Orange as indicator, especially for titrations at low concentration levels. For selection of optimum conditions for these titrations insight into cerium-hydroxide complex formation is necessary. Limited reliable information about the hydrolysis of Ce3+ ions and precipitation of cerium hydroxide is available. Moeller’ investigated the composition and stability of the hydroxide complexes in 0.01-0.3&f cerous sulphate. He supposed CeOH’+ to be formed, the stability constant being log*B, = -9.0. Biedermann and Newman’ measured the pH change in a series of cerous perchlorate solutions (concentration range 0.05-1M; medium 3M perchlorate) when the hydrogen ions were reduced electrochemically by constant-current coulometry. They found strong evidence for the formation of Ce,(OH}z+ with stability constant log*/?,,, = - 35.7 at the pH just before the start of precipitation. Stepanov and Shvedov3 investigated the hydrolysis of cerous nitrate solutions at low concentrations (10-4-10-6M) by studying the electromigration of radioactive tracers. From the dependence of the migration on pH in the range 2-5 it was deduced that mononuclear hydroxide complexes predominate in acid solutions at pCe > 5. Although it was suggested that at low pH polynuclear complexes are formed at slightly higher concentrations, definite conclusions cannot be drawn from their experiments. Buchenko et ~1.~ studied the hydrolysis of cerous sulphate solutions (3.7 x 10e4 and 9.75 x 10w4M) by means of an oscillopolarographic method. Cerium(II1) hydroxide was precipitated in the pH range 6-7.6; a value of 19.1 was obtained for log*& (extrapolated to I = 0). The identity of the soluble hydroxide complexes was not investigated. 147
Kumok and Serebrennikov’ proposed the relationship log*K,,, = a log*&, + b, and tabulated a and b for the lanthanide cations. Baes and Mesmer’j applied this relationship to Ce(II1) and calculated log*K, = -8.3 (I = 0), - 8.6 (I = 0.05) and -9.7 (I = 3). The solubility product of Ce(II1) hydroxide is also given as log*K,e = 19.9 (I = 0). Up till now there is no information about the stability of Ce(OH): and higher hydroxides and the solubility of Ce(OH),(s) over the pH range 6-14 has not been determined. Kragten7 showed that the borderline of precipitation in a pM’-pH diagram can be considered as composed of separate straight-line segments, each holding for a distinct pH region in which a specific hydroxide species predominates. When this theory is applied to an experimentally determined borderline, in principle the identity and stability constants of the various hydroxide species can be determined. In this paper the application to the precipitation of cerium(II1) hydroxide will be described. THEORY
The stability constant of the complex M,(OH), be defined according to IUPAC notation as
can
(note the reversal of p and q). If this complex predominates, the following equation can be derived for the a-coefficient for the side-reaction of the metal ion with hydroxide:‘,s
1%%(OH)=
108*/t&p + 108P
0 I ;
pH+
P
J.
148
KRAGTEN
and L. G.
DECNOP-WEEVER
Table 1. Initial Ce(II1) concentration
where [M’] is the total concentration of the metal present in solution. For a given [M’] every complex Cp,q)gives rise to a straight line on the log CIvs. pH diagram. The maximum solubility of M(OH),(aq) in equilibrium with its precipitate may be expressed as
CWOW,l,,, = *Km= *Bn~*Kso.
(2)
Final pCe’
Initial pCe’
O-O.4 0.4-0.75 0.75-2.0 1.0-3.0 2.1-6.0 >5.0
0 0.3 0.7 1.0 2.0 3.0
Combined with
*B = CMWMCHI” n CM”‘1
and -CM’1 = [M”+] %(OH)
this leads to the following formula for the borderline of the precipitation region: pM&
= -log*&
+ npH -
logcc,,,)
(3)
Substitution of (1) in (3) finally gives the general formula for the straight-line approximation to the borderline of precipitation: PM;,, = (np-q)pH - (P log*&
+ log*&,, + log P) (4)
The different (p,q) combinations lead to a set of straight lines in the pM’-pH diagram. The true curve is the envelope of the line segments corresponding to the lowest pM’ values. When the precipitation region in the pM’-pH diagram has been experimentally established, the straight-line segments, each with its distinct slope (nq - q), can be shifted so that the envelope curve fits the experimental points. From the final position of the lines the stability constants and probable composition of the hydroxide complexes can be deduced. EXPERIMENTAL
The experiments were done with cerous nitrate in 1M perchlorate as indifferent medium under constant ionic strength conditions. The tervalent form is the stable oxidation state of cerium in solution. A cerous hydroxide precipitate, once formed, becomes easily oxidized to the yellowish CeO,.nH,O when exposed to the air. This process lowers the pH, as-it gives rise-to the formation of hydrogen ions. There is also evidence that the solution absorbs COs, with further release of HsO+ ions. In order to prevent these phenomena all experiments were performed under nitrogen. It is difficult to define a state of equilibrium adequate for practical applications where formation of a metal hydroxide precipitate in contact with solution is concerned. Typical phenomena obscuring the equilibrium are supersaturation, dependence of the solubility on particle size, slow reactions in dilute solution and recrystallization. The first two phenomena are especially important in studies of the lanthanides. Our experiments were done with unbuffered solutions and although only very small amounts of HsO’ ions were released in comparison with the amount of precipitate present, the phenomena mentioned could cause a shift of several pH units because the system was near neutrality (pH 7), resulting in a non-equilibrium situation. The reaction proceeds to equilibrium very slowly or not at all. It was found that reproducibility of the results improved remarkably when they were obtained under “fresh precipitate” conditions. To what extent we were then dealing with equilibrium conditions is of minor importance.
Reproducible and comparable circumstances for precipitation over the whole pH region of interest (pH 612) were achieved in the following way. 1. The ionic strength was kept constant at 1 (within a few per cent). 2. The initial Ce(II1) concentration was matched to the final pCe’ values to limit the amount of precipitate formed (see Table 1). 3. The precipitate was removed from solution after about 30 min by filtration (Schleicher and Schiill, Blue-Band paper no. 589/3). The adsorption of Ce(II1) on this paper has been tested and found to be less than 5 x lo-‘M. Apparatus
Precipitation and filtration were done in a glove-box flushed with nitrogen at a rate of 0.2-0.5 l./sec, starting at least 1 hr beforehand. Procedure
A 50% sodium hydroxide solution was added dropwise to 200-300 ml of cerous nitrate solution (in 1M perchloric acid) with vigorous stirring, until a pH of 1 was reached. Then dilute alkali was added carefully until precipitation just began. About 25 ml of the solution were removed and dilute alkali was added to the remaining solution until the pH had increased by about 0.2. This step was then repeated until the desired pH range had been covered. After being aged for about 30 min all the fractions were filtered and the pH of the filtrates was determined. Finally the pH of the filtrates was adjusted to 1 with 5M perchloric acid. pCe’ was determined by complexometric titration, with Xylenol Orange as indicator. Filtrates with cerium concentrations >10W4M were diluted (with O.OlM perchloric acid), so that the metal ion concentration was 10-4-10-5M. Then 5-ml portions of the solution were placed in the titration cell, 1 ml of the indicator solution (10m4M, pH 2) and 5 ml of the buffer solution (0.5M hexamine, pH 5.8) were added, and the solution was titrated with 10m4M EDTA at a wavelength of 575 mn.
RESULTS AND CONCLUSIONS
The experimental results are presented as points in Fig. 1. The slope of the nearly straight part in the region pH 7.12-7.75 and pCe’ 0.74-3.11 has been determined by regression analysis; a value of 4.0 (kO.2) was found. The theoretical value of the slope being (npq), it can be concluded that either Ce,(OH)$+ or Ce,(OH)i+ predominates in this region. The formation of higher complexes such as Ce,(OH)i+ and Ce,(OH):: is most unlikely.* If only Ce,(OH), and/or Ce,(OH)‘:+ are present, the following system of linear equations, representing a set of lines in the pM’-pH diagram, can be introduced (Table 2).
149
Hydroxide complexes of cerium(II1)
6 5 P$
10 11 12 13 PH Fig. 1. The region of Ce(OH), precipitation (solid curve), the region for the Ce,(OH)t+ complex (dashed curve) and the experimentally determined points. The curves are constants constructed with the 1og*p, = -8.1; log*p, = - 16.3; log*/& = -26.0; log */I4 = -38.0; log*&, = -32.8; log*& = 20.1. The straight lines 0, 1, 2, 3 and 4 relate to the approximation of the borderline of precipitation [equations (4f), (4e), (4d), (4c), (4b) respectively]. The numbering gives the slope of the lines. 5
6
7
6
9
The experimental points in Fig. 1 corresponding to concentrations below pCe’ = 0.74 obviously deviate from the best fit with slope 4. This is evidently caused by the high ionic strengths (I = 47), at which precipitate formation necessarily has to take place. These points are not taken into consideration, as theoretical corrections can only be made qualitatively. From our experimental results it directly follows that
(1) the extrapolated steep part of the precipitation borderline intersects the pH axis at pH = 7.0; substitution of this value in the straight-line formulae (4b) and (4a) gives: 3 log*Z& + log*/?,,3 = 27.5
(5)
2log*&
(6)
and + log*&,
= 27.7
(2) from the horizontal part of the precipitation curve in the pH region 10.2-11.5 a mean value of pCe’ = 5.9 + 0.15 can be estimated. Substitution in equation (4f) leads to: log*K,, = 1og*Z& + log*/& = -5.9
It will be clear that the lines with slopes of 0 and 4 certainly contribute to the envelope. As a first approximation, straight lines with definite slopes of 1,2 and 3 can be drawn as tangents to the experimental curve. The line with slope 1 definitely contributes to the envelope. This line intersects the horizontal line at pM’ = 5.9 [equation (7)]. Substituting the pH value of this point of intersection in equation (4e) and using (7) gives the value for log*K, (=log*/3, - 1og*fi.J. In principle, from the points of intersection of the other lines-l and 2, 2 and 3, respectively-we can obtain values for log*Kz and log*Kr. In this area the points of intersection are close together; the different mono-complexes all contribute to the envelope. The straight lines must be shifted upwards+compared with the true tangents-about 0.25 units, as otherwise the exactly calculated envelope will lie too low. The line with slope 2 contributes in a small region (see Fig. 1) and log*K2 (=log*& - log*/?,) can be deduced from equations (4d) and (4e) by substitution of the pH value of the point of intersection. The line with slope 3 may also contribute to the envelope and must be placed to the left of the point of intersection of the lines with slopes 2 and 1, corresponding to equations (4d) and (4e). If the line with slope 3 is placed to the right of the position indicated in Fig. 1, it will certainly contribute to the envelope, which will then change its shape and no longer give the best fit to the experimental points. If the line is chosen left of the position indicated in Fig. 1, it does not contribute to the envelope. The position in Fig. 1 can be regarded as an extreme position. It suggests that a minimum value of -8.1 for log*/I, is reasonable. It is generally agreed by Biedermann and Newman’ and many others that polycomplexes of Ce(II1) are formed only in a small re&on just before precipitation starts. Support for fixing log*/Z,, at -8.1 is given by the fact that this value minimizes the area of polycomplex formation. We introduce the 1% polycomplex borderline’ as a measure for defining the extent of the polycomplex region. The following equations can be derived for the straight-line approximation to the steep left-handside of this region, concerning the two possible Ce(II1) polycomplexes: PM;J = 2pH + log*&,
(7)
+ 2.3
Table 2. Equation
p
4
4a 4b 4c 4d 4e 4f
2 3 1 1 1 1
2 5 0 1 2 3
Slope Wq) 4 4 3 2 1
0
PM’ = 4 pH - (2 log*&, + log*/?,,, + 0.3) PM’ = 4 pH - (3 log*& + log*& + 0.5) pM’ pM’ PM’ PM’
= = = =
3 pH - log*&,, 2 pH - (log*& + log*&) pH - (log*& -I- log*/?,) -log*& = -(log*& + log*&)
(8)
J. KRAGTEN and L. G. DECNOP-WEEVER
150
and pM;,s = 2.5 pH + 3 (log*/!?,,, + 2.5)
(9)
When log*p, is assumed to be less negative it can be proved easily, by using equations (5x7), that log*/& and log*&3 become less negative, which according to equations (8) and (9) shifts the corresponding polycomplex borderlines to lower pH values, thus increasing the polycomplex region. This is not consistent with a minimum region of polycomplexation, so again we may assume log*j, = -8.1. From the graphically estimated values the envelope has been calculated by a computer program. Some minor adjustments turned out to be necessary. (This program is available on request.) The following values can be regarded as giving the best fit: log*,!l, = -8.1 log*/& = -16.3
log*/_?,= -26.0 log*& = 20.1
and log*/&, = - 12.4 or log*fl,,, = - 32.8, depending on which species prevails. Substitution of the appropriate values in (8) and (9) gives two borderlines, of which that for Ce,(OH)i+ leads to the smallest polycomplex region. It makes Ce,(OH):+ the more likely of the two to be present in solution, in agreement with the evidence of Biedermann and Newman.’ Baes and Mesmer6 reported the possibility of the formation of M(OH); hydroxides when various lanthanide hydroxides dissolve in concentrated sodium hydroxide solution. In the case of Ce(II1) no data have been reported for *p4, As we did not observe an increase in solubility below pH = 12, we can only state that log *K4 < - 12. DISCUSSION
The accuracy of the calculated constants can be assessed only qualitatively. The error in log*Ks3 (7) may be taken as equal to the standard deviation of the horizontal part of the approximated precipitation curve: S,, = 0.15. When all the approximated straight lines are shifted by such a distance, the points of intersection also shift. The resulting uncertainty in the constants can be estimated to be about kO.2 units in this way, except for logfi,,, for which the uncertainty is about +l unit. Another approach to the determination of the stability constants uses matrix calculus. Formulae (4d), (4e), (4f) and (4b) can be written as a system of four linear equations with */?r, */12, *p3 and *&3 as the unknown variables and *KS0 as the independent variable. This system has also been solved by standard numerical methods. In this way we found for the best fit: log*K,e = 20.1; log*/?, = -8.2; log*/?, = - 16.4; log*/?, = -26.3 and log*/?,,, = -32.8, in good agreement with the values found graphically. When the pCe’ values of the experimental points are changed by kO.15, the logarithms of the constants
vary by up to 50.2, which agrees with the graphically estimated uncertainty. For a comparison of our constants with values reported by other investigators, the constants should be referred to the same ionic strength. This can be done in principle by using the equations of Pitzer and Brewer.’ However, as the values for the interaction coefficient Bc,x (X = anion) are not available, only approximate corrections can be calculated. Moeller’ neglected the interaction of Ce(III) ions with sulphate and his value of log*/I, may be regarded as too low for this reason. Stepanov and Shvedov3 reported log*fl, = -4.3 (I = 0.005) a value much higher than those found by other investigators for lanthanide hydroxides. The statistical method of Kumok and Serebrennikov’ used by Baes and Mesmer6 results in values for log*p,, which are in agreement with those of Moeller. The statistical method is based on the use of log*/I, values of lanthanides with a great variety of ligands other than OH-; the compilation by Baes and Mesmer seems reliable. Our values for log*b, = 8.1 (I = 1) and log*b,,, = -32.8 f 1 (I = 1) fit very well in this compi1ation.2~6 Small differences can be attributed to different working conditions; the determinations by Biedermann and Newman took 12-15 hr, for instance. Correcting our value for log*KsO by using the formulae of Pitzer and Brewer’ we obtain log*KsO = 21.0 (I = 0). This value does not agree well with that obtained by Buchenko et a1.,4 but these authors kept the heterogeneous system for 24 hr at room temperature, before the filtration. The higher value found by us is in agreement with the fact that fresh precipitates consist of relatively fine particles, for which log*KsO will be higher, compared with aged precipitates. Finally we conclude that, in so far as our constants were comparable to those found in the literature, the agreement is sufficiently good. The method described in this paper seems very promising for the determination of the hydrolysis constants of lanthanides under “freshly precipitated” conditions. Further experiments are in preparation for the other lanthanides. REFERENCES 1. T. Moeller, J. Phys. Cheat., 1946, 50, 242. 2. G. Biedermann and L. Newman, Arkiu Kemi, 1964, 22, 303. and V. P. Shvedov, Russ. J. Inorg. 3. A. V. Stepanov Chem., 1965, 10,541. and M. M. Evstifeev, 4. L. I. Buchenko. P. N. Kovalenko ibid., 1970, 15, 1666. ibid., 1965. 5. V. N. Kumok and V. V. Serebrennikov. 10, 1095. The Hydrolysis of 6. C. F. Baes and R. E. Mesmer, Cations. Wilev-Interscience, New York, 1976. I. J. Kragten, Z%anta 1977, 24, 483. in AnalyticaI Chemistry, In8. A. Ringbom, Complexation terscience, New York, 1963. 9. K. S. Pitzer and L. Brewer, Thermodynamics, (G. N. Lewis and M. Randall revised edition), McGraw-Hill, New York, 1961.