THE THERMODYNAMIC PROPERTIES OF NEODYMIUM HYDROXIDE IN
ACID, NEUTRAL, AND ALKALINE SOLUTIONS AT 25°C.: AN
INTERPRETATION OF THE IONIC SPECIES PRESENT IN
AQUEOUS SOLUTIONS OF NEODYMIUM SALTS
DISSERTATION
Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University
By
RUSSELL STUART TOBIAS, B. Sc.
4 \ «V St i't
The Ohio State University 1956
Approved by:
Adviser Department! of Chemistry AC KNOWLEDGEMENT
The author wishes to express his sincere appreciation to Professor A. B. Garrett for his encouragement and counsel during the course of this investigation. I also wish to thank him for his interest in my welfare while I have been a student at The Ohio State University. I also wish to thank The Ohio State University for the assistant ship granted to me and the Visking Corporation, the General
Electric Corporation, E. I. du Pont de Nemours and Company, and the Allied Chemical and Dye Company for financial assistance during the course of my studies.
Finally, I would like to acknowledge the assistance of Mr. G. W. Leddicotte, of the Oak Ridge National Labora tory, who performed the activation analyses described in this work. TABLE OF CONTENTS
Subject Page
INTRODUCTION ...... 1
HISTORICAL REVIEW ...... 3
The Basicity of the Rare Earth Oxides ...... 3
The System Neodymium Oxide-Water ...... 4
The Hydrolysis of Neodymium Solutions ...... 9
The Analyses of Solutions of Neodymium ...... 11
EXPERIMENTAL . .. 18
General Procedure ...... 18
Preparation of the Reagents ...... 18
Neodymium Oxide ...... 18
Hydrochloric Acid Solutions ...... 20
Sodium Hydroxide Solutions ...... 20
Perchloric Acid Solutions ...... 21
Neodymium and Praseodymium Perchlorate Buffers 22
Sodium Chloride Solutions ...... 22
Sodium Perchlorate Solutions ...... 22
Distilled Water ...... 23
Hydrolysis Studies ...... 23
Experimental Method ...... 23
Electrochemical Cells ...... 25
Electrical Circuits ...... 34
Details of the Experimental Procedure ...... 37
Analysis of the Free Acid Concentration of
the Rare Earth Buffers ...... 4 1 iii TABLE OF CONTENTS (Cont'd.)
Solubility Studies ...... 42
Preparation of Samples ...... 42
Equilibration ...... 43
Sedimentation ...... 44
Transfer of the Solutions for Analysis ...... 44
Measurement of the Hydrogen Ion Concentration . 46
Spectrophotometric Analyses ...... 47
Activation Analyses ...... 55
Analysis of the Solid Phase in theEquilibria . 56
THE DATA .... a ...... 65
AN ANALYSIS OF THE DATA OBTAINED FROM THE DISSOLUTION
OF METALLIC HYDROXIDES IN DILUTE ACIDS AND FROM A
STUDY OF THE RESULTING EQUILIBRIA ...... 104
AN ANALYSIS OF THE DATA OBTAINED FROM THE DISSOLUTION
OF METALLIC HYDROXIDES IN BASIC SOLUTION AND FROM
THE WATER SOLUBILITY ...... 125
AN ANALYSIS OF THE EXPERIMENTAL DATA FOR NEODYMIUM
HYDROXIDE ...... 129
Equilibria with Hydrochloric Acid...... 129
Equilibria with Perchloric A c i d ...... 147
Equilibria with Water and with Sodium Hydroxide
Solutions ...... 148
Hydrolysis of the Tri-valent cations of Neodymium
and Praseodymium ...... 154
CONCLUSIONS...... 166 iv LIST OP TABLES
Table Page
1. A Comparison of the E.M.F. of the Glass and
Quinhydrone Electrodes in the Presence of 0.01
C Pr+3 ...... 32
2. A Comparison of the E.M.P. of the Glass and
Q,uinhydrone Electrodes in the Presence of 0.025 C
Nd+3 ...... 33
3. Powder Photograph Data for the Water Equilibrated
Sample of Neodymium Oxide ...... 61
4. Powder Photograph Data for the Anhydrous Oxide
of N e o d y m i u m ...... 63
5. Hydrolysis of Neodymium Perchlorate, c » 24.45 mC,
Standardization of Electrodes ...... 66
6. Hydrolysis of Neodymium Perchlorate, c = 24.45 mC,
Titration of Buffer Solution ...... 67
7. Hydrolysis of Neodymium Perchlorate, c = 24.45 mC,
Calculation of Average Ligand Number ...... 68
8. Hydrolysis of Neodymium Perchlorate, c = 9.79 mC,
Standardization of Electrodes ...... 70
9. Hydrolysis of Neodymium Perchlorate, c » 9.79 mC,
Titration of Buffer Solution ...... 71
10. Hydrolysis of Neodymium Perchlorate, c = 9.79 mC,
Calculation of Average Ligand Number ...... 72
11. Hydrolysis of Neodymium Perchlorate, c ** 4.895 mC, Standardization of Electrodes ...... 73 v /
LIST OP TABLES (Cont'd.)
12. Hydrolysis of Neodymium Perchlorate, c = 4.895 mC,
Titration of Buffer Solution ...... 74
13. Hydrolysis of Neodymium Perchlorate, c = 4.895 mC,
Calculation of Average Ligand Number ...... 75
14. Hydrolysis of Praseodymium Perchlorate, c = 25.00 mC,
Standardization of Electrodes ...... 78
15. Hydrolysis of Praseodymium Perchlorate, c = 25.00 mC,
Titration of Buffer Solution ...... 79
16. Hydrolysis of Praseodymium Perchlorate, c = 25.00 mC,
Calculation of Average Ligand Number ...... 81
17. Hydrolysis of Praseodymium Perchlorate, c = 12.50 mC,
Standardization of E l e c t r o d e s ...... 83
18. Hydrolysis of Praseodymium Perchlorate, c = 12.50 mC,
Titration of Buffer Solution ...... 84
19. Hydrolysis of Praseodymium Perchlorate, c = 12.50 mC,
Calculation of Average Ligand Number ...... 85
20. Hydrolysis of Praseodymium Perchlorate, c =< 10.24 mC,
Standardization of Electrodes ...... 86
21. Hydrolysis of Praseodymium Perchlorate, c = 10.24 mC,
Titration of Buffer Solution ...... 87
22. Hydrolysis of Praseodymium Perchlorate, c = 10.24 mC,
Calculation of Average Ligand Number ...... 88
23. Hydrolysis of Praseodymium Perchlorate, c «= 5.00 mC,
Standardization of Electrodes ...... 90 vi i LIST OP TABLES (Cont'd.)
24. Hydrolysis of Praseodymium Perchlorate, c « 5.00 mC,
Titration of Buffer Solution ...... 91
25. Hydrolysis of Praseodymium Perchlorate, c *> 5.00 mC,
Calculation of Average Ligand Number ...... 92
26. Solubility of Neodymium Hydroxide in Hydrochloric
Acid at 25°C...... 94
27. Data on the Equilibrium between Neodymium Hydroxide
and Hydrochloric Acid at 25°C...... 96
28. Studies on the Completeness of the Reaction between
Hydrochloric Acid and Neodymium Oxide ...... 99
29. Data on the Equilibrium between Neodymium Hydroxide
and Perchloric Acid at 25°C'...... 100
30. The Water Solubility of Neodymium Hydroxide at
25°C...... 101
31. The Solubility of Neodymium Hydroxide in Sodium
Hydroxide Solutions at 25°C...... 101
32. Data on the Equilibrium between Mercuric Oxide and
Nitric A c i d ...... 116
33. Data on the Equilibrium between Beryllium Hydroxide
and Hydrochloric Acid ...... 119
34. Data on the Equilibrium between Thorium Hydroxide
and Perchloric A c i d ...... 123
35. Summary of Data on Neodymium Hydroxide ...... 171
vil LIST OP FIGURES
Figure Page
1. Hydrolysis C e l l ...... 27
2. A Comparison of the Glass and Quinhydrone Elec
trodes in a 0.01 C Pr+3 Solution ...... 35
3. A Comparison of the Glass and Q,uinhydrone Elec
trodes in a 0.025 C Nd+^ Solution ...... 36
4. Apparatus for Transferring the Filtering Samples ,. 45
5. Standard Curve for Neodymium Analysis-10 cm Cells . 50
6. Standard Curve for Neodymium Analysis-1 cm Cells .. 51
7. Molar Extinction versus Wave Length-1 cm Cells .... 52
8. X-Ray Powder Patterns of Oxide Samples ...... 59
9. Determination of the Free Acid in the Neodymium
Buffers, c => 24.45 and 9.79 mC ...... 69
10. Determination of the Free Acid in the Neodymium
Buffers, c => 4.90 mC ...... 76
11. Hydrolysis of Neodymium Perchlorate ...... 77
12. Determination of the Free Acid in the Praseodymium
Buffers, c = 25.0 and 12.5 m C ...... 82
13. Determination of the Free Acid in the Praseodymium
Buffers, c = 10.24 and 5.00 mC ...... 89
14. Hydrolysis of Praseodymium Perchlorate ...... 93
15. Solubility of Nd(0H)3 in Dilute Hydrochloric Acid . 95
16. as a Function of the Equilibrium Hydrogen Ion
A c t i v i t y ...... 98 viii LIST OP FIGURES (Cont'd.)
17. Solubility of Nd(OH)g in Sodium Hydroxide Solutions. 102
18. Solubility of NdCOHjg in Sodium Hydroxide and
Hydrochloric Acid Solutions ...... 103
ix INTRODUCTION
The purpose of this investigation was to obtain data on the equilibria between crystalline neodymium hydroxide and hydrogen ions and hydroxyl ions in aqueous solution at 25°C. and to study the hydrolysis of the tri-valent neodymium ion at 25°C.
Such data make possible (1) the determination of the ionic species present in aqueous solutions as a function of the hydrogen ion concentration, (2) a calculation of the free energy of formation of the solid, crystalline neodymium hydroxide, (3) the determination of the solubility product of the hydroxide, (4) a quantitative determination of the amphoteric properties of the hydroxide.
As a great deal of work has been done recently in the solution chemistry of uranium, thorium, and the first row transition elements, it is of interest to compare the chemistry of the rare earths to that of these other elements which also contain only partially filled inner electron shells. At the present time, analogy with the rare earths affords the only method of obtaining qualitative informa tion on actinum. Also the chemistry of the actinides with high atomic numbers is quite similar to that of the lan thanides, as the plus 3 oxidation state becomes most stable in these elements.^"
-*-G. T. Seaborg, Nucleonics. 5, 16 (1949). 1 This work is a continuation of a long range program undertaken for the identification of ionic species present in aqueous solution and for a quantitative study of the equilibria existing between these ions and their solid oxides and hydroxides. HISTORICAL REVIEW
The Basicity of the Rare Earth Oxides
A rather large amount of qualitative work has been
done on the basicity of the oxides and hydroxides of the
rare earth elements. Except for the most recent work, this
has been thoroughly covered in an excellent review article
by Moeller an K r e m e r s ^ and more briefly by Rakowsky.^ In
— 1 - 2T. Moeller and H. E. Kremers, Chom. Rev., 57, 97 (1945).
®F. W. Rakowsky, doctoral dissertation, The Ohio State University (1954).
general, most of this work has been in the form of reports
of the preparation of compounds like KNd0 2 ^, observations
40. Beck, Angew. Chem. 52, 536 (1939).
that the moist hydroxides absorb carbon dioxide from the
atmosphere, and estimations of the relative basicity of
5H. Bassett and R. G. Durrant, J. Chem. Soc. , 1942, 277.
scandium, yttrium, and the rare earth hydroxides. 7 There
®G. Endres, Z. anorg. allgem. Chem., 205, 321 (1932).
*7t . Moeller and H. E. Kremers, J. Phys. Chem. 395 (1944). “ ... have been very few measurements of the basicities of the 3 oxides or of the hydroxides of individual elements.
The System Neodymium Oxide-Water
The neodymium oxide water system has been investi gated only briefly by Weiser and Milligan,® Fricke,®
^H. B. Weiser and W. 0. Milligan, J. Phys. Chem., 42, 673 (1938).
®R. Fricke, Z. Naturforsch, 3-A, 62 (1948).
Fricke and Seitz, and Seitz.The compound precipitated
-*-®R. Fricke and A. Seitz, Z. anorg. allgem. Chem., 254. 107 (1947).
1;LA. Seitz, Z. Naturforsch., l^A, 321, (1946). at 100°C. from aqueous solutions of neodymium salts by the addition of hydroxide ion has been identified as a hydrous hydroxide by examination of dehydration isobars.
This has the stoichiometric composition Nd2 0 3 * 3 HgO or
Nd(0H)g. It has been shown that a monohydrate of the oxide (or NdO(OH)) also exists. In the case of neodymium, all efforts to product higher oxides than the sesquioxide have failed. At times various compounds such as NdOg and
NdgOg have been reported in the literature as having been prepared by heating the sesquioxide in a current of oxygen.
Popov and Clockler12 were unable to reproduce any of these
12A. I. Popov and G. Glockler, J. Am. Chem. Soc., 71, 4114 (1949). experiments and concluded that the authors reporting the preparation of NdOg had in reality prepared NdO(OH) which they claim to be stable at temperatures as high as 1000°C.
This is in direct conflict with the results of Weiser and
Milligan^ and Fricke and Seitz‘S which indicate that
B. Weiser and W. 0. Milligan, J. Phys. Chem., 4 2 , 673 (1938).
"^R. Fricke and A. Seitz, Z. anorg. allgem. Chem., 254, 107 (1947).
NdO(OH) should decompose in the range 300°-400°C.
The solubility of the oxide in water at 29°C. was measured by Busch^ from electrometric titrations of the
15W. Busch, Z. anorg. allgem. Chem., 161, 161 (1927). liberated hydroxide ion; however, no attempt was made to identify the solid phase present. The solubility was found to vary with the time and temperature of the ignition of the oxide. The solubility of neodymium sesquixoide is given as 5.75 x 10 moles per liter while that for praseodymium — 7 sesquioxide was determined to be only 6.1 x 10 moles per liter. This certainly seems to be too great a difference in these two solubilities. Moeller and Kremers^® estimate
16 T. Moeller and H. E* Kremers, J. Phys. Chem., 48, 395 (1944). ” * the solubility of freshly precipitated neodymium hydroxide, « * P i from the value of the solubility product, to be 2. 7 x 10" moles per liter at 25°C.
The data on the solubility product of neodymium hydroxide have all been obtained by measuring the pH of a solution of a neodymium salt either at the incidence of precipitation of the hydroxide by added hydroxide ion or at a given ratio of Nd : OH" after the appearance of the solid phase. From measurements of the pH at a ratio of
Nd : OH" = 0.4, Moeller and Kremers^-7 gave the following
17Ibid., 395.
— 2P solubility products: nitrate solution 3.1 x 10 , sulfate solution 2.6 x 10"^, acetate solution 2.8 x 10"~^-, and an ’’average" solubility product of 1.9 x 10"^-*-. All of these were for the freshly precipitated hydroxide at 25°C., but again no investigation was made of the solid phase present. The average solubility product given above is the one generally referred to in the current literature.
Moeller and Fogel^-® extended this study to perchlorate
18 T. Moeller and Norman J. Fogel, J. Am. Chem. Soc. , 73, 4481 (1951). “ solutions, also at 25°C. They determined a value for the solubility product of 3.2 x 1 0 "^. Hildebrand, using
-*-®H. H. Hildebrand, J. Am, Chem. Soc. 3 5 , 847 (1913). a hydrogen electrode, found that precipitation occurred at pH values close to 7 in solutions of neodymium chloride. 90 Britton also measured the pH values at the incidence of
^H. T. S. Britton, J. Chem. Soc. , 127, 2142 (1925). precipitation using a hydrogen electrode and found these to be 7.00 in neodymium nitrate solutions and 7.02 in solutions of neodymium chloride. All measurements were at 17°C. Using a glass electrode, Bowles and Partridge^-*-
^1 One factor which has been essentially ignored is the large difference between the values of the solubility products obtained for the freshly precipitated material and those obtained for the hydroxide which has been digested for any length of time. All of the above values 99 refer to the freshly precipitated material. Sadolin Sadolin, Z. anorg. allgem. Chem., 160, 133 (1927). reported a value for the solubility product of freshly precipitated lanthanum hydroxide of 1.2 x 10“-*-® and for the "aged" material 1.1 x 1 0 both at 25°C. Kolthoff 8 and Elmquist2^ reported a value of 9.1 x'10"22 for the p ’s I. M. Kolthoff and Elmquist, J. Am. (Jhern. Soc. , 53, 1217 (1931). solubility product of "aged” lanthanum hydroxide at 25°C. Oka24 gave the value of 4.3 x 10“^~ for the solubility 24Y. Oka, J. Chem. Soc. Japan. 59, 971 (1938). product of freshly precipitated lanthanum hydroxide at 25°C • There are very few thermodynamic data available for o c; _q the oxides and hydroxides of the rare earths. Matignon, 2^0. Matignon, A n n , chim. phys., viii 8, 243 (1906). 26Ibid., 386. 27Ibid., 402. 28Ibid., 426. 29 G. Matignon, Ann, chim. phys. viii 10, 104 (1907). in a series of papers, studied the dissolution of the oxides of the rare earths in various acids from the stand point of the kinetics of the reaction. Latimer^8 has 3°W. Latimer, The Oxidation States of the Elements and Their Potentials in Aqueous Solutions, Second Ed., Prentice Hall Inc., New York (1952),' p. 288. estimated the free energy of formation of solid neodymium hydroxide to be -309.3 kcal/mole and the free energy of formation of the sesquioxide is given as -420.6 kcal/mole. Both of these values are derived from highly inaccurate 31 data. The National Bureau of Standards tables give a 31 Selected Values of Chemical Thermodynamic Proper ties , Circular of the National Bureau of Standards 500, Feb. 1, 1952, Washington, D.C. value for the free energy of formation of neodymium hydrox ide of -309.6 kcal/mole as determined from the work of 3 9 Endres. Exactly how this value was calculated remains 32q.# Endres. Z. anorg. allgem. Chem. , 205, 321 (1932). somewhat of a mystery, as this paper gives only ratios of the solubility products of the rare earth hydroxides and no absolute values. The Hydrolysis of Neodymium Solutions The hydrolysis of the rare earth salts in aqueous solution has not been the subject of any extensive invest!- 33 gations. Bodlander measured the pH of solutions of 3 3 E. Bodlander, inagural dissertation, Berlin (1915). neodymium chloride with a hydrogen electrode. The pH of 34 0.1 N solutions was found to be 5.31. Neish and Burns C. Neish and J. W. Burns, Can. Chem. Met. , 5, 69 (1921). “ measured the pH in 0.01 N solutions of neodymium nitrate and found a value of 4.526 using a glass electrode. Kleinheksel and K r e m e r s * ^ found a pH of 2.5 in 0.1 N 'Z C J. H. Kleinheksel and H. G. Kremers, J. Am. Chem. Soc., 50, 959 (1928). solutions of the anhydrous chloride of neodymium. Moeller and Kremers^® have questioned this value in their review 3®T. Moeller and H. E. Kremers, Chem. Rev. , 3 7 . 97 (1945) . article, as the anhydrous chloride was prepared by dehydra tion of the hexahydrate in a stream of anhydrous hydrogen 37 chloride. The most recent investigation is that of Moeller 3^T. Moeller, J. Phys. Chem., 50, 242 (1946). on the hydrolysis of solutions of the rare earth sulfates. The pH of solutions prepared by dissolving the pure sulfates in water was measured with a Beckman G pH meter. Large variations were observed in the values of the hydrolysis constants calculated assuming a reaction Nd*3 + Hp0^Nd(0H)'t2 . + E +,o n * (aq) 2 (aq) (aq) to be the only significant one and also assuming negligible interaction between the neodymium ion and the sulfate ion. The variations in the hydrolysis constant were attri buted to the use of concentrations instead of activities in 11 the calculations. The hydrolysis constant for the above -9 reaction was estimated to be about 1 x 10 and therefore for Nd(0H)+2 to be 1 x 10“5. Spedding, Porter, and Wright®® have prepared pure anhydrous neodymium chloride H. Spedding, P. E. Porter, and J. M. Wright, J. Am. Chem. Soc., 74. 2055 (1952). for conductivity studies in aqueous solution. The salt was prepared by dehydration of the hexahydrate in an atmosphere of anhydrous hydrogen chloride, and these solutions of the chloride in conductivity water had pH values ranging from 6.4 to 6.6. The Analysis of Solutions of Neodymium There are a series of very sharply defined bands in the absorption spectra of aqueous solutions of the tri- valent neodymium ion. This makes spectrophotometry a use ful tool for analysis of solutions of the salts of neo- 7 Q dymium. Prandtl and Scheiner00 made the first thorough 39 W. Prandtl and K. Scheiner, Z. anorg. allgem. Chem., 220. 107 (1934). investigation of the absorption spectra of the rare earth chlorides in aqueous solution. It is now generally accepted that these sharp bands in the visible region arise from transitions between 4fn configurations, and that these transitions are normally 12 forbidden In the case of an Isolated atom. In the presence of an electrical field caused by the surrounding ions, transitions may occur where = 0 for the transition but withZ\L and /IS ^ 0. These transitions are similar to those resulting upon the addition of an external field in the case of the Zeeman and Stark effects, and they, occur both in solution and in the crystals of neodymium salts. The position of the absorption bands are essen tially independent of the anion concentration but differ significantly in different solvents.^® The allowed transi- ^J. Bjerrum and C. Klixbull-Jorgensen, Acta Chem. Scand., 7, 951 (1953). tions giving rise to the rare earth spectra have been 41 succinctly summarized by Yost, Russell, and Garner. 41 D. M. Yost, H. Russell, and G. S. Garner, The Rare Earth Elements and Their Compounds, John Wiley and Sons Inc., New York (19471 Chap. 3. According to Servigne,^2 neodymium can be detected M. Servigne, Bull, soc. chim.. 7, 121 (1940). in very small amounts by dilution of the sample with calcium tungstate. Photoluminescence produces spectra which can be used for the detection of quantities of 13 neodymium as small as 10 "'^g. Friend and Hall^ proposed ^ J . N. Friend and D. A. Hall, Analyst, 65, 144 (1940). three principal methods for the quantitative determination of the rare earth elements by the use of the absorption spectra of their solutions. In the first, the width of the chief bands in the visible range are compared with the width of bands obtained from known concentrations. The second method is to observe the dilution of the sample necessary to cause disappearance of the most persistent band. In the third method, the solution to be analyzed is diluted until the intensities of suitable bands appear, by direct comparison, to be equal to standard solutions. 44 According to Rodden, the bands at 521 m^i and 798 m ^ 44 G. J. Rodden, J. Research Natl. Bur. Standards, 26, 557 (1941) Research Paper 1395. are most suited to the determination of neodymium using a spectrophotometer. Sandell^S cites the necessity of using 45 E. B. Sandell, Golorimetric Determination of Traces of Metals, Interscience Publishers, New Yo^k (1945JT very narrow bands of wave lengths for the spectrophotometric determination of the rare earths. Beer's law is said to be followed in the case of neodymium when using wave lengths 14 of 521, 740, and 798 mp. . The molar extinction coefficient is greatest at 798 mjo. but dysprosium interferes; however, praseodymium and samarium do not. Europium interferes with the band at 521 mju . Moeller and Brantley^® have recently Moeller and J. C. Brantley, Analytical Chem., 22, 433 (1950). studied the absorption spectra of solutions of neodymium chloride using a Beckman DU spectrophotometer and 1 cm cells. Beer's law was found to apply to solutions with, a concentration as high as 25 g neodymium per liter, using o the absorption band at 5218 A. Acid-free chloride solutions were treated with varying amounts of hydrochloric acid and ammonium chloride to test whether excess hydrogen or chloride ion had any effect on the spectra. None was observed with a mole ratio of Cl": Nd+^ as high as 10.00. A 'H Wiley investigated the absorption of solutions of neo- 47 J. C. Wiley, J. Soc. Chem. Industry, 69, 143 (1950). dymium chloride and nitrate at 512, 522, 741, and 796 mfa- . Beer’s law was followed, using 1 cm cells, to concentra tions as high as 26 g of neodymium per liter at 512 mfu, 522 mjx , and 741 m ^ . Deviations were observed at 796 m ^ for concentrations greater than 16-20 g neodymium per liter. The readings at 741 mja were least affected by the presence of dust or other particles in the solutions 15 or by the condition of the cell surfaces. The use of lake forming reagents has been suggested 48 for trace analysis of the rare earth elements by Sandell^ B. Sandell, Colorimetric Determination of Traces of Metals, Interscience Publishers, New York (194 5*77 p. 374. and investigated by Becke^® and Komarsvskii and Korenman.^O 49 G. Becke, Mikrochemie ver. Mikrochem. Acta, 27, 49 (1939). S. Komarovski! and I. M. Korenman, Z. anal. Chem., 94, 247 (1933). Because of the slight tendency of the rare earths to form stable complexes, use of these colorimetric reagents has not proven particularly satisfactory. Since transitions of the 4fn electrons in which JSH = 0 are responsible for the spectra of the rare earths in the visible range, environmental factors affecting only the outermost 5d and 6s orbitals should have no significant effect on the rare earth absorption spectra.^ 51 T. Moeller, Inorganic Chemistry An Advanced Text book, John Wiley and Sons, Inc., New York (1952) p. 900. Thus it has been observed that the rare earth spectra remain the same as that of the simple hydrated ion in the presence of many eomplexing agents even when definite 16 complexes are supposedly formed. The absorption spectra of the (3 di-ketone chelates^ of the tripositive rare earth 52 W. F. Ulrich, doctoral dissertation, University of Illinois, (1952). ions in a variety of organic solvents closely resemble the spectra of the uncoraplexed species in aqueous solution. In most of these cases, the complexes have been proposed on the basis of a study of the infared absorption spectra of the solutions. In other cases, definite shifts are observed in the rare earth absorption band position. Tevebaugh.53 observed definite displacements in the positions 53 A. H. Tevebaugh, Atomic Energy Commission Declassi- fled Report No. 2749, Nov. 194 9. of the absorption bands, using a grating spectrograph, in solutions containing citrate ion. Moeller^ has reviewed 54 T. Moeller, Record Chem. Progr., 14, 69 (1953). the complex chemistry of the rare earths. Moeller and Brantley0lJ claim the resolution of the absorption bands — — ' T. Moeller and J. C. Brantley, J. Am. Chem. Soc., 72, 5447 (1950). - of the rare earths into two or more bands In the presence 17 of ethylenediamine tetracetate Ion, while weaker completing agents merely intensify the absorption. Since complexes of the rare earths frequently pro duce only very slight changes in the absorption spectra, these spectra cannot be used, in general, to detect the formation of complexes. In the cases where colorimetric reagents have been suggested, the change in the absorption spectra that is used for analytical purposes Is not that of the rare earth ion, but the change occurring in the spectra of the complexing color reagent. EXPERIMENTAL General Procedure The experimental procedure followed in this work is similar to that of Garrett and Heiks,56 Gayer and 5 6 A. B. Garrett and R. E. Heiks, J. Am. Ghem. Soc., 63, 502 (1941). Garrett,*^ and Gilbert and Garrett.^® ^ K . Gayer and A. B. Garrett, J. Am. Chem. Soc., 71, 2973 (1949). Sft R. A. Gilbert and A. B. Garrett, J. Am. Chem. Soc., at press. In general, this consists of the determination of the concentrations of the various ionic species present at the equilibrium existing between a solid hydroxide and aqueous solutions of acid and base. A study is also made of the hydrolytic reactions of the uncomplexed metallic cation to determine the ionic species present in solution at hydrogen ion concentrations down to that at which the solid hydroxide precipitates. Standard free energy changes may then be calculated from the equilibrium data. Preparation of the Reagents Neodymium Oxide. The oxide used in these experiments was obtained from Johnson Matthey and Company, London, England, through their American representative, the Jarrell Ash Company in Cambridge, Massachusetts. All of the oxide 18 19 used was their "Specpure" grade, and the final purification of this was by fractional crystallization. Spectrophoto- metric measurements were made on a solution of the nitrate containing 500 g of the oxide per liter and using 4 cm cells. These data indicate approximately 0.07 per cent of praseodymium oxide and less than 0.003 per cent of samarium oxide. The oxide was also standardized by emission spectra. None of the rare earths were detected. Traces of calcium, magnesium, and silicon in amounts of less than 0.001 per cent were the only elements detected. In addition, before using each lot of oxide, solutions were made up that were 0.01 M in neodymium chloride, and plots of extinction coefficient versus wave length were made in the Beckman DU spectrophotometer using 10.00 cm cells. These were compared with those given by Moeller and Brantley.^ No ^T. Moeller and J. C. Brantley, Analytical Chem., 22, 433 (1950). traces of any other of the rare earths could be detected. Before use, the oxide was purified once further as follows. The oxide was dissolved in an excess of reagent grade perchloric acid. To the resulting solution doubly recry stallized oxalic acid was added. The precipitate of neo dymium oxalate was collected, washed free of soluble impurities, and dried at room temperature. It was ignited 20 In platinum at higher than 850°C. in a stream-of oxygen and stored in a desiccator in an atmosphere of nitrogen. The resulting material was examined by X-ray diffraction, and the results are given in the section on the solid phase analysis. Hydrochloric Acid Solutions. All standard hydro chloric acid solutions were prepared from C. P. reagents and standardized against standard sodium hydroxide solutions using ph.enolphthale.in as an indicator. Sodium Hydroxide Solutions. The sodium hydroxide solutions used for the solubility studies were prepared by the dissolution of reagent grade sodium hydroxide pellets in recently boiled distilled water to give an approximately 1M solution. Barium hydroxide was added in a slight excess to precipitate all carbonate. The standard solutions were prepared by dilution of this stock solution in a closed system. All stirring and transfer of the solutions was done by pressure with nitrogen. Standard ization was against potassium acid phthalate using phenol- phthalein as an indicator. The sodium hydroxide solutions used in the hydrolysis studies (0.01G) were prepared by dissolution of reagent grade sodium hydroxide in boiled distilled water. Sodium perchlorate was added to give an ionic strength of 3.00. The solutions were standardized against standard 21 hydrochloric and perchloric acids using methyl red as an indicator and while constantly stirring the solution being titrated with nitrogen. Perchloric Acid Solutions. All of the perchloric acid solutions were prepared by dilution of reagent grade 60 per cent perchloric acid with distilled water. These may be divided into three groups; (a) the acid 0.01 M used in the hydrolysis studies, (b) the acid with constant ionic strength used in the solubility measurements, (c) the acid used.for solubility studies which was not controlled at a constant ionic strength. The acid used in the hydrolysis studies was made to have a constant ionic strength of 3.00 by the addition of sodium perchlorate. This was standardized against potassium iodate according to the method of Oesper®^ and ^ P . Oesper, _J. Chem. Educ. , 26, 588 (1949). checked against the standard sodium hydroxide with an ionic strength of 3.00 which was also to be used in the hydrolysis work. The acid for solubility studies was controlled at an ionic strength of 3.00 by the addition of sodium perchlo rate and standardized against standard sodium hydroxide solutions. It was also checked against potassium iodate. 22 The perchloric acid solutions for the solubility studies in which the ionic strength was not held constant were prepared and standardized as above except the addi tion of the sodium perchlorate was omitted. Neodymium and Praseodymium Perchlorate Buffer Solutions. The neodymium and praseodymium perchlorate solu tions used in the hydrolysis studies were prepared by dis solving weighed amounts of the ignited oxides in standard perchloric acid. As it was desirable that the solutions have a pH of approximately 3, the excess acid was titrated with standard sodium hydroxide solution, following the pH with a Beckman G pH meter. Additional sodium perchlorate was then added to give a total concentration of perchlorate of 3.00. Sodium Chloride Solutions. All of the sodium chloride solutions used in the half cell Hg Hg2 Clg 01“ in the hydrolysis studies were prepared from C. P. sodium chloride that had been dried in platinum at 600°C. for three hours. Standard solutions were prepared from weighed amounts of the dried salt. Sodium Perchlorate Solutions. The sodium perchlorate solution used as a salt bridge electrolyte was prepared by dissolving weighed amounts of anhydrous sodium perchlorate in distilled water. The sodium perchlorate for this and also that used in the adjustment of the ionic strength of 23 the solutions was dissolved in water ethanol mixtures, filtered, and recrystallized as described by Biederman and ✓ 61 Sillen. No trace of chloride ion could be detected in Biederman and L. G. Sillen, Arkiv Kemi, 5, 425 (1953). the solutions prepared in this manner. Distilled Water. The distilled water used in all of the experiments was triple distilled. The last distil lation was from permanganate solution. It was boiled before use to free it of dissolved gases, cooled, and stored sub sequently under an atmosphere of nitrogen in Pyrex glass. Hydrolysi s Studies Experimental Method. From the data given in the historical section, it is evident that the hydrolysis of the rare earths is very slight. All of the data available in the literature were determined by measuring the pH of solutions of various salts. Much has been written in the last ten years of the defects in this kind of an experiment, and such data are now considered next to useless. It is absolutely necessary to work at a constant ionic strength as the effect of the variations in the activity coeffi cient of a tri-valent ion due to changes in the ionic strength would cause large variations in any "equilibrium constant" calculated from concentration data. To avoid errors due to slight deviations from the formula sto ichiometry of the salt or to the occlusion of traces of acid during the crystallization, it is desirable to work with solutions in which there is a small but accurately known concentration of hydrogen ion. If one is to deduce the nature of the hydrolysis reaction, it is essential to have data on the hydroxyl ion bound per metal Ion as a function of the hydrogen ion concentration and the total metal concentration. One experimental procedure which satisfies the above requiremants is that used by Kil- 62 Patrick and Pokras who studied the hydrolysis of the 62 M. Kilpatrick and L. Pokras, J. Electrochem. Soc., 100, 85, (1953). trivalent scandium ion. As the solutions studied by this method must be handled In the open atmosphere, the ions must show significant hydrolysis at pH values less than 4, which is the highest pH solution that can be exposed to the atmosphere without absorption of significant amounts of carbon dioxide. Rakowsky, using this method, P. W. Rakowsky, doctoral dissertation, The Ohio State University (1954). was unable to detect any hydrolysis in solutions of praseodymium perchlorate from pH 2.1 to 4.0, working at 25 an ionic strength of 1 .0 0 . Another procedure that satisfies the above require- ✓ ments is that developed by Sillen and co-workers. It has been used to study the hydrolysis of the iron (II) ion, + P 64 Fe , by Hedstrom , who calculated for the reaction ®^B.0.A. Hedstrom, Arkiv Kami, 5, 457 (1953). j+HgO-v^ FeOH|aqj+H|aq), pK& « 9.5 ± 0.2, and hence this type of procedure is suitable for the study of slightly hydrolyzed aquo-ions. Electrochemical Cells. The electrode and titration apparatus used in this work was essentially that described f 65 by Forsling, Hietanen, and Sillen, and the hydrolysis 65 ✓ W. Forsling, S. Hietanen, and L. G. Sillen, Acta Chem. Scand., 6 , 901 (1952). data were obtained from the E.M.F. values of the cell: HC104 Pt Me (CIO4 ) 3 C NaC104 4 C NaCl Hggdg quinhydrone NaC104 The E° for the couple N d ^ N d t 3 ,+3e“ is so large there is (aq) e no reduction of the Nd||qj in the presence of hydroquinone, so the quinhydrone electrode should be suitable for 26 • measurement of the hydrogen ion activity. The apparatus is diagrammed in figure 1. The titra tion vessel consisted of a 600 ml beaker from which the top had been cut off using a hot wire. This was ground flat, and a top and bottom for the vessel were constructed from 3/8” lucite. Seven holes were drilled through the top to admit the burettes A and B, the two gold plated platinum electrodes C, the tube, D, admitting nitrogen to flush the space above the solution, the tube E also admitting nitrogen to stir the solution, the salt bridge F, and a mercury sealed stirrer G. When using the glass electrode to check the quinhydrone electrode, it replaced the mercury sealed stirrer. The gold plated platinum electrodes were carried through the titration vessel cover in 4 mm glass tubes. The upper end of each platinum elec trode was sealed through a male standard taper plug which was seated securely in its female counterpart sealed to the upper end of the 4 mm tubes. In this way, all glass to metal seals were eliminated. These have been reported as the cause of irreproducibility in the E.M.F. values of cells of this type.®® 66A. B. Garrett, E. Hogge, and R. E. Heiks, Science, 92. 18 (1940). The nitrogen used to exclude the atmosphere during the measurements was purified by successive washings in SIDE VIEW - UNFOLDED TO WASTE NaCI SALT BRIDGE TO WASTE TITRATION VESSEI__ CALOMEL HALF CELL -B GLASS ELECTRODE- TOP VIEW V INLET L' \ NITROGEN © £ - = = — PLATINUM ELECTRODES TO STIR nitrogen! VO r Q f BURETTES FIGURE 1 HYDROLYSIS CELL 28 concentrated sodium hydroxide solution, alkaline sodium anthroquinone (3 sulfonate solution, concentrated sulfuric acid, aqueous silver nitrate, distilled water, and finally 3 G sodium perchlorate solution. The E.M.P. of the cell, as measured, should be given by the equation (III-l): E « e°+E -+E •1 - in (aH)gx (acl)2x (a^) x (aHg)2 3 3 2P (aHggClg) x (a QH2) where Q, and Q3 g refer to quinone and hydroquinone respec tively, and where E = measured E.M.F. of cell E°= thermodynamic reversible E.M.P. when the activities of all reactants and products are unity. E. = junction potential at the interface between J the solution in the titration vessel and the 3 C NaC104 salt bridge electrolyte EjT = junction potential at the interface between the 3 C NaClO^ salt bridge electrolyte and the 4 C NaCl calomel half-cell electrolyte. The value of E j 1 is maintained constant throughout the measurements by the design of the cell. A three way stop cock is provided at the liquid-liquid junction, so that this junction may be flushed frequently during the measure ments. This was done by flushing alternately with the 4 C NaCl solution and the 3 C NaC104 solution out to 29 waste as shown in figure 1. Wo measurable variation in the cell E.M.F. was observed in readings made before and after flushing. The magnitude of the potential Ej between the solu tion being titrated and the salt bridge electrolyte has been the subject of an extensive investigation by / 6*7 Biedermann and Sillen. Although the ionic strength in ^G. Biedermann and L. G. Sillen, Arkiv Kemi, 5f 425 (1953). the two solutions is essentially the same, a potential may be expected to develop during the course of the titration as the hydrogen ion in the solution under study is replaced by sodium ion. Because of the high mobility of the hydrogen ion, this should be essentially due to diffusion of the hydrogen ion and hence a function of the hydrogen ion concentration. The value of this potential was found to be a function of the design of the salt bridge as well as of the hydrogen ion concentration, and with J-shaped capillary tips, as used in this work, Ej was found to obey the expression Ej(V) - 0.000018 h (mC). (III-2) h = hydrogen ion concentration in millimoles per liter Since hydrolysis does not occur until h is about 10"2mC, the potential Ej should be negligible in this work. 30 In equation (III-l), the values for E° and Ej' may be combined into one constant, and if the value for E-j is negligible, we may write E = E'» - 0.05916 log-m aH+ x aCl~ x aQ_ (III-3) aQH2 The values of E and E ' 1 are measured in volts and at 25°G. The activities of Hg and Hg2 Cl2 in equation (III-l) are both unity at 25°C. as they are in the standard thermo dynamic states. If the values of E and E ’ 1 are measured In milli volts, and equation (III-3) is written in terms of concentrations, the following equation is obtained. E = E' ' - 59.16 log1 0 [h+] x aCl~x fcj x ^H+x /q (III-4) jftHg] / q Hq The value of the ratio M - is unity as quinhydrone was the source of these species. Since the ionic strength was essentially constant throughout the measurements, the values for the activity coefficients together with aCl", which is also a constant, may be included with the constant E* 1 in the cell constant. The measured E.M.P. is then given by the equation E = E ’q - 59.16 log10h (C) (III-5) In practice the E.M.F. values of two such cells were read, i.e., each platinum electrode was read against the calomel half cell at every point in the titration to 31 determine if any poisoning of the electrodes was occurring. If the values of successive readings differed by more than 0.1 mV, the run was usually discontinued. The entire cell and titration vessel were immersed in a water thermostat which was controlled at 25°±0.01°C. by means of alternate heating with a knife blade heater and cooling by evapora tion from the surface. In addition to the above cells, readings were also made in some of the hydrolysis experiments with the cell glass Me(C104 )3 3 C 4 C AgCl HG1 NaC104 NaCl Hg2 Cl2 Hg (electrode) hcio4 NaC104 n. The equation relating the E.M.P. of the above cell to the hydrogen ion concentration of the solution may be written in an analogous fashion to that of the quin- hydrone-calomel cell as E - Eq. - 59.16 log10 h (C). (III-6 ) A Beckman 1190-80 general purpose glass electrode was used, together with the calomel half-cell described above, for these measurements. Data are given in tables 1 and 2 for the E.M.P. of cells of both type I and of type II over a wide range of hydrogen ion concentrations and in the presence of praseodymium and of neodymium ions. This was done to 32 Table 1 A COMPARISON OF THE E.M.F. OF THE GIASS AND QUINHYDRONE ELECTRODES IN THE PRESENCE OF O.Ol C Pr+3 -EQ 1 mv "Eq2 inV -Eq mV H x 105 C -log H 247.31 247.31 269 30.76 3.512 242.36 242.16 264 25.83 3.588 236.62 236.62 259 2 1 . 0 1 3.678 229.43 229.43 251 16.28 3.788 219.87 219.87 241 11.64 3.934 206.04 206.33 228 7.09 4.149 179.48 180.12 2 0 2 2.62 4.582 133.58 134.78 158 0.42 5.377 33 Table 2 A COMPARISON OF THE E.M.F; OF THE GLASS AND QUINHYDRONE ELECTRODES IN THE PRESENCE OF 0.025 C Nd + 3 -Eqi mV **eQ2 mV “Eq. raV H x 105 C -log H 255.44 255.44 277 50.4 3.294 252.11 252.11 272 44.5 3.352 248.22 248.22 270 38.7 3.412 243.86 243.86 264 33.0 3.482 238.93 238.93 261 27.3 3.564 232.84 232.84 254 2 1 . 8 3 • 662 225.30 225.30 248 16.4 3.785 214.67 214.67 237 1 1 . 1 3.955 199.38 199.38 2 2 1 5.84 4.234 174.77 174 . 77 197 0.716 5.145 34 determine if any reaction occurred between the rare earth ions and the quinone or hydroquinone which would change the E.M.P. values of the cell of type I, causing deviations from equation (III-5). This precaution was taken as the rare earths have been observed to form some complexes with oxygenated species, coordination occurring in several cases through carboxyl groups in organic acids. The data are plotted in figures 2 and 3, and it is seen that the slopes of the plot of Eq and Eq. versus log h are similar indicating that there is no interference with the quinhydrone elec trode. The set of points where the log h i s less than -5.0 do not fall on the curve, as hydrolysis occurs in this region; therefore, H is no longer an accurate estimate of the hydrogen ion concentration, H being the stoichio metric hydrogen ion concentration calculated during the titration assuming no hydrolysis. It is to be noted, however, that E^ and Eq. still have the same constant dif ference indicating that there still is no interference due to complex formation. Electrical Circuits. The electrical circuit used to measure the E.M.F. values of the quinhydrone-calomel cell consisted entirely of standard components. A Leeds and Northrup type K-2 potentiometer was used to measure the potentials. The two volts required for the potenti ometer was supx^lied by one cell of a lead storage battery. A GLASS ELECTRODE O EQ-I X EQ-2 - 1001— -3.00 -4.00 -5.00 -6.00 log (H - Moles i~l) FIGURE 2 A COMPARISON OF THE GLASS AND QUINHYDRONE ELECTRODES IN A 0.01 C Pr+3 SOLUTION. IUE3 A OPRSN F H GAS N QIHDOE LCRDS N A IN ELECTRODES QUINHYDRONE AND GLASS THE OF COMPARISON A 3 FIGURE E.M.F. - MV. -300 -200 -100 -100 L_ 3. 0 .0 -3 .2 C N+ SOLUTION. Nd+3 C. 0.025 LS ELECTRODE GLASS Q I - EQ Q - 2 EQ- -4.00 o ( Mls "') /" Moles (H log -5.00 - 6.00 37 A Weston type cell, the E.M.F* of which was certified by the National Bureau of Standards, was used as a reference and was checked frequently against other Weston cells. As the hydrolysis cell had a rather high internal resistance, a Leeds and Northrup type 7673 thermionic amplifier was used to amplify the current produced. A five cell nickel-cadmium battery wired in series with a 250-flt variable resistor was used to supply the filament current for the amplifier. A nine volt anode battery was used to gain greater sensitivity than that obtained with the normal 4.5 volt battery. All leads were shielded and the shielding grounded to the amplifier chassis which was in turn connected to an external ground. A masonite plate was attached to the top of the amplifier chassis. This plate was fitted with a jack to take the plugs at the end of the leads from the platinum electrodes. In this manner, these could be interchanged easily and readings taken with both electrodes. The unbalance of the circuit was determined by means of a Rubicon 2402HH galvanometer, which had a sen sitivity of 0.004 microamperes per millimeter. When using the glass electrode, the E.M.F. values were read with a Beckman model G pH meter set to the +mV position. Details of the Experimental Procedure. During all 38 of the hydrolysis studies, the part of the cell apparatus to the right of line A-B in figure 1 was left in the thermo stat. The titration vessel was removed at the end of a run by disconnecting the salt bridge at the standard taper joint (D). At the beginning of a run, the top and bottom were fitted to the titration vessel, and the salt bridge inserted through the proper hole in the top. The salt bridge tube was filled, before being fitted to the vessel, by drawing the 3 C NaClC>4 solution into the tube with suction. When the tube was full, the stopcock (C) was closed. After the titration vessel had been assembled, the male standard taper fitting was inserted in its female counterpart at (D) and the apparatus clamped securely in the thermostat. With stopcock (P) in the completely closed position, stop cock (E) was opened. Stopcock ( The platinum electrodes were cleaned with hot cleaning solution, washed with distilled water, and finally washed in absolute ethanol. The electrodes were gold plated by dipping them in a solution of auric chloride dissolved in absolute ethanol and burning the alcohol off in an alcohol 39 flame. The electrodes were again cleaned in distilled water and absolute ethanol and ignited in a gas flame. They were allowed to cool in place in the.titration vessel in an atmosphere of nitrogen to prevent the absorption of oxygen. If the glass electrode was to be used, it was fitted at this time* otherwise the mercury sealed stirrer was connected. A calibrated pipet was used to add 50.00 ml of 0.01 G perchloric acid (solution S) which had an ionic strength of 3.00. Finally the two burettes were inserted in the cover of the vessel. One was filled with ^-'0.01 C sodium hydroxide (solution B) which also had an ionic strength of 3.00. The other was filled with the rare earth buffer solution, (M), under investigation. 1 0 0 mg of quinhydrone was added and the solution stirred with nitrogen. The constants Eq and Eq. in equations (III-5) and (III-6 ) respectively were determined before each run from an acid base titration, titrating the 0.01 C perchloric acid with the 0.01 C sodium hydroxide, i.e., solution (S) with solution (B). In this manner, errors due to the slow aging of the calomel half-cell are eliminated, as are errors due to the day-to-day fluctuations of the glass electrode. At the completion of this titration, 100.00 ml of the rare earth buffer solution, (M), were added to the 1 0 0 . 0 0 ml of solution in the titration vessel. 1 0 0 mg 40 more of quinhydrone were added, and the burette containing the 0.01 C sodium hydroxide refilled. The diluted rare earth buffer solution was then titrated with equal volumes of the 0.01 C sodium hydroxide solution, (B), and the rare earth solution, (M). The perchlorate concentration of the buffer solution was 3.00 G in all cases, and as the rare earth concentration was low, the ionic strength was ap proximately 3 in all cases. Although little is known of the behavior of ions at such high ionic strengths, it seems valid to assume that the activity coefficients remain essentially constant under these conditions, even though there are very slight variations in the ionic strength. Thus, in the calculations, the activities of the ions may be replaced by concentrations. It is also to be noted that the total rare earth ion concentration remains constant throughout a given run. In this manner, sets of data are taken using several rare earth buffer solutions of different total metal ion concentration. Constant values of the E.M.P. were rapidly attained during the titration of the solution(S) with (B). Con stant values were also attained rapidly for the titration of the buffer solutions (M) until the equivalence point of the free acid was reached, i.e., until all of the hydrogen ion from the added perchloric acid in the solu tions was neutralized. Past the equivalence point, plots 41 of E versus time were made to determine when constant values had been reached. The hydrolysis reaction was so slow at 25°C. that the measurements had to be discontinued shortly after the equivalence point had been reached. No solid phase was formed upon the addition of the base (B), and the slow reaction was definitely a homogeneous one. The E.M.P. values of the quinhydrone-calomel cell were read to the hundredth of a millivolt, and in general these readings were easily reproduced to within 0.05 mV. In most cases if the readings of the two quinhydrone electrodes differed by more than 0.10 mV, the run was stopped. The E.M.F. values of the glass electro de-cal omel electrode cell were read to a millivolt, as this is about the limit of accuracy of a glass electrode. All of these E.M.F. measurements were carried out at 25°±0.01°C. The temperature of the bath was continually checked by means of a Beckman thermometer clamped next to the cell. The knife blade heater used was controlled, through a relay, by a Precision Scientific Micro-Set differential range thermoregulator employing a tungsten to mercury contact. Analysis of the Free Acid Concentration of the Rare Earth Buffers. The free acid concentration of the buffer solutions is defined as the concentration of 42 hydrogen ion that is bound only to solvent molecules. In addition to the measurement of the pH of the rare earth buffer solutions made with the Beckman G pH meter before the addition of the sodium perchlorate, an accurate determination of the hydrogen ion concentration of these solutions was made using the method of Gran.®® 6 8 G. Gran, Acta Chem. Scand., 4 , 559 (1950). Essentially, this consists of plotting the function, A vb/AS, i.e., the volume of base added divided by the difference in the E.M.F. of the cell before and after the addition of the base, versus the volume of base added, V-^. This plot gives a straight line which intersects the Vk axis at the equivalence point. The data were obtained during the hydrolysis run, so no separate analyses of the solutions were necessary. Solubility Studies Preparation of Samples. The acid samples were pre pared by adding the standard hydrochloric or perchloric acid solutions to dry nitrogen filled 2 0 0 ml round bottom flasks to which solid HdgOg had been added. The flasks were immediately sealed with a gas-oxygen torch. In the preparation of the water equilibrated samples, freshly boiled distilled water was transferred by nitrogen 43 pressure to 250 ml polyethylene bottles which were then sealed with paraffin. The samples using sodium hydroxide were prepared in a similar fashion, using carbonate free sodium hydroxide solutions. Equilibration. Two one-hundred fifty milliliter samples were prepared at each concentration of acid and base. One sample was equilibrated in a thermostat at 35° C. for a period of seven days. These were then transferred to a thermostat at 25°±0.05°C. and agitated for a period of three weeks. The mates of the above samples were placed directly in the 25°C. thermostat. In this manner, equi librium was reached from both above and below saturation. In the case of the samples prepared later in the work, equilibration was at 25°C. only, as it was observed that the samples reaching equilibrium from above saturation tended to give colloidal sols frequently. In the samples where sol formation did not occur, the neodymium concen trations of the 25° and 35° solutions was found to check within the experimental error. As the rate of dissolution of oxides is generally a function of the past history and method of preparation of the oxide, a study was made to determine if equilibrium had been reached in the samples. Four samples were pre pared and agitated for varying lengths of time and the solutions analyzed. These data are given in table 28. 44 It appears that equilibrium is certainly., reached within seven days. Sedimentation. After completion of the agitation period, the samples were transferred to another thermo stat, controlled at 25°±0.02°C. and clamped in an upright position for a period of seven days. Transfer of the Solutions for Analysis. The sample bottles were opened in a stream of nitrogen by touching the molten end of a hot glass rod to a file mark on the neck of the flask. The apparatus used to transfer the samples is diagrammed in figure 4. The stopper (S) was was immediately put in place and the joint sealed with Scotch electrical tape. Prior to connecting, the entire apparatus used for the transfer had been flushed with nitrogen and the two electrodes seated in place. At no time during the transfer was the solution allowed to con tact the atmosphere, as the rare earth hydroxides are strong bases, and hence the hydrogen ion concentration at equilibrium is very low. Unbuffered solutions of this type absorb carbon dioxide from the atmosphere, and very short exposures may cause errors of several tenths of a pH unit. When sufficient solution had been forced into the electrode chamber, the stopcock at (C) was closed. By maintaining the nitrogen pressure in the sample flask, SINTERED m GLASS PLATES 250 ML. SAMPLE ERLENMEYER FLASK FLASK GLASS ELECTRODE -CALOMEL ELECTRODE On FIGURE^ APPARATUS FOR TRANSFERRING AND FILTERING SAMPLES 46 and by reopening the stopcock at (C), several samples could be removed without danger of stirring up the solid hydroxide in the bottom of the flask. To insure against the possibility of the presence of any hydroxide suspended in the sample which would cause erroneous values in the optical density, the solutions used for the spectrophotometric analysis were filtered through two sintered glass plates. After the pH of the samples had been determined, the electrode chamber was removed by separating the apparatus at point (B). The tube carrying the filters was then connected, and solution forced through the filters by nitrogen pressure. Measurement of the Hydrogen Ion Concentration. The hydrogen ion concentrations of the samples after equili bration were determined with a Beckman model G pH meter, using a Beckman general purpose glass electrode and a calomel reference electrode. As the hydrogen ion concen trations at equilibrium covered only a short range, it was necessary to standardize the electrodes only at pH 7.00. This was done with Beckman pH 7 buffer solution, accurate to ± 0.02 pH units. For the equilibrium pH measurement of the water equilibrated samples, standardiza tion was with a boric acid-sodium hydroxide buffer at pH 9.00. For the pH measurements of the samples equilibrated 47 with perchloric acid with JciO^Js 3.00, the calomel cell electrolyte was 4 C sodium chloride instead of potassium chloride to avoid precipitation of potassium perchlorate at the liquid-liquid junction. Spectrophotometric Analysis. A Beckman DU spectro photometer was used to determine neodymium in the acid equilibrated samples. Standard curves of optical density versus concentration were drawn for both the 10 cm and the 1 cm cells. Corex cells were used for these measure ments, as the absorption was in the infared. Large scale working graphs were used to relate the optical density of the unknowns to the concentrations. This was necessary as slight deviations from the Lambert-Beer law were observed at the higher concentrations. It has been suggested that these deviations are probably due to errors caused by the loss of light by reflection from the cell surfaces; however, the blank consisted of an identical cell filled with distilled water and errors of this type should be reduced to a minimum. It is also possible that they may be due to traces of dust in the solutions, as this would tend to give erroneously high values of the optical den sity at the very low concentrations. Whatever the cause of these deviations, one would expect the neodymium ion in solution to absorb similarly to an ideal gas and hence to follow Beer’s Law. ... 48 The samples used to obtain the standard curve were prepared by the dissolution of neodymium oxide in excess hydrochloric acid and evaporation of the resulting solu tion to a small volume to remove most of the excess acid. The solution was then diluted with distilled water. The absorption band at 796 mp. was used, as the molar extinction coefficient is greatest at this wave length. Other considerations such as interference from other rare earths were not important in this particular case. The wave length setting of the instrument was always adjusted with a standard solution 0.005 M in Nd+^ to give maximum absorption, as it is rather difficult to reproduce accurately the wave length settings on the Beckman DU. Also the 796 mp- band is extremely sharp, and slight errors in the wave length setting cause large differences in the values of the optical densities obtained. A constant slit width of 0.05 mm was used in all measure ments. This selected a narrow band of wave lengths of about 5.8 mp_ in width. Narrower bands than this made the setting of the wave length scale, with sufficient accuracy to reproduce readings, extremely difficult. The construction of two curves for 1cm and 10 cm cells was necessary, as the absorption of solutions more concentrated than 0.01 M became too large to determine accurately when the 10 cm cells were used. The range was 49 extended to more concentrated solutions by using 1 cm cells. These curves are shown in figures 5 and 6 . As solutions of neodymium perchlorate were also to be analyzed, and in some of these the perchlorate con centration was controlled at 3.00 M, it was necessary to determine if these high perchlorate concentrations had any effect on the absorption spectra of the hydrated neodymium ion. Plots of the molar extinction coefficient versus wave length are given in figure 7 for neodymium chloride and for neodymium perchlorate, |ci0^j = 3.00 C solutions. No shifts in the position of the absorption bands could be detected in the range 500 m y. to 900 mj> which was investigated. Points are also given on the standard curves in figures 5 and 6 for the neodymium perchlorate solutions with ^lO^j® 3.00 C. There is no observable intensification of the absorption bands. The lower limit of the spectrophotometric analyses was about 2 x 1 0 “^ gram atoms Nd/1000 g water. The analyses were reproducible to within 2 per cent in most cases. Before analysis, the samples were checked for any turbidity that would give high readings for the optical density of the solutions. This was done by measurement of the optical density at 930 m^». , 620 mjji , and 310 mjjk. where absorption of the Nd+ ion was negligible. Samples showing measurable turbidity were discarded. Measurements IUE TNAD UV FR EDMU AAYI, 0 M CELLS CM. 10 ANALYSIS, NEODYMIUM FOR CURVE STANDARD 5 FIGURE Log 0.7 0.3 0.5 0.6 0.2 0 OCNRTO - (RM OSIOg 2) I03 x H20) lONS/IOOOg (GRAM - CONCENTRATION ' c - 2 o I/I = 084 c' 4 8 .0 0 = I I0/ Log 3 4 NdCI3 O dC0) = 3.00 = Nd(CI04)3 A 5 6 7 FIGURE 6 FIGURE -4 1 Log O 4- .4 0 0.3 0 TNAD UV FR EDMU AAYI - I M CELLS. CM. I - ANALYSIS NEODYMIUM FOR CURVE STANDARD CONCENTRATION-C — (GRAM IONS NEODYMIUM/lOOOg NEODYMIUM/lOOOg IONS — (GRAM CONCENTRATION-C 2 3 o A Nd(CI04)3 Nd(CI04)3 A 4 NdCI3 log 5 p I 3.00 = q 0.086 = I / 6 Hfi) I02 x 7 8 - vo z o I- o z t— X LU a. < _i 6000 6500 7000 7500 8000 85005500 WAVE LENGTH X - ANGSTROMS FIGURE 7 MOLAR EXTINCTION VERSUS WAVE LENGTH. - A. Nd(Cl04)3 = 3.00* B. NdCI3 - I CM. CELLS 53 of the optical density were then taken on the original samples and also on samples acidified to pH 3. The results were the same within the experimental limits, indicating that the optical density measurements were related to the total neodymium in solution. Since the solubilities in water and basic solution were so slight, it was necessary to have a method of determining very small amounts of neodymium in solution. Quinalizarin has been suggested as a color reagent for rare earth analyses,and in the course of this work, B. Sandell, Colorimetric Determination of Traces of Metals. Interscience Publishers, New York (1945), p. 374. it was observed that colored complexes were also formed with alkannin, which has been used as a color reagent for 7Q beryllium ion. As alkannin was available only as a ^A. L. Underwood, The United States Atomic Energy Commission Declassified Document MDDC-1569 (1947). natural product, it was desirable to use another compound which could be easily synthesized and purified. Underwood r71 and Neumansuggested the use of napthazarin in the analysis 7 ^A. L. Underwood and W. P. Neuman, Anal. Chem., 21, 1349 (1949). ' of beryllium, and the use of this reagent for the analysis 54 of traces of neodymium was studied. All of these organic reagents have the common structural unit OH O and differ only in the side chains R and R'. Two of the organic molecules are involved in complex formation with a rare earth ion. The reaction is generally pictured as R R' 2 OH O The effect of pH and the naphthazarin concentration on the absorption spectra of the solutions was studied. The color change in the naphthazarin caused by complex formation with neodymium was the same as that caused by removal of hydrogen ions from the hydroxyl groups, as the molecule is an acid-base indicator. The complex could only be produced at pH values almost as high as that n eces sary to cause the same color change due to removal of hydrogen ions alone. Because of this, it was impossible to buffer ...the solution accurately enough to obtain repro ducible analytical data. The reaction was also very slow at room temperature, and it was. necessary to heat the samples to 100°C. and then to quench them in cold water to obtain measurable amounts of the complex. This method was abandoned as an analytical tool, and the neutron 55 activation method of analysis described in the next section was used for these analyses. Recently, Moeller and Tecotzky^ have also observed the formation of complexes *^T. Moeller and N. Tecotzky, J. Am. Chem. Soc., 77, 2649 (1955). of the rare earths with naphthazarin. Activation Analyses. Since the solubility of neo dymium hydroxide in water and in base was well below the limit of sensitivity of the spectrophotometric analysis, it was necessary to analyze these samples by the neutron- activation method. The samples were transferred in a closed system, by nitrogen pressure, from the equilibration bottles to 250 ml polyethylene bottles, which were sealed with paraffin, and shipped to the Oak Ridge National Laboratory where the complete analyses were performed. There, aliquots of the sample material were irradiated for one week in the ORNL Graphite Reactor. A cooling period of about 5.0 days after the reactor discharge was main- 24 tained to allow the Na (15.0 h) to decay from the sample, so that a minimum of radiation hazard would be experienced. After the cooling period, at least duplicate 5 ml aliquots of each sample were processed by a radiochemical separation using known amounts of inactive yttrium as "carrier'1 for the neodymium radioactivity. The yttrium carrier was initially precipitated with, alkali hydroxide. The hydroxide precipitate was then dissolved, and "scavenging” carriers such as copper, barium, sodium, strontium, etc. were added and removed by additional precipitations. The yttrium was finally precipitated as yttrium oxalate. After filter ing onto a tared filter paper, the precipitate was dried by suction. The chemical yield of the experiment was determined by weighing the oxalate compound as YgCCg0 4 )3 * 9 £[3 0 * The radioactivity of the induced ^ (11.3 d), produced in the reaction Nd^®(n, 2f ) N d ^ ^ was measured by means of gamma counting. The radiochemical purity of the separated radioactivity was checked by decay studies and gamma spectral analysis by means of a single channel gamma scintillation spectrometer. The comparator samples were NdgOg, and these were processed in the same way as the unknown samples. The results are based upon a com parison of the Nd ^ V radioactivity in both the standards and the test sample. Analysis of the Solid Phase in the Equilibria. The solid phases remaining upon the equilibration of the neodymium oxide with hydrochloric acid, perchloric acid, water, and sodium hydroxide solutions were all investigated by X-ray diffraction. The oxide obtained from the ignition of the neodymium 57 oxalate was blue-gray in color. It was observed during the tests on the completeness of the reaction of Nd 2 0 3 that the oxide changed to a solid with the characteristic rose color of the hydrated neodymium ion upon equilibra tion with the aqueous solution. An approximately 1.5 g sample of the oxide was equilibrated with distilled water, transferred to a porcelain boat, and dried in a tube fur nace at 80°C. in a stream of dried nitrogen. The nitrogen 73 was dried according to the method of Weiser and Milligan. 7 3 H. B. Weiser and W. 0. Milligan, J. Phys. Chem., 38, 512 (1934). These same authors studied the dehydration of neodymium hydroxide obtained by the action of NH^(OH) on solutions of NdGl 3 at 100°C.7^ The material was dehydrated in air 7 4 H. B. Weiser and W. 0. Milligan, J. Phys. Chem., 42, 673 (1938). dried as described above. Prom X-ray powder photographs, together with the dehydration isobars, they concluded that a crystalline hydroxide was obtained by precipitation at 100°C. This material was stable to about 200°C., and there was evidence for the formation of an intermediate phase consisting of a mono-hydrate of the oxide, i.e., NdgOg'HgO or NdO(OH), in the vicinity of 500°C. Under these con ditions, the anhydrous oxide was obtained at about 700°C. 58 7*5 Fricke and Seitz have investigated single crystals of 7R R. Fricke and A. Seitz, Z. anorg. Chem. 254, 107 (1947). NdCOH)^ in a similar fashion and have definitely shown the existence of the monohydrate which decomposed at approximately 350°G. The 1.5 g sample of water equilibrated oxide des cribed above was weighed after the drying at 80°C. It was then ignited in platinum in a stream of oxygen at 900°C. and reweighed. The loss of weight was calculated to be 13.78 per cent. The theoretical weight-per cent of water in NdgOg.SHgO is 13.84 per cent. No traces of chloride ion could be detected in the solid phase remaining after the equilibration with hydro chloric acid. This was determined by dissolution of the solid residue in dilute nitric acid and the addition of silver nitrate solution. In order to definitely characterize the solid phases, X-ray powder photographs were taken using a tube with a copper anode and filtering through nickel to obtain copper K o( radiation. The hydrated oxide samples were all dried as described above and sealed in 0.3 mm capillary tubes. The powder patterns for all of the equilibrated samples were observed to be the same and are shown, together with the pattern for Ndg0 3 , in figure 8 . RELATIVE INTENSITY IUE XRY ODR ATRS F XD SAMPLES OXIDE OF PATTERNS POWDER X-RAY 8 FIGURE ~ r ~ 10 5 25 o 7 15 jl X j _ R G ANGLEBRAGG ■ U- U- il I 1 1 - 6 II I 1 I DEGREES — 30 r~ 35 SAMPLE EQUILIBRATED N 1.0M NdzOj WATER SAMPLE EQUILIBRATED O M HCI MQOI 0.1 HCI04 M EQUILIBRATED SAMPLE SAMPLE EQUILIBRATED ~i— 40 g OH cn (D 60 The spacings in the samples of the hydrated oxide were calculated, indexing the reflections according to the data of Roy and McKinstry.7^ The calculated spacings 7 6r. Roy and H. A. McKinstry, Acta Cryst., 6 , 365 (1953). for the water equilibrated sample of IM 2 O 3 , together with those given by these authors for Nd (OH)^ are given in table 3. Neodymium hydroxide crystallizes in the hexagonal system, and the dimensions of the unit cell are given by Roy and McKinstry7 7 as a = 6.42110.010 A, c = 3.74±0.02 A. 7 7 Ibid., 365. These values agree favorably with those given by Zacha- riasen7® of a = 6.42±0.Q2 £ and c = 3.74i0.02 A. Fricke 7®W. H. Zachariasen, J. Chem. Phys., 16, 254 (1948). 79 „ 0 0 and Seitz gave a ** 6.27 A and c = 3.52 A which differ 7 Q R. Fricke and A. Seitz, Z. anorg. allgem . C h e m . , 254, 107 (1947). from the values of the unit cell dimensions considerably. This has been attributed to the use of impure rare 80 earths. The hydroxide is of the so-called UCI 3 type in 80 R. Roy and H. A.. McKinstry, Acta Cryst., 6 , 365 (1953). 61 Table 5 POWDER PHOTOGRAPH DATA FOR THE WATER EQUILIBRATED SAMPLE OF NEODYMIUM OXIDE o o obs. ^obs. d/n A d A * I* Line Indiees*- 8,25 4 5.38 5.57 80 1 0 0 13.6 1 / 2 3.29 14.0 4 3.20 3.20 65 1 1 1 14 « 5 5 3.09 3.08 85 1 0 1 15.0 1 / 2 2.98 15.5 3 2.89 16.1 1 / 2 2.77 2.768 10 2 0 0 20.3 5 2.28 2.217 1 0 0 2 0 1 21.5 1 / 2 2 . 1 0 2.092 10 2 1 0 23.8 1 / 2 1.91 24.6 1 1 . 8 6 1.848 50 300 24.9 3 1.83 1.842 1 0 0 2 1 1 25.9 1 1.77 26.9 1 1.71 28.6 4 1.61 1. 605 30 2 2 0 *R. Roy and H. A. McKinstry, Acta Cryst., 6 . 365 (1953). 62 which each metal ion is surrounded by 9 OH" with 6 at equal distances and 3 farther away. There are two molecules of N d (O H )3 per unit cell. The anhydrous oxide was also examined and found to be the A type of NdgOg, and the Bragg angles found for the reflections are given in table 4 together with the angles found by Zachariasen^l for A-Ndg 0 3 . The values of ^^do not H. Zachariasen, Z. Phys. Chem. , 123, 134 (1926). agree exactly, although the pattern'is obviously the same. It seems likely that the oxide used by Zachariasen was probably contaminated by rather large amounts of other rare earths, as the purification procedures for the rare earths were unsatisfactory as long ago as 1926. The faint lines in the water equilibrated sample of NdgOg which do not correspond to spacings in Nd( 0 H )3 are due to small amounts of unhydrated oxide or possibly to traces of a monohydrate which shows most of the lines of the oxide plus a few which correspond to neither the oxide or hydroxide. This may be seen by comparison of tables 3 and 4. Vickery8 *2 - R. C. Vickery, Chemistry of the Lanthanons, Academic Press, New York (1953), p. 208. states that only oxides capable of forming the A type lattice appear to slake and give true hydroxides. The A-MgOg structure belongs to the hexagonal system. Each 63 Table 4 POWDER PHOTOGRAPH DATA FOR THE ANHYDROUS OXIDE OP NEODYMIUM o* Line Indices-:!- I obs o •^obs* 13.5 2 13.32 2 1 0 1 0 13.67 2 1 0 1 1 15.0 3 14.82 2 0 0 0 2 15.2 5 15.32 5 1 0 1 1 20.3 3 20.16 2 1 0 1 2 23.8 4 23.60 3 1 1 2 0 26.8 4 26.59 4 1013 27.8 1/4 27.54 1 2023 28.6 4 28.39 1 1 2 2 5 28.9 3 28.64 2 0 2 1 31.0 1 / 2 30. 78 1/ 2 - 1 0004 32.1 2 31.88 1 2 0 2 2 ■^W. H. Zachariasen, Z. Phys. Chem. , 1231 134 (1926). 64 metal ion has a coordination number of seven, four oxide, ions being at an equal distance and three farther away. In the samples equilibrated with chloride ion, there was no evidence for the formation of basic salts. The sample equilibrated with 0.1 M perchloric acid gave no lines other than for the hydroxide; however, the diffraction was weak and the lines less sharp than in the case of the other samples. Some material may have been present that was amorphous to X-rays. During the course of the study of the dissolution in acid, an effort was made to work at a con stant ionic strength of 3.0 in perchloric acid. The ionic strength was controlled by the addition of NaClO^. During the equilibration, the solid phase increased very noticeably in volume, and the equilibrium data Indicated the formation of a basic salt. As the anion concentration was so great, one might anticipate the formation of a basic salt; however, it is somewhat surprising that one is formed with the per- pO chlorate ion. It has been observed by Dutt0^ that basic k. Dutt, J. Indian Chem. Soc. , 2 2 , 97, 107 (1945). nitrates of neodymium of the type Nd 0 (N0 3 ) and Ndg0 3 . 2 NdOfNOg) exist, and that they are insoluble in water. Little other data are available on the basic salts of the trivalent rare earths. THE DATA The data for the equilibria of neodymium hydroxide and hydrochloric acid, perchloric acid, sodium hydroxide solutions, and neutral water are given in tables 26 to 31. The results of the hydrolysis studies are tabulated in tables 5 to 25. 65 66 Table 5 HYDROLYSIS OF NEODYMIUM PERCHLORATE, c * 24.45 mC Standardization of Electrodes Solution Bs 12.28 mC (OH); 3000^0 mC Hat 2987.7 mC CIO4 Solution Sr 9.931 MC H; 2990.1 mC Ha; 3000.0 mC CIO4 Solution H i: H d + 3 48.9 mC; Ha+ 2852.0 mC; CIO4 3000.0 mC; H + l.25 mC Titration of 50.00 ml of S with 42.75 ml of B vb ml -E^_ mV -Eg m V H mC -Ex1mV -Eg1mV 0 . 0 0 334.48 334.48 9.931 452.98 452.98 3.00 331.47 331.47 8.674 453.45 453.45 6 . 0 0 327.70 327.70 7.551 453.24 453.24 9.00 324.22 324.22 6.543 453.44 453.44 1 2 . 0 0 320.56 320.56 5.632 453.63 453.65 15.00 316.68 316.68 4.805 453.84 453.84 18.00 312.52 312.52 4.052 454.05 454.05 2 1 . 0 0 308.06 308.06 3.362 454.39 454.39 24.00 303.36 303.36 2.750 454.85 454.85 27.00 297.38 297.38 2.143 455.28 455.28 30.00 290.88 290.88 1.602 456.26 456.26 35.00 276.13 276.13 0.785 459.83 459.83 42.75 plus 7.25 ml HgO E 1 0 * = E g o 1 -453.4 mV 67 Table 6 HYDROLYSIS OF NEODYMIUM PERCHLORATE, o =» 24.45 mC Titration of Buffer Solution Solution Bg : 12.46 mC (OH)7 3000 .0 mC Na; 2987.5 mC CIO, ^ i ^ 1 0 0 ml of solution Nj were added , and equal amounts of and were added during the titration. B 2 Vb ml -E2 mV -Eg mV A V t / A E ! x 1 0 1 AV'b/'YEg x 1 0 1 Vb ml ml/mV m l / m V 50.00 261.49 261.49 34.6 34.6 50.50 51.00 258.60 258.60 31.7 31.7 51.50 52.00 255.44 255.44 30.0 30.0 52.50 53.00 252.11 252.11 25.7 25.7 53.50 54.00 248.22 248.22 22.9 22.9 54.50 55.00 243.86 243.86 20.3 20.3 55.50 56.00 238.93 238.93 16.4 16.4 56.50 57.00 232.84 232.84 13.3 13.3 57.50 58.00 225.30 225.30 9.41 9.41 58.50 59.00 214.67 214.67 6.54 6.54 59.50 60.00 199.38 199.38 4.06 4.06 60.50 61.00 174.77 174.77 61.50 162.24 162.24 62.00 140.83 140.83 62.50 109.51 109.51 63.00 90.59 90.59 63.90 73.11 73.11 Equivalence point of the "free acid” 1 1 . 2 0 ml Bo P.A. mC ■ •iii.2 0 x 12.28 mC Table 7 HYDROLYSIS OF NEODYMIUM PERCHLORATE. c « 24.45 mC Calculation of Average Ligand Number Results of the titration in table 6 Vb ml H x 105 C h x 10 5 C (h-H) x 105 C Z x 104 -log h 50.00 62. 6 57.1 -5. 5 3.243 51.00 46.5 51.0 -5.5 3.292 52.00, 50.4 45.0 -5.5 3.357 53.00' 44.5 39.5 -5.0 3.403 54.00 38.7 34.0 -4.7 3.460 55.00 33.0 28.8 -4.2 3.541 56.00 2 7.3 23.7 -3.6 3.626 57.00 2 1 . 8 18.7 -3.1 3.729 58.00 16.4 13.9 -2.5 3.856 59.00 1 1 . 1 9.27 -1 . 8 4.033 60.00 5.34 5.09 -0.75 4.293 61.00 0.716 1.95 1.23 5.0 4.709 61.50 -0.181 1 . 2 0 1.39 5.6 4.922 62.00 -4.32 0.520 4.84 19.8 5.284 62.50 -6.81 0.154 6.96 28.4 5.813 63.00 -9.03 0.0736 9.10 37.2 6.133 63.90 -12.35 0.0372 12.39 50.5 6.429 A Vb/^E x 10' ml mV 40 20 30 0 2 4 6 8 0 2 64 62 60 58 56 54 52 50 IUE9 EEMNTO O THE OF DETERMINATION 9 FIGURE A. 24.45 mC 24.45 A. +3 RE CD N H NOYIM BUFFERS NEODYMIUM THE IN ACID FREE AVb/AE x 10 1 ml mV" b ml.Vb 14 6 0 1 2 3 4 5 56 55 54 53 52 51 50 - . = .9 C Nd+3 mC 9.79 = C B. E. O E X © 0 L J CD 70 Table 8 HYDROLYSIS OF NEODYMIUM PERCHLORATE, c ~ 9.79 mC Standardization of Electrodes Solution B: 12.28 raG (OH)J 3000.0 mC Ha; 2987.7 mC CIO4 Solution S: 9.931 mC H; 2990.1 mC Na; 3000.0 mC CIO4 + 3 * Solution Nor 19.58 mC Nd ; 2980.2 mG Na; 3000.0 mC GIO4 1.318 m C H + Titration of 50.00 ml of S with 50.00 ml of B v b ml -E}_ mV -Eg mV H mC -E-l * mV - E g 1 mV 0 . 0 0 333.52 333.36 9.931 452.02 451.86 3.00 330.36 330.28 8.674 452.34 452.26 6 . 0 0 326.83 326.83 7.551 452.37 452.37 9.00 323.17 325.15 6.543 452.39 452.39 1 2 . 0 0 319.16 319.16 5.632 452.25 452.25 15.00 315.26 315.18 4.805 452.42 452.35 18.00 311.28 311.37 4.052 452.81 452.90 2 1 . 0 0 306.98 306.88 3.362 453.31 453.21 24.00 302.22 302.33 2. 750 453.71 453.82 27.00 296.52 296.52 2.143 454.42 454.42 30.00 289.67 289.67 1 . 602 455.05 455.05 35.00 273.66 273.66 0.785 457.36 457.36 50. f 00w v VV E 1 0 1 =-■452. 3 mV E 2 0 ‘ =-■452. 2 mV Average value -452.3 mV used in calculations. 71 Table 9 HYDROLYSIS OF NEODYMIUM PERCHLORATE, c - 9,79 mC Titration of Buffer Solution 1 0 0 ml of solution Ng were added, and equal amounts of B and Kg were added during the titration. V b ml -E1 mV -Eg mV A V b / ^ % x 1 0 1 Z\Vb/ £ E 2 x 1 0 1 Vb ml ral/mV ml/mV 50.00 231.90 231.90 11.4 11.4 50.50 51.00 223.16 223.16 8 . 0 8 . 0 51.50 52.00 210.97 210.97 4.8 4.8 52.50 53.00 190.02 190.02 4.6 4.6 53.25 53.50 176.33 176.33 2.4 2.4 53.75 54.00 155.93 155.93 1 . 2 1 . 2 54.25 54.50 115.62 115.62 2 . 0 2 . 0 55.25 55.00 90.63 90.06 55.50 73.24 73.17 55.80 65.71 65.69 Equivalence point of the '‘free acid" 3.90 ml B P.A mC 11*13 x 12a28 mC 103.90 72 Table 10 HYDROLYSIS OF NEODYMIUM PERCHLORATE, c = 9.79 mC Calculation of Average Ligand Number Results of the titration in table 9 Vb ml H x 106 C h x 10 5 C (h-H) x 105 C Z x 104 -log : 50.00 21.4 18.8 -2 . 6 3.725 51.00 15.7 13.4 -2.3 3.873 52.00 1 0 . 2 8.34 -1.9 4.079 53.00 4.8 3.68 -1 . 1 4.434 53.50 2 . 1 2.16 0.04 4 4. 665 54.00 -0.53 0.977 1.51 15.3 5.010 54.50 -3.15 0.204 3.35 34.2 5.691 55.00 -5.74 0.0755 5.82 59.4 6 . 1 2 2 55.50 -8.31 0.0391 8.34 85.2 6.408 55.80 -9.81 0.0293 9.84 1 0 1 . 6.533 73 Table 11 HYDROLYSIS OF NEODYMIUM PERCHLORATE. c » 4.895 mC Standardization of Electrodes Solution B: 12.28 mC (OH); 3000.0 mC Na; 2987.7 mC CIO4 Solution Si 9.931 mC Hj 2990.1 mC Na; 3000.0 mC CIO4 Solution N3 : 9.79 mC Nd+3; 2988.7 mC Na| 3000.0 mC CIO4 1.540 mC H+ Titration of 50.00 ml of S with 50.00 of B v b ml -Ej mV -E mV H mC -E-j/ mV -E2 » ml 0 . 0 0 335.26 335.26 9.931 453.76 453.76 3.00 331.78 331.78 8.674 453.76 453.76 6 . 0 0 328.38 328.38 7.551 453.92 453.92 9.00 324.86 324.86 6.543 454.08 454.08 H to 0 0 0 321.24 321.24 5. 632 454.31 454.31 15.00 317.25 317.25 4.805 454.41 454.41 18.00 312.96 312.96 4.052 454.49 454.49 2 1 . 0 0 308.58 308.58 3. 362 454.91 454.91 24.00 303.37 303.37 2.750 454.86 454.86 27.00 297.31 297.31 2.143 455.21 455.21 30.00 290.23 290.23 1.602 455.61 455.61 35.00 274.05 274.05 0. 785 457.75 457.75 50.00 % 0 ’ c E 2 0 ’ = -454.0 mV 74 Table 12 HYDROLYSIS OF NEODYIVHUM PERCHLORATE, c « 4.895 mC Titration of Buffer Solution 1 0 0 ml of solution Ng were added, and equal amounts of B and N 3 were added during the titration. vb ml -E]_ mV -Eg mV ^ V b/AE-l x 1 0 1 A V b/ A E 2 x 1 0 1 Vb ml ml/mV ml/mV 50.00 246.17 246.17 22.5 23.0 50.50 51.00 241.73 241.73 17.5 17.2 51.50 52.00 236.03 236.03 13.6 13. 6 52.50 53.00 228.68 228.68 9.7 9.8 53.50 54.00 218.36 218.52 5." 9 6 . 0 54.50 55.00 201.46 201.80 3.1 3.0 55.25 55.50 185.22 185.22 2 . 2 2 . 2 55.75 56.00 162.61 162.61 1 . 0 1 . 0 56.25 56.50 109 . 73 109.73 56.90 84.80 84.80 Equivalence point of the ’’free acid” 6.05 ml P.A. mC - 15.50 x 12.28 mC 106.05 75 Table 15 HYDROLYSIS OF NEODYMIUM PERCHLORATE, o = 4.895 mC Calculation of Average Ligand Humber Results of the titration in table 12 Vb ml H x 10 5 C h x 105 C (h-H) x 105 C Z x 104 -log h 50.00 32.5 30.7 -1 . 8 3.513 51.00 26.9 25.8 -1 . 1 3.589 52.00 21.3 2 0 . 6 -0.7 3. 685 53.00 15.9 15.6 -0.3 3.-808 54.00 1 0 . 6 10.4 -0 . 2 3.982 55.00 5.40 5.40 0 . 0 0 0 . 0 0 4.268 55.50 2.80 2 . 8 6 0.06 1 . 2 4.544 56.00 0.28 1.19 0.91 18.6 4.926 56.50 -2. 25 Oo 15 2.40 49.0 5.820 56.90 -4.19 0.057 4.25 86.9 6.241 4.90 me. Ndf3 3 0 > E 20 e UJ jQ > < 1 I I I I I I 1 50 51 52 53 54 55 56 57 58 Vb - ml. FlGURE/0 DETERMINATION OF THE FREE ACID IN THE N NEODYMIUM BUFFERS. Os pKQ = 8.0 pKa = 8.5 120 100 80 X 24.45 mC O 9 7 9 mC * 9 60- A 4.90 mC X n 40- 20 0 1 4 0 5.0 6.0 7.0 -log h =£ pH ■N -M FIGURE // HYDROLYSIS OF NEODYMIUM PERCHLORATE 78 Table 14 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE. o = 25*00 mC Standardization of Electrodes Solution B: 10.17 mC (OH); 3000.0 mC Na; 2989.8 mC CIO4 Solution S: 9.968 mC H; 2990.0 mC Na; 3000.0 mC CIO4 Solution Pit 50.00 raG Pr+3j 2848.9 mC Na; 3000.0 mC CIO I 1.099 mC H+ Titration of 50. 00 ml of S with 50.00 ml of B Vb ml -Ex mV -Eg mV H mC -Ei* mV ' -E* mV 0 . 0 0 333.94 334.01 9.968 452.36 452.43 3.00 330.79 330.79 8.819 452.34 452.34 6 . 0 0 327.52 327.52 7.811 452.18 452.18 9.00 324.10 324.10 6.897 451.97 451.97 1 2 . 0 0 320.73 320 . 73 6.071 451.87 451.87 15.00 317.26 317.26 5.320 451.80 451.80 18.00 313.59 313.59 4. 737 451.65 451.65 2 1 . 0 0 309.71 309.71 4.011 451.51 451.51 24.00 305.54 305.54 3.436 451.30 451.30 27.00 300.95 300.95 2.906 451.02 451.02 30.00 295.54 295.54 2.416 450.36 450.36 35.00 285.01 285.01 1.675 449.24 449.24 50.00 Eiof = SgQ* ® -452.1 mV 79 Table 15 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c - 25.00 mC Titration of Buffer Solution 1 0 0 ml of solution P^ were added, and equal amounts of B and P-^ were added during the titration. vb ml -E]_ mV -Eg mV A V h / A E x x 1 0 l & V h / A E 2 x 1 0 1 V b ml ml/mV ml/mV 50.00 257.00 257.00 33.1 34.7 50.25 50.50 255.49 255.49 36.5 36.5 50.75 51.00 254.12 254.12 31.4 31.4 51.50 52.00 250.93 250.93 29.0 29.0 52.50 53.00 247.48 247.48 26.5 26.5 53.50 54.00 243.70 243.70 21. 7 21.7 54.50 55.00 239.09 239.09 19.3 19.0 55.50 # 56.00 233•90 233.82 14.9 15.0 56.50 57.00 227.18 227.18 12.4 12.4 57.50 58.00 219.08 219.08 8 . 0 8 . 0 58.50 59.00 206. 65 206.65 5.2 5.2 59.50 60.00 187.35 187.35 3.3 3.3 60.25 60.50 172.33 172.33 2 . 6 2 . 6 60.75 61.00 153.35 153.35 3.5 3.5 61.15 61.30 144.78 144.78 61. 60 137.45 137.45 62.00 127.06 127.06 62.50 106.74 106.66 Table 15 (Cont^.) HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c - 25.00 mC Titration of Buffer Solution ml -E^ mV -Eg mV x 10^ ZlV-^/^lEg x 10^ ml ml/mV ml/mV 63.00 85.31 85.31 63.50 68.55 68.55 64.00 62.76 62. 76 Equivalence point of the "free acid" 11.20 ml Bg Table 16 81 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, o = 25.00 mC Calculation of Average Ligand Number Results of the titration in table 15 vb ml H x 10 5 C h x 1 0 5 (h-H) x 105 C Z x 104 -log h 50.00 49.9 50.4 0.5 3. 298 50.50 47.4 47.5 0 . 1 3. 323 51.00 44.9 45.0 0 . 1 3.347 52.00 40.0 39.8 -0 . 2 3.401 53.00 35.2 34.8 -0.4 3.458 54.00 30.5 30.0 -0.5 3.523 55.00 25.9 25.1 -0 . 8 3.600 56.00 21.4 20.5 -0.9 3.689 57.00 17.0 15.8 -1 . 2 3.802 58.00 1 2 . 6 11.5 -1 . 1 3.938 59.00 8.33 7.13 -1.15 4.150 60.00 4.13 3.36 -0.77 4.474 60.50 2.06 1.87 -0.19 4. 730 61.00 0 . 0 0 0.89 0.89 3.56 5.049 61.30 -1 . 2 1 0.58 1.79 7.16 5.194 61. 60 -2.42 0.48 2. 90 1 1 . 6 5.319 62.00 -4.02 0.32 4.34 17.3 5.494 62.50 -6.04 0.14 6.18 24.7 5.838 63.00 -8 . 0 1 0.06 8.07 32.3 6 . 2 0 0 63. 50 -9.96 0.03 1 0 . 1 2 40.5 6.482 64.00 -11.93 0 . 0 2 11.95 47.8 6.582 25iOmC Pr+3 12.5 m C Pr+3 4 0 40 > E E O x « 20 20 ■Q > < 50 52 54 56 58 60 62 64 50 56 62 64 Vb ml Vbml 00 FIGURE 12 DETERMINATION OF THE FREE ACID IN THE PRASEODYMIUM BUFFERS 83 Table 17 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE. o » 12.50 mC Standardization of Electrodes Solution B: 9.951 mC (OH); 3 0 0 0 . 0 raG Na; 2990.O mC CIO4 Solution S: 9.931 mC H; 2990.1 mC Na"j 3000.0 mG 010^ Solution Po: 25.00 raC Pr+3; 2924.0 mC Na; 3000.0 mC CIO4 0.9627 mC H+ Titration of 50 . 0 0 ml of S with. 50.00 ml of B Vb ml -E^ toV -Eg mV H mC - E i 1 mV -E2 T mV 0 . 0 0 336.36 336.36 9.931 454.86 454.86 3.00 333.24 333.24 8.806 454.83 454.83 6 . 0 0 330.08 333.08 7.802 454.78 454.78 9.00 326.81 326.81 6.898 454.67 454.67 1 2 . 0 0 323.02 323.02 6.084 454.65 454.65 15.00 319.50 319.59 5.343 454.02 454.02 H CO O O * 316.04 316.04 4.669 453.94 453.94 2 1 . 0 0 312.28 312.28 4.051 453.82 453.82 24.00 308.31 308.31 3.484 453.73 453.73 27.00 303.84 303.84 2. 960 453.45 453.45 30.00 298.74 298.74 2.476 452.93 452.93 35.00 289.23 289.23 1.745 452.42 452.42 E 1 0 * = ^20* “ "454.5 mV 84 Table 18 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c ■ 12.50 mC Titration of Buffer Solution 100 ml of solution Pg were added, and equal amounts of B and Pg were added during the titration. x 1 0 1 A v h / m 2 1 0 1 Vb ml -Ei mV -Eg mV x Vb ml ml/mV ml/mV 50.00 258.22 258.22 35.4 35.4 50.50 51.00 255.39 255.39 33. 7 33.7 51.50 52.00 252.42 252.42 28.0 28.0 52.50 53.00 248.85 248.85 25.4 25.4 53.50 54.00 244.91 244.91 2 1 . 6 2 1 . 6 54.50 55.00 240.28 240.28 18.7 18.7 55.50 56.00 234.92 234.92 14.8 14.8 56.50 57.00 228.18 228.18 1 1 . 2 1 1 . 2 57.50 58.00 219.25 219.25 7.5 7.5 58.50 59.00 205.98 205.98 4.3 4.3 59.50 60.00 182.89 182.89 4.8 4.8 60.25 60.50 162.25 162.25 61.00 137.36 137.36 61.50 111.00 111.00 62.00 91.47 91.47 Equivalence point of the "free acid" 10.60 ml B /50.00 - 50.00 0.009951^ P.A. mC - 10.60 + \______0.009951 / x 9.951 110.60 85 Table 19 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c = 12.50 mC Calculation of Average Ligand Number Results of the titration in table 18 Vb ml H x 105 C h x 10 5 C (h-H) x 105 C Z x 104 -log h 50.00 47.6 47.9 0.3 3.320 51.00 42.7 43.1 0.4 3.365 52.00 37.9 38.4 0.5 3.416 53.00 33.2 33.5 0.3 3.475 54.00 28.5 28.7 0 . 2 3.543 55.00 24.0 24.0 0 . 0 3.620 56.00 19.5 19.4 -0 . 1 3.712 57.00 15.1 15.0 -0 . 1 3.825 58.00 1 0 . 8 1 0 . 2 -0 . 6 3. 992 59.00 6.60 6.31 -0.29 4. 200 60.00 2.45 2.57 0 . 1 2 0.97 4.591 60. 50 0.41 1. 15 0.74 5.9 4.941 61.00 -1.62 0.44 2.06 16.5 5.360 61.50 -3.62 0.16 3.78 30.3 5.860 62.00 -5. 62 0.07 5.69 45.5 6.136 86 Table 20 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE. o ■ 10.24 mC Standardization of Electrodes Solution B: 9.951 mC (OH)J 3000.0 mC Na; 2990.0 mC ■ClOj Solution S: 9.931 mC H; 2990.1 mC Na; 3000.0 raC CIO^ Solution P„: 20.48 mC Pr+3; 2938.0 mC Na; 3000.0 raC CIO4 0 0.625 mC H+ Titration of 50.00 ml of solution S with. 50.00 ml of B V b ml - E ± mV -Eg mV H mC -Ex' mV - E g 1 mV 0 . 0 0 337.25 337.25 9.931 455.74 455.75 3.00 333.94 333.94 8.804 455.53 455.53 6 . 0 0 330.61 330.61 7.800 455.31 455.31 9.00 327.28 327.28 6.897 455.15 455.15 1 2 . 0 0 323.82 323.82 6.082 454.92 454.92 15.00 320.35 320.35 5.342 454.78 454.78 18.00 316.53 316.53 4.558 454.43 454.43 2 1 . 0 0 312.72 312.72 4.049 454.27 454.27 24.00 308.43 308.43 3.482 453.85 453.85 27.00 303.51 303.51 2.958 453.13 453.13 30.00 297.78 297.78 2.475 451.97 451.97 50.00 E]_q ' “ Ego' c -455.2 mV 87 Table 21 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c ■ 10.24 mC Titration of Buffer Solution 1 0 0 ml of solution Pg were added, and equal amounts of B and P^ were added during the titration. vb ml -E-j_ mV -Eg mV AV^/AE-l x 1 0 1 ZWb/lEp x 1 0 1 Vfc ml ml/mV ml/mV 50.00 247.31 .247.31 2 0 . 2 19.4 50.50 51.00 242.36 242.16 17.4 18.1 51.50 52.00 236.62 236. 62 13.9 13.9 52.50 53.00 229.43 229.43 10.5 10.5 53.50 54.00 219.87 219.87 1 4. 7.2 7.4 54.50 55.00 206.04 206.33 3.8 3.8 55.50 56.00 179.48 180.12 1 . 1 1 . 1 56.25 56.50 133.58 134. 78 57.00 123.90 123.90 57.50 103.71 103.71 58.00 81.70 83.08 58.50 64.27 65.37 59.00 58.22 58.49 59.50 54.35 54.35 Equivalence point of the "free acid" 6.60 ml B /50.00 - 50.00 x .009931 ) 6.60+1 106.60 / x 9.951 106.60 88 Table 22 HYDROLYSIS OF PRASEQDYMIUM PERCHLORATE, c = 10.24 mC Calculation of Average Ligand Number Results of the titration in table 21 vb ml H x 105 C h x 105 C (h-H) x 105 C Z x 1 0 ^ -log h 50.00 30.8 30.6 -0 . 2 3.515 51.00 25.8 25.2 -0.5 3.599 52.00 2 1 . 0 2 0 . 2 -0 . 8 3.695 53.00 16.3 15.2 - 1 . 1 3.817 54.00 1 1 . 6 10.5 -1 . 1 3.978 55.00 7.0ST 6.16 -0.93 4.210 56.00 2.62 2 . 2 1 -0.41 4. 655 56.50 0.42 0.38 -0.04 5.426 57.00 -1.73 0.25 1.98 19.3 5. 600 57.50 -3.86 0 . 1 2 3.98 38.8 5.941 58.00 -6.05 0.05 6 . 1 0 60 6.302 58.50 -8.18 0.03 8 . 2 1 80 6.598 59.00 -10.28 0 . 0 2 10.30 1 0 1 6.710 59.50 -12.36 0 . 0 2 12.38 1 2 1 6.775 IUE 3 EEMNTO O TE RE CD N H PAEDMU BUFFERS PRASEODYMIUM THE IN ACID FREE THE OF DETERMINATION 13 FIGURE AVb/AE x I0 1 ml. mV" 030 30 20 50 2 53 52 = 02 C Pr+3 mC 10.24 C= 5 6 7 0 1 2 3 4 5 6 7 58 57 56 55 54 53 52 51 50 57 56 55 20 b ml. Vb 5.00 mC pr pr + 3 mC5.00 89 90 Table 25 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c ■ 5.00- mC Standardization of Electrodes Solution B: 10.17 mC (OH); 3000.0 raC Na; 2989.8 mC CIO4 Solution S: 10.08 mG h| 2989.9 mC Na; 3000.0 mC CIO 4 Solution P4 : 10.00 raC Pr+3; 2969.2 raC Na| 3000.0 mC CIO4 ; 0.769 mC H+ Titration of 50. 0 0 ml of solution S with 50.00 of B Vb ml -Eq_ mV -Eg mV H mC -Ei'mV -Eg1 ntf 0 . 0 0 335.33 335.33 10.08 453.45 453.45 3.00 332.30 332.30 8.934 453.51 453.51 6 . 0 0 329.13 329.13 7.911 453.47 453.47 9.00 325.96 325.96 6.992 453.47 453.47 1 2 . 0 0 322.64 322.64 6.161 453.40 453.40 15.00 319.29 319.29 5.406 453.41 453.41 18.00 315.84 315.84 4.721 453.45 453.45 2 1 . 0 0 311.90 311.90 4.090 453.19 453.19 24.00 398.94 398.94 3.512 453.25 453.25 27.00 303.58 303.58 2.979 453.01 453.01 30.00 298.42 298.42 2.486 452.50 452.50 35.00 288.63 288.63 1.741 451.87 451.87 50.00 E 1 0 1 = Ego* = -453.4 mV Table 24 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE, c ■ 5.00 mC Titration of Buffer Solution 1 0 0 ml of solution P4 were added, and equal amounts of B and P^ were added during tbe titration. vb ml -E]_ mV -Eg mV A V b/ A E x x 1 0 1 ZiVb/AEg x 101 Vb ml ml/mV ml/raV 50.00 249.98 249.98 23.6 23.6 50.50 51.00 245.75 245.75 17.2 17.2 51.50 52.00 239.94 239.94 17.5 17.5 52.50 53.00 234.22 234.22 14.0 14.0 53.50 54.00 227.06 227.06 11.7 11. 7 54.25 54.50 222.77 222.77 10.5 10.5 54.75 55.00 218.00 218.00 8.5 8.5 55.25 55.50 212.11 212.11 6 . 6 6 . 6 55.75 56.00 204.54 204.54 4.8 4.8 56.25 56.50 194.24 194.24 3.5 3.5 56.75 57.00 179.94 179.94 2.4 2.4 57.25 57.50 158.98 158.98 1 . 6 1 . 6 57.75 58.00 128.75 128.75 1 . 6 1 . 6 58.25 58.50 96.56 96.56 59.00 70.54 70.20 59.30 58.78 58.35 Equivalence point of the 11free acid" 7.70 ml B f 50.00 - 50.00 x .01008 1 F .A. mC « 7. 70 + .01017 / x 10.17 107.70 92 Table 25 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE. c « 5.OQ mC Calculation of Average Ligand Number Results of the titration in table 24 V b ml H x 105 C h x 105 C (h-H) x 105 C Z x 104 -log : 50.00 36.2 36.4 -0 . 2 3.440 51.00 31.2 30.9 -0.3 3.510 52.00 26.3 24. 6 -1.7 3.610 53.00 21.5 19.6 -1.9 3.706 54.00 16.7 14.9 -1 . 8 3.827 54.50 14.4 1 2 . 6 -1 . 8 3.899 55.00 1 2 . 1 10.5 -1 . 6 3.980 55.50 9.81 8.32 -1.49 4.080 56.00 7.55 6.18 -1.37 4. 209 56.50 5.31 4. 14 -1.17 4.383 57.00 3.08 2.38 -0.70 4. 624 57.50 0 . 8 8 1.05 0.17 3.40 4.978 58.00 -1.30 0.32 1.62 32.4 5.488 58.50 -3.46 0.09 3. 55 71.1 6.032 59.00 -5.60 0.03 5.63 113 6.474 59.30 -6 . 8 6 0 . 0 2 6 . 8 8 138 6.671 pKo = 8.0 PKq = 8.5 _ O 25.00 mC 120 A 12.50 mC 100 __ □ 10.24 mC X 5.00 mC 80 * 2 60 X N 40 20 0 - 5.04.0 6.0 7 0 - log h - pH ^ Ca> FIGURE 14 HYDROLYSIS OF PRASEODYMIUM PERCHLORATE 94 Table 26 SOLUBILITY OP NEODYMIUM HYDROXIDE IN HYDROCHLORIC ACID AT 25°0. Initial Equilibrium Number of Temperature Concentration Concentration Samples of the of HC1 of Neodymium Initial Moles/1000 g g Atoms/1000 g Agitation H20 HgO o c. 0.1004 0.0335 1 25 0.0502 0.0168 1 25 0.0502 0.0168 1 35 0.0125 0.00380 1 25 0.0125 0.00380 1 35 0.0101 0.00357 1 25 0.0101 0.00340 2 25 0.0101 0.00340 2 35 0.0099 0.00329 1 25 0.0099 0.00330 1 25 0.0079 0.00263 1 25 0.0051 0.00170 1 25 0.0051 0.00180 1 25 0.0040 0.00139 1 25 0.0040 0.00140 1 3 5 0.0025 0.00084 1 25 0.0025 0.00084 1 35 0.0020 0.00065 1 35 0.0010 0.00031 1 25 0.0005 0.00017 1 25 0.0005 0.00015 1 35 GRAM ATOMS Nd/IOOOg HLO x I03 4 3 2 0 FIGURE IS OUIIY F d0) I DLT HDOHOI AI 01 HYDROCHLORIC ACID DILUTE IN Nd(0H)3 OF SOLUBILITY 2 = OE HllOg^ x I03 x HCl/lOOOgH^O MOLES = H 4 6 d 030 + .0 I0"5 x 4.80 + H 0.330 = Nd 3° SAMPLE 35° O 2° SAMPLE 25° X 8 10 12 <0 Table 27 DATA ON THE EQUILIBRIUM BETWEEN NEODYMIUM HYDROXIDE AND HYDROCHLORIC ACID AT 25°C. Initial Equilibrium Concentration Concentration Nd+3 Activity Activity * 1% Hydrochloric Dissolved Acid-Moles/lOOOg Neodymium- M * 3. n* B / * loie x 1 0 3 x 1 0 ° H20 g Atoms/lOOOg h 20 0.1004 0.0335 0.0778 2.61 7.9 0.333 5.3 0.0502 0.0167 0.129 2,15 7.9 0.332 4.4 0.0502 0.0167 0.129 2.15 6.2 0.332 9.0 0.0502 0.0167 0.129 2.15 6.2 0.332 9.0 0 . 0 1 0 1 0.00337 0.309 1.04 5.6 0.334 5.9 0 . 0 1 0 1 0.00337 0.309 1.04 4.4 0.334 1 2 . 0 . 0 1 0 0 0.00335 0.309 1.04 6.3 0.335 4.2 0 . 0 1 0 0 0.00335 0.309 1.04 5.8 0.335 5.3 0.0099 0.00350 0.314 1.04 7.9 0.334 2.1 4.8 0.0099 0.00330 0.314 1.04 6.0 0.334 CO 1.04 . 0.334 9.4 0.0099 0.00330 0.314 0.0099 0.00330 0.314 1.04 4.2 0.334 14. Table 27 (Cont«d.) DATA ON THE EQUILIBRIUM BETWEEN NEODYMIUM HYDROXIDE AND HYDROCHLORIC ACID AT 25°C. Initial Equilibrium Concentration Concentration Nd+3 Activity Activity Kg Hydrochloric Dissolved Acid-Moles/lOOOg Neodymium- H + b { X 1018 x 1 0 3 x 1 0 8 x HgO g Atoms/lOOOg h20 0.0050 0.00167 0.415 0.693 4.8 0.334 6.2 0.0050 0.00167 0.415 0.693 4.5 0.334 7.6 0.0049 0.00165 0.419 0.691 5.4 0.342 4.4 0.0049 0.00165 0.419 0.691 5.1 0.342 5.2 0 . 0 0 1 0 0.00033 0.988 0.33 3.6 7.0 0 . 0 0 1 0 0.00033 0.988 0.33 3.5 8 . 0 0 . 0 0 1 0 0.00033 0.988 0.33 2.5 2 2 . 0 . 0 0 1 0 0.00033 0.988 0.33 2.1 36. 0.0005 0.00017 1 . 0 0 0.17 3.5 3.9 0.0005 0.00017 1 .00 0.17 3.0 6.3 Kq - 8.7 * ' 7 x 1018 «0 -3 0.4 (3) 0.3 f = 0.33 .c i x 0.2 ^z ii 3 4 5 6 7 8 9 10 II EQUILIBRIUM aH+ x I08 10 FIGURE Ife f* Nd/(H-h) AS A FUNCTION OF THE HYDROGEN ION ACTIVITY 00 AT EQUILIBRIUM. 99 Table 28 STUDIES OH THE COMPLETENESS OF THE REACTION BETWEEN HYDROCHLORIC ACID AND NEODYMIUM OXIDE Initial Equilibrium Equilibrium Days Days Hydrochloric Acid Concentration Hydrogen Ion Agi- Sedi- Conc entration Dissolved Activity tated merited Moles/lOOOg H20 Neodymium x 10° g Atoms/lOOOg HgO 0.00988 0.0033 21. 2.5 5 0.00988 0.0033 0.42 7 5 0.00988 0.0033 0.48 14 5 0.00988 0.0033 0.79 21 5 100 Table 29 DATA ON THE EQUILIBRIUM BETWEEN NEODYMIUM HYDROXIDE AND PERCHLORIC ACID AT 25°C. Initial Equilibrium Activity Concentration Concentration H x 10s Perchloric Acid Dissolved f Moles/lOOOg H20 Neodymium g Atoms/lOOOg h 2o 0.0998 0.0329 4.9 0.330 0„01051 0.00340 6.3 0.323 0 . 0 0 2 1 0 0.00070 3.8 0.35 Table 50 THE WATER SOLUBILITY OF NEODYMIUM HYDROXIDE AT 25°C. Moles of Nd(OH) Equilibrium per lOOOg H 2 0 ^ Hydrogen Ion Activity 4.8 x 10“ 5 8 x 10“ 10 8 x 1 0 -1° Table 31 THE SOLUBILITY OF NEODYMIUM HYDROXIDE IN SODIUM HYDROXIDE SOLUTIONS AT 25°C. Initial Moles of Solubility of Hydroxyl Ion Nd(OH)g Moles per lOOOg K q O per lOOOg HoO x 105 0.0607 1.98i(0.10) 0.1800 0.58-(0.05) 0.1800 0.51*(0.10) 0.5273 1.42^(0.10) 0.5273 0.83 *(0.07) 1.0125 4. 30 * (0 •80) 1.0125 3.47-(0.14) IUE 7 OUIIY F d0) I SDU HDOIE SOLUTIONS. HYDROXIDE SODIUM IN Nd(0H)3 OF SOLUBILITY 17FIGURE NEODYMIUM - G. ATOMS/lOOOg Q 2 OIM YRXD MLSIOg HgO MOLES/IOOOg HYDROXIDE SODIUM . 06 . 1.0 0.8 0.6 0.4 201 1-0.04 -0.03 - 0.02 - 0.01 0.02 Q 04 0.06 0.08 0.10 0.12 MOLES NaOH/lOOOg H20 MOLES HCI /lOOOg H^O 1 03 FIGURE IQ SOLUBILITY OF Nd(OH)3 IN SODIUM HYDROXIDE AND HYDROCHLORIC ACID. AN ANALYSIS OP THE DATA OBTAINED PROM THE DISSOLUTION OF METALLIC HYDROXIDES IN DILUTE ACIDS AND PROM A STUDY OF THE RESULTING EQUILIBRIA Previously, data of this type have been treated by plotting the total concentration of all metal dissolved versus the initial concentration of the acid used in the preparation of the solutions. Certain reaction products were assumed, and the data were used to calculate the equilibrium constants for these reactions. This does not seem to be the best method of treating the data in the case of the dissolution of multivalent metal hydroxides and oxides. Recent work in the field of inorganic solutions has shown that a wide range of ionic species exist in aqueous solution, and therefore one has little justification in assuming certain products to the exclusion of others which are equally probable. Hydrolysis studies have shown that most solutions contain polymerized species containing hydroxyl ions at pH values considerably lower than that at which precipitation of a solid phase results. Almost no work has been done to determine the ionic species present in equilibrium with the solid hydroxide or oxide, but it seems likely that polymerized species' exist in equilibrium with the solid hydroxide or oxide not only at the pH values resulting from the equili bration with acid solutions but also in highly basic solu tions. 104 105 Thus the use of a single solubility product does not seem to be generally justified in calculations involving a solid hydroxide. For example, solutions of ferric ion have been shown,8 ^ * 84 to contain appreciable amounts of 8 ^B. 0. A. Hedstrom, Arkiv Kemi, 6 , 1, (1953). 84 T. V. Arden, J. Chem. Soc., 1951, 350. F e(0 H)*^ F e ( 0 H)2 , and F © 2^°-^^4 hydrogen ion concen trations as high as 1 x 10-i4C. Thus the use of the rela- tion, aFe x (aOH“) « K 3p, together with the assumption that all of the iron is present as F e ^ is certainly not justified in .calculations involving solid Fe(0H)g. Poly merized cations have been found to be the rule rather than the exception in aqueous solutions of this type. This same O C concept has just been emphasized by Pokras. 8 5 L. Pokras, J. Chem. Ed., 53, 223 (1956). It is to be noted, however, that high metal ion concentrations as well as high pH values favor the forma tion of these hydroxy-bridged cationic polymers. In the presence of a solid phase, the metal ion concentration and the hydrogen ion concentration cannot be varied Independently. Thus, a high metal ion concentration goes with a high hydro gen ion concentration, and this effect tends to counteract the formation of polymers. 106 On© treatment of the dissolution of oxides and hydroxides, in which an attempt has been made to take all of these factors into consideration, is that which follows. It is based on the assumption of stepwise equilibria between the solid hydroxide, dissolved complexes containing hydroxyl ion, and the uncomplexed cation.■ This assumption has been shown to be valid in the equilibria existing among the hydroxylated species and the cations in the absence of a solid phase, i.e., in the case of hydrolysis reactions. Consider a function, zeta J f , which is defined as the total concentration of all of the metal in solution divided by the concentration of the hydrogen ion that has reacted during the dissolution. ^ is therefore the average number of hydrogen ions that have reacted per metal atom In solution. The treatment that follows is patterned after the analysis of polynuclear complexes / q g_ g developed by Sillen and his co-workers to explain G. Sillen, Acta Chem. Scand., 8 , 299 (1954). 8 7 Ibid., 318. 88 / S. Hietanen and L. G. Sillen, Acta Chem. Scand., 8 , 1607 (1954). 0. A. Hedstrom, Acta Chem. Scand., 613 (1955). hydrolysis data. 107 Thus j; = total metal H +reacted, Let us consider all of the possible reactions that may give rise to solvated metal species. First we may con sider the generalized reaction with hydrogen ion. (V-l) qMe(0H)a(g)+ J H + ^ M e p (0H)q + (aq) + J H 20 The requirement of electrical neutrality necessitates that (qZ-p) = J, where Z is the valence of the metallic ion in the solid hydroxide. This treatment excludes any cases involving the oxidation of reduction of the cation involved. Second, we need consider ionic species that arise from simple dissolution of the oxide with ionization, i.e., for strong electrolytes. (V-2) qMe(0H)a(s)^ M e q(0H)^(aq) + J <0H)^q) Finally, for weak electrolytes, reactions of type 2 but without ionization. (V-3) nMe(0H)a(s)^- [Me(0H)Jn (aq) Assuming that the activity of water remains essentially constant, we may write the following equilibrium constants. _ aMeq(0H)g+ _ [Meq (°H)pj Y t * P9 (aH+ )J (h )j < ^ ) j (V-5)i , a Meq(0H)^3c k / _ [MeqCOH)^ K»J frj+ (aH+)j [h +]j < n ) J assuming Kw remains essentially constant 108 0 (V-6) n Therefore, the total metal in solution, M, is given by + (V-7) In the above equation, h is the equilibrium hydrogen ion activity. The summations extend over all sets of p and q from q «= 1 to OO and from p = 0 to CD . The factor f is included in the second summation, as some of the species included in the summation may be the same as those in the first summation and would therefore be counted twice. As the oxides and hydroxides studied are very slightly soluble substances, solution due to reactions of types (V-5) and (V-6 ) may be disregarded except in the case of the solubility in essentially neutral water. Hence, only the first term in the above summation need be considered for the dissolution in acid. Thus (V-8 ) M Also, the analytical excess of hydrogen ions in the initial acid solution used to prepare the samples is 109 given by (V-9) H =» h - V ^ Z j h J ^ ^ n (<^)J -fZ J hJ 3 > p q pq pq \yJ+ pq j — "7“ irJ+ (k w ) ^ k -^-pq (V-ll) in this case.' pq t “hr (tf+)J J h -Apq ------, solving equation (V-10) for Zpq this quantity, we obtain the relation H-reacted = H - h. _ Z _ q h J 3 C pq (Z)J/ lfJ+ - Tiien> p ^ = m = r (v-ii) Z J X p q (^+ )J/ ^ J + H " h pq u The quantities M, the total metal in solution, H, the hydrogen ion concentration of the acid solution used to prepare the samples, and h the equilibrium hydrogen ion concentration can usually be measured without diffi culty. The function ^ can then be plotted as a function of h and an attempt made to evaluate the constants 110 It Is assumed throughout that equilibrium conditions prevail. It is evident that, in general, the determination of the various reactions giving rise to solution of the hydroxide is not a simple problem. The calculation of absolute values of the various constants X pq appears to be an almost impossible task in all but the simplest cases. First, it has been assumed that no reactions occur involving the anion present in the acid solution. Because of this, perchloric acid is, in general, best as the perchlorate Ion has little tendency to form complexes. Under certain conditions, with metal ions of low complexing ability, it is possible to use nitric or hydrochloric acids. is also a function of the ionic strength, as may be seen if values are sub stituted for the activity coefficients from the Debye Huckel limiting law. (V-12) pq Ideally, the experiments should be performed at a con stant ionic strength, so that the activity coefficients remain constant and can be included in the equilibrium constants, pq, as is done in the hydrolysis work. Ill This is frequently not possible because the solid phase is converted to a basic salt in the presence of the very high concentration of the "inert11 salt necessary to keep the ionic strength at an approximately constant value. In practice, it may be necessary to ignore the activity coefficients in the analysis of the experi mental data. This will not cause significant errors in the analysis, as the effect is slight. It can be seen from equation (V-12) that the effect of the ionic strength is to give increased weight to the terms in the summation where J is large. In this type of work, dilute acid solutions are used so that the ionic strength is usually no larger than 0.05. It is unlikely that large values of J will occur, as these highly charged ions would be unstable in solution. The effect of the polymerization of the cations is counteracted by the coordination of further hydroxyl groups giving the ions a rather low net charge. We shall then assume that is given by the following relation. (V-13) The variation of with h can now be grouped into three general classes. 112 B. o f is an inverse function of h. C. ^ is a direct function of h. If ^ is to be independent of h, it is apparent that J can have only one value in the expression for given in equation (V-13). Then the equilibrium hydrogen ion concentration, h, cancels from the numera tor and denominator of (V-13). The activity coefficient expressions also cancel in equation (V-12), in this case, making (V-13) an exact relation. Thus z q X pq P<1 / — — ------(V-14) ^ p q pq The simplest case where J is single valued is when p and q are also single valued, i.e., when one constant pq is much larger than all others, or, in other words, the free energy change for one dissolution reaction is much greater than all others. In this case, one ionic species predominates, and the ratio piq may be found by the solution of the simultaneous equations, 1. q = J 2 . (qZ-p) ** J In case B, where is observed to increase as h decreases, it is apparent that two or more species are involved. This behavior would be predicted for a divalent 113 hydroxide, since, for example, divalent ions would tend to result at high values of h, while univalent ions would tend to be formed at low values of h. Thus for dissolution in more concentrated acids M(OH)g^sj +2 + 2HgO equilibrium constant-Kg, while for low acid concentrations the reaction would be primarily M(0H)o . ^ M(OH) *. . + Ho0 equilibrium constant K 2(s) ( a q ) ^ (aq) 2 This should be true in all cases except that in which Kg^>K]_. In general, In cases similar to the one des cribed above, would go from a maximum value of unity to a minimum value of 0.5 as the hydrogen ion concentra tion increased. The third case, G, where function of h can be explained only if higher values of J are significant in accounting for the dissolution of the hydroxide, and that higher values of q are associated with these values of J, i.e., the case of polynuclear complex formation. At very low values of h, these higher order terras become'negligible, but as h increases they become appreciable. This is the type of behavior expected for some polynuclear systems. It can be seen that a great number of possibilities 114 exist, and an exact solution to the problem is impossible without further data. One method of obtaining further data is to study the hydrolysis of the cation by a method such 90-1 as that developed by Sillen. This allows one to deter- G. Sillen, Acta Chem. Scand., 8, 299 (1954). 91Ibid., 318. mine what ionic species exist at values of the pH up to that necessary to cause precipitation of the hydroxide. In this way, quantitative relations are also obtained for the concentrations of these ions. Ideally, if a set of constants are known for the hydrolysis reactions of the type N (qZ-p)+ q Mez + + pHpO"^-Me (OH) , , + pH+ (aq) * <1 p(aq) . £ pq . ['feq (0H)p (qZ"p)4] hP ( y.)P iTpq ____ (V_1B) [m 6z+] q Vz+ then all of the constants X pq may be written in terms of a single constant with q = 1 and p = 0. Thus "X pq ** (Xoi)q • <^Pq (V-16) and may be written in terms of the single constant ^Xoi, which then cancels from the numerator and denominator of the expression for / , giving ^ as a function of h alone. 115 The first example is the case of mercuric oxide. q q The data are taken from the paper of Garrett and Howell. QP A. B- Garrett and W. W. Howell, J. Am. Chem. Soc. , 6 1 , 1750 (1939). Since the water solubility of mercuric oxide is due to a reaction of type (V-3), i.e., mercuric hydroxide behaves like a weak elec-trolyte, was not neglected and M was corrected accordingly. The data are given in table 32. ^ was- not calculated for the samples prepared at the lower values of H, because of the uncertainty in the values of h determined with the glass electrode. Throughout the range studied, ^ appears to be independent of the value of h. As ^ has a value close to 0.5, it appears also that the principal reaction is that giving the divalent mercuric ion. The fact that ^ is actually slightly greater than 0.5 can be explained by the formation of some of the monovalent ion Hg(0H)+. Sillen and Hietanen^ reported a value for the 93 y L. G. Sillen and S. Hietanen, Acta Chem. Scand., 6, 747 (1952). hydrolysis constant for the formation of Hg(0H)+ as 2.5 x 10“^. If we assume Table 52 116 DATA ON THE EQUILIBRIUM BETWEEN MERCURIC OXIDE AND NITRIC ACID Hxl04M.* hjcl04M.* Mxl04M. *'*’ (H~h)xl04M. o^obs. «^calc. 0.5 0.32 0.18 1. 0.55 0.45 2 . 0.95 1.05 4. 2.9 0. 71 1.1 6. 4.0 0.95 2 . 0.88 8 . 15. 1.40 0.80 10.3 20.0 11 3. 68 9 0.77 40.0 38 9.7 2 0.62 500 100 215 400 0.538 0.56 585 140 234 485 0.482 0.54 634 130 260 494 0.526 0.55 683 130 297 553 0.537 0.55 703 130 310 573 0.541 0.55 722 130 327 592 0.552 0.55 743 130 331 613 0.540 0.55 761 130 347 631 0.550 0.55 780 120 367 660 0.556 0.55 976 160 447 816 0.548 0.54 1170 140 534 1030 0.518 0.54 1400 180 594 1220 0.487 0.53 '“"A. B. Garrett and W. W. Howell, J. Am. Chem. Soc., 61. 1730 (1939). 117 l m *-^nh + 1# ^oih2 1* X n h + 2* Xo]>2 and as X^l = j^ll * Xoi = 2.5 x 10 ^01 2.5 x 10”3 + h ( 2.5 x 10“3 + 2h The values of" ^ calculated In table were obtained in this way, and reproduce the experimental values well. The value of q2 may be easily obtained in this simple case, because the metal in solution is related to h by the following equation: M «= 2.5 x 10”3 h + h 2 A plot of M/(h 2.5 x 10"3) versus h should give a straight line with slope Q 2_ which passes through the origin. This type of data is rarely accurate enough to permit an evaluation of both X" q -^ and X-q from a plot of M/h without recourse to hydrolysis data, and the treatment given above is usually necessary. A value of = 160 was obtained in this manner. In the original paper, the authors gave a value of 53. This was calculated assuming initially that the two reactions producing Hg+^ and Hg(0H)+ occurred to the same extent, and the equilibrium hydrogen ion concentration was calculated from the initial concentration and the amount reacted giving Hg+2 and Hg(OH)? 118 The solubility of the oxide was then calculated by suc cessive •approximations until self consistent values of the two constants were obtained. Also, assuming only the reaction giving Hg+2 was important, the order of magnitude of 100 was estimated for the constant, and it was noted that the value of 53 was too small to accurately reproduce the solubility data at the higher values of h. The agree ment is good when one considers that the value used for the hydrolysis constant, 2.5 x 10“^, was a concentration constant referred to perchlorate solution. It should be noted that the complete behavior of the HgO system would fit case % as at low values of h, f should approach unity as the reaction producing Hg(0H)+ occurs predominately. The second example is that of beryllium hydroxide, and the data are taken from the paper of Gilbert and Garrett.94 As the water solubility of Be(0H)g is very Q4 R. A. Gilbert and A. B. Garrett, J. Am. Chem. Soc. , at press. small, it was assumed to be negligible in comparison to the beryllium in solution as a result of reaction with hydrogen ion. The data are given in table 33. In this case ^ is a direct function of h. As discussed in case C, this can only result from reactions involving higher orders of J with values of q ) 1 being important 119 Table 53 DATA ON THE EQUILIBRIUM BETWEEN BERYLLIUM HYDROXIDE AND HYDROCHLORIC ACID H x 10 5M."* h x 10^M.*“' M x 104M.* (H-h) x 104M. dobs. 50 0.478 3.22 4.95 0.650 100 0.617 7.02 9.94 0. 706 300 0.981 21.5 29.9 0.719 500 1.32 38.8 49.9 0.778 650 1.41 51.0 64 . 8 0.787 800 1.55 64.8 79.8 0.812 1000 1.62 81.3 99.8 0.815 1200 1.70 97.4 119.8 0.813 '“'R. A. Gilbert and A. B. Garrett, J. Am. Chem. Soc., at press. 120 in describing the dissolution of the hydroxide. In this paper, it was assumed that the only products were Be + 2, Be(0II)+ and a polymeric species Be(BeO)+2. If this is true, the function j can be written OU / Xll* h+ JClO*h2+ < ^ - X 2 x , (x+1)*h2 * (x+1) — x= 1 / ~ z All* h+2ZX10*h2 + 2 ^X2x, (x+1) -h2 x« 1 + Z + p Be(BeO)x and Be(Be(0H)2) a^e assumed equivalent as they differ only by x molecules of water. The authors further . simplified the situation by assuming that the only poly- meric species was that with x = 1. Then, "Xll’b. + Xi0*h2 + 2 X 22*bL2 f' X l l - h + 2 X i o ,h2 + 2 ^ Z 2 - h 2 Xll + XlO-h + 2 X22‘h J- X l l + 2 XlO«h + 2 "X22‘tl It is apparent from the experimental data that X ^2 must be very small in comparison to the other terms in the series or p ? would approach unity at the low values of h. Since ~ X ]_i i-3 very small, and this is verified from hydroly- ■ f sis studies, 1 may be written as follows. / co 1 X l O + (x+1) X*2x, (x+1) { X 10 + X 2x, (X d X = 1 121 Thus as Be+2 and Be(Be(0H)g)+2 are the only significant species for high values of h, should he independent of h according to the equation above. As this is not ob served to be the case experimentally, it is apparent that species other than Be+2 and Be(Be(OH)g)+ 2 must occur and have charges, J, greater than +2. Also as $) gets as large as 0.8 in the most acid solutions, species must occur in which the ratio qrJ is greater than 1:2. All of these observations are in agreement with those based on hydrolysis data. Mattock23 proposed two treatments of 9 5 G-. Mattock, J. Am. Chem. Soc. , 76, 4835 (1954). the hydrolysis data for beryllium solutions. One involves the species Be+^, Be(OH)? BegCOHjg, and Be3(0H)g. The other is a Sillen "core plus links” mechanism with the species Be+2, Be(OH)? Be2 (0H)+3 , Be3 (0H)gt Be4 (OH)J5 ,... If we attempt to treat the solution in terms of the ionic species Be2 + Be(OH)? and Be2(0H)^+ we obtain the expressing following, using the hydrolysis constants given by Mattock. 23 96 Ibid., 4835. 122 f> 0.3 x 10”6 X d + ^Xoi h+ 2*0.3 x 10“3 A01-h2 0.3 x 10"6 "Xoi+2 Xoi^+ 3*0.3 x 10-3 ' X . O l ' b ? r - 0.3 x 10 “6 + h + 0.6 x 10-3h2 ^ - _ 0.3 x 10"6 + 2h + 0.9 x 10“3h2 As this is not sufficient to accurately describe the equilibria, it is apparently necessary to consider a very large number of polymeric species, and this cannot be done with the limited information available. A third example is taken from the paper of G-ayer 9 6 and Leider. These authors studied the dissolution of H. Gayer and II. Leider, J. Am. Chem. Soc. , 76, 5938 (1954). ThO(OH) in perchloric acid. In the calculation of from their data, it was necessary to neglect h as only H and M were given. As the magnitude of h was less than 1 per cent of H, this should cause no appreciable error. As seen from the data in table 34, ^ appears to increase to a value of 0.5. In the original paper, it was assumed that a plot of M versus H was a straight line with slope 0.5, and the points where is 0.3 were ignored in draw ing the line. These variations at the low acid concen trations are probably due to experimental errors. Using the hydrolysis data of Kraus and Holmberg,we may obtain 97 K. A. Kraus and R. W. Holmberg, A.E.C.D. 2919 (1950). 123 Table 54 DATA ON THE EQUILIBRIUM BETWEEN THORIUM HYDROXIDE AND PERCHLORIC ACID 'H x 102M.* M x 102M.* 4 obs. 2.03 0.648 0.320 4.06 1.48 0.364 10.1 4.04 0.400 20.3 9.80 0.483 40.6 20.0 0.492 81.1 36.2 0.446 ^’K. H. Gayer and H. Leider, J. Am. Chera. Soc., 76, 5938 (1954). 124 as a function of h. These authors found Th(OH)g to he negligible, and only Th+4, ThO+^, and ThgO+® are con sidered. Then 5.1xlQ-3h2 + h4 + 5.4xl0-5h6 6.2xl0~3h2 + 4h4 + IS.2x10"5h6 As h for these samples was less than 10“3 , should have a value of 0.5 and be independent of h in the range studied. Thus, as the authors assumed, the solubility should be due to the reaction giving Th0+2, and the equilibrium constant calculated accordingly. This is an example where a con sideration of polymer formation is necessary to explain the hydrolysis data but not the solubility data. Because of the basicity of the hydroxide, the metal ion concentra tion is so low at pH values where polymers form that the concentrations of these species are negligible. \ AN ANALYSIS OP THE DATA OBTAINED PROM THE DISSOLUTION OF METALLIC HYDROXIDES IN BASIC SOLUTION AND PROM THE WATER SOLUBILITY Theoretically, the case of dissolution in base can be treated in an analogous manner to the dissolu tion in acid. In practice, an analysis of the data is even more difficult than in the acid dissolution. Thus in basic solutions, we may neglect reactions with hydrogen ions, and consider solution to arise from the following reactions. (V-2) qMe(OH) , .^ M e (0H)J+ x + J(OH)" a(s) q p(aq) (V-3) nMe(OH)a(s)^(Me{OH) ) ( afn(aq) and also a special case of reaction (V-2) where p qZ, (VI-1) qMe(OH) (s)+ J (0H)“ ^ Mea(OH)J" , ^ p(aq) Again polymeric species are considered. Since these have been definitely shown to exist to pH values up to that at which precipitation occurs, there seems no reason for assuming them to be absent at higher pH values. An expression for M as a function of the equilib rium hydroxyl ion concentration may be written in terms of the equilibrium constants in equations (V-5) and (V-6), remembering that J » (qZ-p) and that it may have + or - values. 125 126 M - S T <1 iPpq f/j)"1 ♦ ^ pq n An analysis of the dissolution in base depends upon the explanation of the behavior of M as a function of the equilibrium hydroxyl ion concentration. In theory, a function analogous to I , and equal to the total metal in solution divided by the hydroxyl ion that has reacted, could be developed in terms of the various equilibrium constants-. This is, however, of little value, as the reaction with hydroxyl ion is usually so slight that the function could not be determined experimentally with any accuracy. An approximate expression for the hydroxyl ion concentration at the minimum in the solubility curve, that occurs in the case of hydroxides that act as strong electrolytes, may be obtained as follows. Activity coefficients are ignored in the expression. At the extreme, An exact description of the reactions occurring in basic solution is, as yet, an unsolved problem. Almost no data have been obtained on the ionic species present in these solutions. In the past, an increase in solubility of a hydroxide with increasing hydroxyl ion 127 concentration was taken as evidence that the hydroxide had acidic properties and could ionize to produce hydrogen Ions. More recently, it has been assumed that a molecule of hydroxide could coordinate one or more additional hydroxide ions giving a negatively charged ion, i.e., a concept differing from the older one only in that molecules of water are not actually split off in the reaction. In many cases, however, the conductivities of such solutions are equal to those of alkalis in the same concentrations, suggesting that the ’’solubility” of the hydroxides is more probably due to the formation of sols which are stabilized by the 0H~ ions.®® There is 98 A. P. Wells, Structural Inorganic Chemistry, Second Edition, Oxford University Press (1950) p. 411. very little difference in this concept in which aggregates of hydroxide molecules are stabilized in some way, pos sibly by the adsorption of hydroxyl ions, and in the concept of polynuclear species in basic solution. The molecular weights are low enough that the particles do not scatter light measurably, so that the solutions are different from the classical sols such as that of Pe(0H)g. In most of these cases, the reaction is slight, and only small amounts of hydroxide Ions are coordinated by the metallic hydroxide. The mobility of these polymers 128 should be low, so the conductivity would be due almost entirely to alkali ions. Thus the conductivity would be essentially equal to that o f the unreacted alkali solu tion alone. AN ANALYSIS OF THE EXPERIMENTAL DATA FOR NEODYMIUM HYDROXIDE Eguilibri'a with Hydrochloric Acid The equilibria possible in solutions of a trivalent cation such as neodymium are almost unlimited. The follow ing equations may be written as those most likely to repre sent the reactions occurring during the dissolution in acid of the samples of neodymium oxide. (VII-1) A-Nd2 03 , .+3H20 ^ ,Nd2 03 *3H2 0 (s) or 2Nd(0H)g (s ) (VII-2) Nd(0H)3 (a)- ^ N d ( Q H ) 3(aqj (VII-3) Nd(OH),. . ^ N d ( O H ) ^ . + (OH) “ ^(s) 2 (aq) (VII-4) Nd(OH)3 (s)- ^ N d ( O H ) ^ j+ 2 (OH ) ” ' (VII--5) Nd(0H)3(s^ Nd"(aq) + 3(0H>~ (VII-6 ) Nd(0H)3(g) + H+ -^ Nd(OH)g(aq) + H20 (VII-7) Nd(OH),, . + 2H+^ N d (OH)*2 . + 2Ho0 o ( s ; (aq) * (VII-8 ) N d (OH) 3 (s ) + 3 H+# N d j ^ + 3H20 Considering the fact that recent investigations have shown that solutions of scandium, thorium, uranium, and the transuranium elements contain significant amounts of polynuclear hydroxyl complexes, it is necessary to consider the possibility of these ionic species. Thus, in general, (VI1-9) qNd( OH )3 + J H+^ Ndq (O H ) ^ ^ }++ J H 2 0, 129 130 Since the water solubility is very low for Nd(0H)3, it was ignored in the calculation of ^ . Thus the solu bility in acid was assumed to be described by a general reaction of type (VII-9), of which the reactions (VII- 6, 7, and 8) are but special cases with q * 1. Then, from the treatment developed in the section on dissolution in acids, the following equation may be written. / m ^ * K H -h zpq j K L < H oHC<3q"p)] P and in terms of the generalized equilibrium constant, ^ pq - (vix-ii) [ h *JJ ( $ J aKd(0H)3(s) we may obtain an expression for ^ . If crystalline Nd(0H)g at 25°C. is considered the standard thermodynamic state, is given by the following equation. q hfaHgO ) ”J ($J/ V "X Pq E9------ES ------where J = (3q-p). Z J hJ(aH20)-J [ X F / y bCpq (VII.12) pq 0 pq Prom the experimental data plotted in figure 16, is shown to be independent of h throughout the range of acid concentrations studied. Therefore, J can have only one value. While this requirement could be satisfied by a set of polynuclear complexes with 3q-p = constant, the 131 most likely case is that when only one constant ~Xpq is significant in the summations in equation VII-12. In other words, the A F° for one reaction of type 9 is very much more negative than all others. From equation (VTI-12), we see that for J « constant, - ^ ^ V (VII-13) j T = Q..P5 L . s q/j, for one set p,q. J^ Xpq From figure 16 ,J^* « 0.'33 = q/j and so J = 3q. / Also from the requirement of charge balance, 3q-p = J, and hence p = 0. Hence, all hydroxyl complexes can only be present in negligible amounts, and the Nd+3 ion is the only one present in measurable quantity. Then q = 1 and J = 3, and the dissolution of A-Nd203 may be represented by the equations following for HC1 in the range of con centrations studied. (VII-1) A-Ndg03 + 3 Hg0-»2 Nd(0H)3 (s) (VII-8) Nd(OH),, . + 3 H+ . ^ N d + 3 , + 3 Ho0 ) (aq;^ (aq) 2 The equilibrium constant for reaction 8 was found to be Kg «= 8.7± 4.7 x 10lS = aNd+^(aCl“)5 »(aH20)5______aNd(0H)3. (aH)3-(aCl“)3 This corresponds to a standard free energy change of ^ F ° 298 = -25.9 ± 0.3 kcal mole Nd(0H)3 The activity coefficients for Nd+^ in the neodymium chloride -2 solutions in the concentration range 1 x 10“° to 5 x 10 were obtained by interpolation of the data of Spedding and Porter.®^ These data give the mean activity coefficient in ®9F. H. Spedding and P. E. Porter, J. Am. Chem. Soc., 74, 2781 (1952). aqueous solutions of neodymium chloride. The mean activity 11 coefficient was found to obey the Debye-Huckel limiting law throughout the range of concentrations studied, and /* is given as a function of the concentration by the equat ion A' = 3.7446 a = 5.92 x 10 ° l°g10 X ± = -A' \ T ^ , B» = 0.8949 x 108 o erroneously given as 1 + a B' \f~Cm x 10“8 in article According to the Debye-Huckel theory, V + -A • 3 • 1 liJL 1o Sio « “ " h.-- for a 3:1 electrolyte like 1 + a B f J Z NdClg. In this case, the Debye-Huckel theory also pre dicts the value of the trivalent cation as given by the following equation. log 0 Y * ‘ and thus /Hd+3 = (^NdCls) 1+a B It was therefore assumed that the activity coefficient for the neodymium ion in aqueous solutions of neodymium 133 chloride could be accurately estimated from the cube of the mean activity coefficient for these solutions. At concentrations lower than 1 x 10"^M, the activity coef ficients were obtained from the equation given, below. /+3 -11.234 Nd ‘ — -- p = — 1+5.92 x 0.8049 Vcm The crystalline neodymium hydroxide was chosen as the standard thermodynamic state, so the activity of the solid hydroxide at 25°C. is unity. The activity of the solvent, water, may be accu rately approximated for a given temperature by the relation ^ P a HgO “—n where P <= vapor pressure of water Pu above the solution at temperature T, and is the vapor pressure of pure water at temperature T. As discussed by Johnston, Cuta, and Garrett^®this quantity may be approxi- lOOjh L. Johnston, P. Cuta, and A. B. Garrett, J. Am. Chem. Soc.. 5 5 , 2311 (1933). mately set equal to unity in dilute solutions, and actually this has been found to be satisfactory to 0.5 M for 1:1 electrolytes. This approximation should not cause any appreciable error in the dilute solutions studied in this work even for a 3:1 electrolyte, although no vapor pressure data are available for solutions of neodymium chloride. 134 Prom the value of Kq and the dissociation constant for water at 25°C., the solubility product of the crystal line neodymium hydroxide may be calculated. K8 x Kw3 = (aHg0)3 x (aH)3x UOH') , R sp aNd(OH)3 x (aH+ )3 (aHgO)3 Ksp = 8.7 ± 4.7 x 1018x (10”14)3 = 8.7 i 4.7 x 10"24 and for the reaction Nd(OH) + 3 OH” ^ f°298 = 31,5 ± 0,3 kcal As would be expected, since reaction 8 describes the dissolution and Kg is very large, ^ is constant, the plot of the total neodymium dissolved versus the initial acid concentration is a straight line with slope 0.33. This is shown in figures 15 and 18. As was noted in the section on the solid phase analysis, the A-type NdgOg used in the dissolution studies was observed to hydrate giving crystalline Nd(0 H)3 . The solid phase in all of the equilibria was identified as the crystalline form of neodymium hydroxide. The highly negative value of F298 f°r reac‘fc^on 8* and the absence of measurable concentrations of ionic species containing hydroxyl ion indicate that Nd(OH),, u is an extremely basic hydroxide. Unfortunately, a lack of thermodynamic data for the hydroxides and aqueous 135 ions of other elements in the +3 oxidation state prevents a quantitative comparison. The solubility product was found to be 8.V x 10-2^ which is smaller by a factor ranging from about 10 to as much as 100 when compared to the most recent values cited in the literature. These are the values of Moeller and Kremers-^^- and Moeller and Fogel,-*-®2 which were calculated 101T . Moeller and H. E. Kremers, J. Phys. Chem., 48, 395 (1944). 102ip# Moeller and N. J. Pogel, J. Am. Chem. Soc., 35, 73, 4481 (1951). from the pH at the incidence of precipitation and at + r2; certain mole ratios of 0H“: Nd . The solubility products given below are averages of the solubility products calculated from the pH values at the incidence of pre cipitation and at 0H“: Nd+3 mole ratios of 0.6, 1.2, and 1.5 for each solution. Nd(N03) solution - KSp = 3.1 x 10~^ Nd2 (S04 )3 solution - Ksp = 2. 6 x 10"21 Nd(Ac)g solution - Ksp » 2.8 x 10 ( Also, an average-average solubility product was given as — PI KSp = 1.9 x 10 for these three solutions. This is the value most often encountered in the current literature for the solubility product of Nd(0H)3. The solubility product was also determined from the pH at the incidence 136 of precipitation and at a rao'le ratio OH": Nd+^ = 0.4 in perchlorate solution to be 3.2 x 10"^. These authors gave the following values of the pH during the precipita- -3 tion. All solutions are approximately 0.1 C in Nd Solution NOj SOJ Ac" 010^ pH at incidence 7.31 6.95 7.59 7,30 of precipitation pH at OH": Nd+3=0.4 7.40 7.23 7.65 7.34 It should be noted that these authors were primarily interested in obtaining relative values of some physical property of the rare earths which could be compared throughout the series of the 4f elements. 103 Bowles and Partridge gave the following values of 1 03 J. A. C. Bowles and H. M. Partridge, Ind. Eng. Chem. Anal. Ed.. 9, 124 (1925). the pH at the Incidence of precipitation in 0.01 C neodymium solutions: For sulfate solution, 6.73 and' for chloride solutions 7.40. Britton^0^ gave the following 104 H. T. S. Britton, J. Chem. Soc. , 127, 2142 (1925). values for the incidence of precipitation: For nitrate solution, 0.0133 C -pH 7.00 and 2.38 equivalents of OH" completely precipitate the Nd+3: For chloride solu tion, 0.0114 C -pH 7.02 and 2.53 equivalents of Oh " completely precipitate the Nd+3. These last two references i 137 are included to show that chloride solutions appear to behave similarly to nitrate and perchlorate solutions. These data are difficult to interpret, as there is an inherent assumption in these calculations that the +3 only ionic species present in solution is Nd , and that the solid phase at equilibrium is Hd(0H)3. In some of the cases, neither assumption is valid, and it is highly unlikely that both are valid in any of them. The high pH values, and hence the large solubility product in the acetate solution, were attributed to complexes with the acetate ion. This is certainly true as it is well known that the rare earth ions form complexes with most of the organic acids such as acetic, citric, tartaric, etc. which increase in concentration as the pH increases. In this case, the species in solution was most certainly a citrate complex and not Nd+3. This complexing ability of these organic anions is the reason for their use as elution agents in ionic exchange separations of the rare earths. Recently, studies on the conductivity of neodymium If) CL sulfate solutions by Spedding and Jaffe have shown that H. Spedding and S. Jaffe, J. Am. Chem. Soc., 76, 882 (1954). ~ the Nd+3 ion exists almost entirely as the complex NdSO|, 138 and that the instability constant for this complex is 2.3 x 10“4. As Pokras-f-O® has recently pointed out, the Pokras, J. Chem. Ed. , 35, 152 (1956). neodymium ions in the sulfate solutions used in the work of Moeller and Kremers'1'^ existed as ^ 99 per cent sulfato 107 T. Moeller and H. E. Kremers, J. Phys. Chem. , 48, 395 (1944). complex. Although the rare earth ions were said to form no complexes as recently as ten years ago, Davie^measured 1 OR C. W. Davies, J. Chem. Soc., 1950, 2421. the instability constant for LaSO^ in 1930, and obtained a value of 2.2 x 10“^ from solubility measurements. It is generally assumed that the nitrate and per chlorate ions have weak comploxing ability. From the data on the pH values at the incidence of precipitation, it appears that chloride solutions act similarly to nitrate and perchlorate solutions, and hence that there are no appreciable complexes with chloride ion. The data of Moeller and Brantley^® indicate that there is no change Moeller and J. C. Brantley, Analytical Chem., 2 2 , 433 (1950). in the absorption spectra of neodymium chloride solutions in the presence of a Cl": Nd+3 mole ratio as great as 10. 139 This seems to indicate the absence of significant complex- ing of neodymium ions by chloride ions, although complexes might be formed without causing a measurable shift in the absorption peaks. Furthermore, the data on the co'nduc- 110-11 tivity and transport numbers of the rare earth chlorides ^^°F. H. Spedding, P. E. Porter, and J. M. Wright, J. Am. Chem. Soc., 74, 2055 (1952). 111Ibid., 2278. IIP and the perchlorates-1- are very similar. The conduc- H. Spedding and S. Jaffe, J. Am. Chem. Soc., 76 , 884 (1954). tivities of the rare earth chlorides and perchlorates are found to decrease with increasing atomic number, because of increased hydration of the ions. For neodymium chloride and perchlorate solutions, plots of „A_ versus show the Onsager limiting slope. The plot pf-A-o versus c approaches infinite dilution with zero slope showing that the Onsager relation is followed in dilute solutions. The values of 8, the "radius of the ionic atmosphere," were constant throughout the range of concentrations examined from n . o.5 M to infinite dilution. The conductivity fol lowed the limiting law to T o - 0.1 M. The authors claim o that the values found for a of 5.7 A for chloride solutions o and 6.7 A for perchlorate solutions are consistent with 140 the physical picture of a mono-layer of counter ions about the central hydrated ion, as the perchlorate ion is o expected to be approximately 1 A larger than the chloride ion. It has been found, however, that the assignment of o this physical picture to a, the mean distance of approach of the ions, is not generally satisfactory, and this comparison may be somewhat idealistic. The behavior of 113 the nitrate solutions is similar but has not been reported 113Ibid., 884. in as great detail. The transport numbers of the neodymium ion In both chloride and perchlorate solutions have been found to be a linear function of the \To to approximately 0.5 M for chloride solution and 0.6 M for perchlorate solution, the highest concentrations investigated. The limiting slope, however, differed from the Onsager limiting value. According to these data, complexing in chloride and perchlorate solutions Is very slight, and the assumption that no interaction with chloride ion occurred in the solu bility measurements in hydrochloric acid seems to be justified. Since the sulfate solutions consist almost entirely of NdSO^, it would be expected that the pH at the beginning of precipitation would be high as in the case of the 141 acetate solutions. Actually the opposite of this was observed to be true, and precipitation occurred from sulfate solutions at a lower pH than from any other of the solutions. This fact brings into consideration the second major assumption, that the solid phase obtained was Nd(0H)3. In no cases in the literature were the solid phases investigated except to note as done by Britton114 and by Moeller and Fogel115 that precipitation 114H. T. S. Britton, _J. Chem. Soc., 127, 2142 (1925). T. Moeller and N. J. Fogel, J. Am. Chem. Soc., 73, 4481 (1951). of the rare earth was complete at mole ratios of OH": Nd+3 116 of less than 3. It was also observed by Moeller and Fogel 116Ibid., 4481. and Moeller and Kremersl1^ that each addition of base after 117 00 T. Moeller and H. E. Kremers, J. Phys. iChem., 1 395 (1944). precipitation had begun caused a sharp rise in the pH which then decreased slowly to a reasonably constant value. This was attributed by them to the formation of basic salts, which then reacted slowly with the added (OH)” with the resultant observed decrease in the pH. It was assumed that the solid phase was the hydrous hydroxide* because 142 lift of the observations of Weiser and Milligan that the B. Weiser and W. 0. Milligan, J. Phys. Chera., 42, 673 (1938). crystalline hydrous hydroxide was obtained by precipitation from neodymium solutions at 100°C. The precipitate ob tained at 25°C. is an amorphous, gelatinous substance similar in appearance to freshly precipitated aluminum hydroxide. These gelatinous '’hydroxides’' have recently come to be regarded as long polymers involving both OH and appreciable quantities of the anion present in the solution in which precipitation occurred. Therefore, the solid phase in all of these, .works varied depending on the anion present in solution, and, in any case, was far different from the standard thermodynamic state for neo dymium hydroxide. It is likely that all of the basic salts have similar structures in which the bonding is essentially ionic. The basic sulfate would certainly be the least soluble, and thus precipitation would occur from sulfate solutions at a lower pH than from the solutions of other salts, as was observed. The solubilities of the other basic salts probably increase in the order-chloride, nitrate, and per chlorate. The conversion of these basic salts to the hydrous hydroxides would depend upon the pH of the 143 surrounding solution, the concentration of the anion in solution, the lattice energy of the basic salt, the state of aggregation of the solid phase, etc. As discussed by Emeleus and Anderson,^^ these anions are not merely 119 / H. J. Emeleus and One final error in all of the literature references is that concentrations were used in all of the equilibrium "constants", which can easily cause the values to be in error by a factor of 10 in these calculations in which the activity of a tri-valent ion is under consideration. From the standard free energy change determined for reaction 8 , together with the free energy of formation of the Nd.*^ ion given by Spedding and Miller-^® which (aq) Spedding and C. F. Miller, J. Am. Chem. Soc 74, 4195 (1952). appears to be the most reliable value available, and the free energy of formation of liquid water from the National 121 Bureau of Standards tables, the free energy of formation -L^lselected Values of Chemical Thermodynamic Proper ties, Circular of the National Bureau of Standards 500, Feb. 1, 1952, Washington, D.C. 144 of the crystalline hydroxide may be calculated as follows. Nd(s)^ H d (aq) + Se" ^ P 29S' -155.40 kcal (-)Nd(0H)3 (3 )+3H|aq)^ H d ^ q)+3Hs0 (1 )4pOs8, - 25.9^0.3 kcal N d (s)+3H20(1 )^Md(0H)3 (s) + 3H'Jaq)+3e-4F°98= -129.510.3 kcal 3H2 (g )+3/202(g) ^ 3 H 2 0(1} £Fg98= -170.07 kcal Nd(s )+3H2 (g)+3/20 2 {g ) ^ N d (0H)3 (s ) + 3H(aq)+ 3e" ^ F 298= -299.6l0.3 kcal (-) 3/2H2(g)^ 3Hfaq)+ 3e- 0 0 . 0 kcal N d (s)+3/2H2 (g)+3/2°2 (g )^3Nd(0H)3(s)ZlF|98= -299.6±0.3 kcal The value of -299.6 kcal/moleNdtOH)^ for the 1 2 2 Ibid. tables give -309.6 kcal/mole and list the work of Endres^2^ 123 G. Endres, Z. anorg. allgem. Chem. , 205, 321 (1932). as the reference for this, as discussed in the introduction. The paper gives only relative values of the 145 "basicities" or solubility products which were obtained from data on the rare earth ion concentrations at which precipitation begins in ammonia ammonium nitrate-cadmium nitrate buffer solutions. It was assumed that the hydroxyl ion concentration would be the same in the different rare earth buffers, and hence that the following relation would hold. K sp This assumption alone is subject to all of the previous criticism of the solubility product work as to the ionic species of the rare earth and to the identity of the solid phase. In addition, one can only guess as to how these data were used to obtain a free energy of formation of Nd(OH)g. The basicities were given on the basis of KSp yttrium hydroxide = 1. It is most likely that the ratio K^/K-j^* 47/1300, together with one of the early values for Kpw was used to estimate the solubility product for neo dymium hydroxide, % d. No reference is given for the value of the free energy of formation of the tri-valent neodymium ion necessary for the calculations, but as all of these values were highly inaccurate, according to the work of 146 Spedding and Miller, ^ 24 little further need be said about 124p# jj. Spedding and G. P. Miller, J. Am. Chem. Soc. , 74, 4195 (1952). the reliability of this value. The value given by Latimer^2^ of 309.3 kcal/mole was 1 2 5 W. L. Latimer, The Oxidation States of the Ele ments and Their Potentials in Aqueous Solutions, Second Ed., Prentice Hall Inc., New York (195277 pT 288. calculated from the average of the solubility products 126 •for neodymium hydroxide given by Moeller and Kremers ^2 ®T. Moeller and H. E. Kremers, J. Phys. Chem. , 48, 395 (1944). together with a rough estimate of the free energy of forma tion of Nd+3, and thus is unreliable. Also, the potential of the neodymium couple in basic solution may be calculated. Wd(s)^Nd(aq) + 3e" AF298= " 1 5 5 *4 0 kcal (-)Nd(0H)3 (s)^Nd(fq)+3(0H)“ ^ 2 9 8 “ 31.5*0.3 kcal Nd(3)+3(0H)' x- Nd(OH) , + 3e A p ° * -186.9±0.3 kcal ; ' (aq) 3(s) _ 2 9 8 186.9±0.3 kcal E b = ______*= 2.701 ± 0.004 V. 23.066 kcal 147 Latimer-*-^ gives values of from 2,90 to 2.72 V for lanthanum 1 27 W* L. Latimer, The Oxidation States of the Elements and Their Potentials in Aqueous Solutions, Second Ed., Prentice Hall Inc., New York (T952), p. 293. to lutecium which are too high because of errors in P°f of the solid hydroxides and the tri-valent ions. Equilibria with Perchloric Acid As was indicated in the section on the treatment of data obtained from dissolution in acid, it Is desirable, If possible, to work at a constant ionic strength. An attempt was made to study the dissolution in perchloric acid at an ionic strength of three, and hence in the same reference state as used for the hydrolysis measurements. The solid phase was observed to change in appearance and increase noticeably In volume. The values of obtained upon analysis were erratic and approximately equal to 0.2. As neodymium ions with a valence of greater than +3 are unknown, this can only indicate the conversion of the solid phase to a basic salt containing perchlorate ion. This is not un reasonable at a perchlorate concentration of 3 .0 0 , as was discussed in the section on the solid phase analysis. To check the measurements made in hydrochloric acid solutions, a small number of samples were prepared using dilute perchloric acid. These data are given in table 29. The data are essentially the same as those taken from the 148 hydrochloric acid solutions. These solutions had a pro nounced tendency to form sols, much more than any other of the solutions examined. For this reason, the investigation was not pursued farther. There appears to be a more pro nounced tendency to form basic salts with perchlorate ion than would be expected. Equilibria with Water and with Sodium Hydroxide Solutions The water solubility of the crystalline neodymium hydroxide was determined to be 4.8 x 10“^moles/l000g H2 O. The solubility in base describes a minimum at about 0.2 M NaOH and increases to approximately the water solubility in 1M NaOH. This is shown in figure 17. The curve was considered to be formed of two independent parts, one accounting for the initial decrease in solubility where Nd = k/(0H)^ and the other describing the dissolution at high concentrations of hydroxyl ion where Nd = k 1 (OH)1?1 This follows from the discussions in the section describing the equilibria in basic solution. The fact that Nd is inversely proportional to the hydroxyl ion concentration in the initial portion of the curve indicates that the solubility is essentially described by a reaction of type (V-2), involving dissociation giving hydroxide ions. On the other hand, the fact that the minimum in the solubility occurs at as high a hydroxide ion concentration as 0.2 M cannot be explained by simple reactions like 149 Nd(OH),/a v ' ^ Nd*3 . + 3 (OH) “ u \s ) {aq ) Nd(0H)3(s)^ Nd(OH)^ } + 2 (OH) ” Nd(OH),,_v Nd(OH)+, + (OH)“ 2 (aq) Empirically, this initial portion of the curve is roughly represented by a relation of the type Nd = k(OH) where n has a value of approximately 3. This is an impossible case representing a fractionally charged ion, according to the treatment in the section on solubility in base. An almost identical situation was found in the case / % 128 of the dissolution of ThOtOHjg in sodium hydroxide at ■^®K. H. Gayer and II. Leider, J. Am. Chem. Soc. , 75, 5938 (1954). 25°C. In this work, it was found that the solubility of the Th0 (0 H )2 decreased from a water solubility of approxi mately 5 x 10“5moles/l000g HgO to 3.7 x 10"6moles/l000g HgO describing essentially the same curve drawn for NdCOHjg. The solubility of ThO(OH)g, however, continued to decrease slightly and showed little tendency to rise at higher concentrations of base. In the analysis of the equilibria in both acid and base, it was assumed that equilibrium conditions were rapidly attained. Thus the following type of reaction proceeds, certainly, in a stepwise manner, and it was assumed that equilibrium conditions existed between the 150 ions and the solid phase. 2Nd(0H)2(aq)+0HV,Nd2 (0H)5(aq)+Nd(°H)2(aq)+0H" ^ Nd3 (0H)8(aq)+ 0H"^3Nd(0H)3 (g) . N dt3 + 0H~^Nd(0H) + 2 + OH“^Nd(OH)*+OH“^Nd(OH)„ . (aq) (aq) 2 <=>^3) The existence of an extremely slow step in one of these reactions might account for the observed behavior. An alternate, and perhaps more satisfactory, explanation for the case of Nd(0H)g is that the relatively few points obtained by the activation analysis do not permit one to observe a much sharper decline in the solubility. The curve describing the increase in solubility at base concentrations higher than 0.2 M is essentially parabolic in shape and is empirically described by the equation, Nd = 3,9 x 10”® [pH"”^2 For the formation of an ion with a -2 charge, the solubility would be described by the relation Nd = q ^ p q is tempting to take this behavior as evidence for the forma tion of a divalent anion, but as no predictions can be made as to the behavior of these high concen trations, this similarity may be fortuitous. It is diffi cult, however, to explain this behavior in terms of an ion with a charge of less than 2. The increase in the 151 concentration of the undissociated species to the effect of the ionic strength on the activity coef ficient should be slight since the particle is uncharged. If singly negative charged ions are formed, the solubility should vary with the hydroxide ion concentration as given by the following equation. OH" It seems unlikely that the activity coefficient for the singly charged neodymium anion would decrease more sharply than the hydroxyl Ion coefficient, at least not sufficiently to account for the solubility behavior. It seems possible that the solubility in base may be due to the formation of large polymeric anions. Profes- 129-30 sor R. Fricke and co-workers developed a method for ■^®R. Pricke and A. Seitz, Z. anorg. allgem. Chem., 254, 107 (1947). Seitz, Z. Naturfor3ch., 1-A, 321 (1945). preparation of single crystals of the rare earth hydroxides by digestion of the gelatinous hydroxide with concentrated sodium hydroxide solution at 200°C. in an autoclave. It was found that the concentrated base solutions dissolved relatively large amounts of the rare earths, which were reprecipitated as the amorphous hydroxide upon dilution 152 of the base solutions with water. It was found that 6.92 M NaOH dissolved 0.137 g per liter of La(OH)3 , 7.06 M NaOH dissolved 3.5 g per liter of ErfOHjg, and 7.2 M NaOH dis solved 3.6 g per liter of Y(0 H)3 * Extrapolation of the parabolic curve found in the plot of Nd versus OH” to NaOH = 7M gives a value of 0.4 g per liter, which should be of the right order of magnitude for Nd(0 H)3 * The only direct determination of the water solubility “ I 'Zl of Nd2 0 3 is that of Busch. The solubility was determined Busch, Z. anorg. allgem. Chem. , 161, 161 (1927). to be 5.75 x 10“® and 6.08 x 10"dmoles per liter, calculated as Ndg0 3 which would give 1.15 x 10"® and 1.22 x 10“® moles of Nd(0H)g per liter. The value determined in this work was 4.8 x 10”®moles Nd(0H)£ per liter. It is not surprising that this is higher than the literature values as- these were determined by adding more 0.01 N sulfuric acid than necessary to neutralize the OH" in solution from the Nd 2C>3 and then back titrating the excess acid with KOH of the same normality. The solubility of the oxide was then calculated assuming that all of the hydroxyl ion came from the reaction Nd203(s) + 3H20 ^ 2Nd|fq) + ®(°H)“ . It seems unlikely that the neodymium would be entirely in the form of the tri-valent cation, Nd+^, at a pH as high 153 as 9.10, the pH of the water sample. If this assumption is false, the calculations based on it would give low values for the solubility, i.e., NdgOs-moles per liter moles^(OH)”/6. The behavior of the curve representing the solubility in base also indicates that the dissolved Nd(0 H )3 is only partially ionized, as does the fact that the neodymium concentration was found to be 4.8 x 10"° raoles/lOOOg HgO and the hydroxyl ion concentration 1.25 x 10”^moles/l000g HgO in the water sample. The time and temperature of the ignition of the oxide was found to affect the values determined for the solubility, according -| r z p to Busch. This seems to indicate that equilibrium had 152Ibid., 161. not been reached, as the solid phase at equilibrium would be the hydrated oxide or hydroxide. These factors are known to affect the rate of solution of oxides but should not change the equilibrium. Moeller and Kremers-*-^ also gave water solubilities — T. Moeller and H. E. Kremers, J. Phys. Chem., 48, 395 (1944). calculated, assuming complete dissociation of the hydroxyde dissolved, from the relation, Solubility-moles liter-"*' = 4i I k ^ 127 154 Again the value is too small, because the only species in solution considered were Nd+^ and OH". Davies-^^ has discussed the fact that the hydroxides 134 G. W. Davies, J. Chem. Soc., 1951, 1256. of metal ions are weaker electrolytes than would be expected from a consideration of the size of the hydroxyl ion as compared to other anions. There seems to be no particular property of the hydroxyl ion that could account for this, and it is postulated that this is due to the absence of a hydration sphere protecting the metal ion. In the case of anions other than hydroxyl ion, the closest approach of the cation and anion may be represented as M+^-Hg0-X7 but with hydroxyl ion M+Z-H20-0H“ —*-M+Z-0H“-H20. Harned and O w e n ^ ^ have suggested that the proton resonates between 135 H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions. Second Edition, Reinhold Pub lishing Corporation, New York (1950), p. 385. the water molecule and a proton accepting anion as 2 ^2: — M+ -OH --H+— OH . Dissociation of this would give M (OHj+BgO preferentially. Hydrolysis of the Tri-valent Cations of Neodymium and Praseodymium These measurements were all made in solutions in which the perchlorate concentration was 3 C. Throughout r 155 th.ls work, the terminology of the Swedish school is used in which, for molarity, c is used for the quantity and C for the unit. The quantity, molarity, is symbolized m and the unit M. The hydrolysis of both neodymium and praseodymium ions was found to be a slow reaction. The E. M.F. of the hydrolysis cell reached a constant value within five minutes for all of the readings taken before the equivalence point of the "free acid", that is the H+ bound only to solvent molecules, had been reached. After this point, however, when the hydrolysis began, a very long time was required to obtain constant readings. Because of this, values of Z greater than about 10“2 could not be obtained. Also, it is seen in the plot of Z versus -log h that the curves diverge for the higher values of the pH, probably because of the reaction proceeding very slowly at that point and equilibrium not being attained. This slow reaction was a homogeneous one, as no solid phase occurred at any time during the base additions. If a generalized hydrolysis reaction is considered, after Hietanen and Sillen, v the following equation may be ■^®S. Hietanen and L. G. Sillen, Acta Chem. Scand. , 8, 318 (1954). written. (VI1-14) qNd+f .+pH20 ^ NdQ (OH)+ 53q7p) +pH+ . . (aca) q p(aq) (aq) 156 A function Z is defined as the hydroxyl ion hound per metal atom, or the hydrogen ion released per metal atom. The total metal in solution, Nd, is given by the equation following. (VII-15) Nd - [Nd+^ + 2 _ < l £w q (0H,p(aq)P>] 1? Q. The analytical excess of hydrogen ion in the solution, i.e., the sum of the proton excess in the solution and in the complexes minus the proton deficiency in the solution and in the complexes, is given by the expression H = h - [OH-] - ZL p |Nd (OH)+ S3q’”P)l , (VI1-16) L J pq L q P(aq) J ' where h is the true hydrogen ion concentration of the solution. The analytical excess of the hydrogen ion, H, is thus equal to the hydrogen ion concentration that the solution would have if no hydrolysis occurred. A general ized equilibrium constant for the reactions of type (VII-14) may be written, / s "'V' Tnd (OH)+ )"? P (vn-17) Xpq = L q p J h The activity coefficients are included in the constant ■Xpqj as this is restricted to a constant ionic strength solution. The activity coefficients are then assumed to remain con stant. Substituting for the concentration of the species Ndq(OH)* (^ “P) from the equilibrium constants, we obtain Jr 157 the following. (VII-18) Nd = [Nd+f) + [Nd+^jq • h “P X p q and pq (VII-19) H = h + K^bT1 - 2 1 P & d +^lq h “p X pq L Kyj = ion product of water at 25°C. In the expression for H, Kwh_q is negligible in comparison with the other terras. Then the r ~ 1 q f hydroxyl ion bound = y> p iNd+"jP . • h-P}.h P X = h - H (VII-20) pq pq and the function Z is given by . (VII-21) Z = h - h “ -Ip lm+3j 9 • h ' p Pq Nd [Nd+3]-pq +2! q Lh P ]J q • h-P X' pq It is impossible to determine accurately the hydrolysis mechanism from the curves in figures 11 and 14, because of the difficulty caused by the slow reactions. The curves for praseodymium and neodymium are similar, as would be expected for these ions. Since the deviation of the curves occurs, for different total metal concentrations, in the opposite direction from that observed when polynuclear complexes are formed, it seems unlikely that there is any appreciable reaction occurring giving polymer formation in this case. When polymers are formed, it is observed that the curve for the highest value of M, the total metal, occurs at the lowest pH. Prom the general shape of the curves, reactions giving a univalent ion seem to be ruled out, since the slope of the plot of Z versus log h would be much greater than that observed. These have been postulated to be of the type NdtJ . + HpO^NdO* + 2H+ (aq) 2 x (aq) (aq) 137 and were also disregarded by Moeller. For the initial T. Moeller, J. Phys. Chem., 50, 242 (1946). portion of the curve, it will be assumed that Z is in dependent of the total metal concentration, and hence that only mononuclear complexes exist. Then the expression for Z simplifies to give where q has only the value of unity, and only mononuclear complexes are considered. It is further assumed that the only product formed is Nd(0H)+2, i.e., p is unity, the expression simplifies to h “ X (VII-23) Z » ___ ii i 1 + 1 + b / v ' X ' n - i ^ n The solid curves in figures 11 and 14 were calculated as sum ing -log X" 2 1 ” and 8.5, and give Z as a function of 159 -log h. By comparison of the experimental data with these curves, it appears that the constants for the hydrolysis reactions + 3 + 2 (VII-24) Nd (HgO )n + H20^Nd(0H) (H^O) ^ + H30+ {VI1-25) Pr(H20)+3 + H20^rPr(0H) (HgOJn-i + H30 + are equal within the limit of accuracy of the determina tion, and that pKa = 8.5. This corresponds to an equilib rium constant of 3 x 10"^. The rare earth ions therefore rank among the weakest of the aquo-acids. Since the hydrolysis is so small, the uncertainty in the Ka value was rather large. To judge from the spread of the data, the true value probably lies within the limits pK^ = 8.5 - 0.4. Attempts to perform a "static titration11, i.e., one in which samples could be prepared for each point in the curve and allowed to reach equilibrium over a period of weeks, were unsuccessful, as Z is determined by the dif ference of two extremely small numbers, and the experimental errors were too great. Examination of the data in tables 5 to 25 shows that in the beginning of the titrations, where h was relatively large, and the hydrolysis of Nd+3 and Pr+3 was negligible, H was larger than h. Ideally the quantity (h-H) should be 0 at these pH values. These negative values of (h-H) are 160 probably due to slight errors in the values of h and H, as this quantity is the difference between two relatively large numbers. This difference, (h-H), rarely decreased —5 to values less than -1 x 10 C. The same difficulty was observed in the determination of the hydrolysis of Fe+^ ^®B. 0. A. Hedstrom, Arkiv Kemi, 5, 457 (1953). — 5 where differences averaging about 8 x 10 C. were observed. The difference in these two values decreases until at about pH *= 5, (h-H) changes sign as the hydrolysis of the rare earth ions commences. It is also possible, since the hydro lysis is so slight, that minute amounts of basic impurities may be present in the solutions giving slightly small values of h. The extremely weak action of Nd+® and Pr+^ as aquo- acids is to be expected, as the forces acting between the central ion and the surrounding water molecules must be almost purely electrostatic. The "ionic potential", defined as Z^/r by Hedstrom,where Z is the ionic charge and r 139Ibid., 457. o Is the crystallographic radius in A units, is 9.0 and 9.1 for praseodymium and neodymium ions respectively. These 161 + 2 140 values are considerably larger than Fe = 5.3 (pKa=9.5), 140 Ibid., 457. Ca+2=4.0 (pKa=12.7),141 and Mg+2=6.2 (pKa=11.4), and it G. Kilde, Z. anorg. allgem. Chem. 218, 113 (1934). would be expected that the hydrolysis would be more pro nounced with the rare earths than with these divalent ions, as was observed to be the case. For trivalent ions, the following ionic potentials may be given: Al+®=18, Fe+®=15, Sc+^=11.1, and Y +3=10. Actually it would seem more to the point to consider the function Z/r as the potential about the central ion, i.e., the "ionic potential" divided by Z. This, however, fails to give as good agreement with the experimentally observed order. The solutions of Al+^, Fe+^ and Sc+^ have all been investigated and found to be quite highly hydrolyzed with the formation of polymerized species. Solutions of yttrium have not been investigated, but the degree of hydrolysis should fall between that of scandium and of the trivalent rare earth ions. These data are only approximate as the use of crystallographic radii to approximate ionic radii in aqueous solution can at best only give the correct order. Also, in the case of the transition elements and those where the ionic potential 162 is large, the bonding of the hydrated water is due to more complicated forces than ion dipole attractions. The constants for the following reactions are given below for Al+3, Sc+3, and Fe+3. ^1 KO reference Al3 - 1.07 x 10“6 - 5.82 x 10“9 142 Sc3 - 1.17 x 10“5 - 1.02 x 10"6 143 Fe3 - 9.0 x 10-4 4.9 x 10-7 1.2 x 10“3 144 "*"4^J. Faucherre, Compt. rend. , 227, 1367 (1948). 143 M. Kilpatrick and L. Pokras, J. Electrochem. Soc., 100, 85 (1953). 1 44 B. 0. A. Hedstrom, Arkiv Kemi, 6, 1 (1953). It is seen that the hydrated rare earth ions are much weaker aquo-acids than the other tri-valent ions that have been studied. The only other tri-valent ions which are stable in aqueous solution and which should be as weak aquo-acids as the trivalent rare earth ions are those of the heavier transuranium elements. The ionic radii of these elements are very similar to those of the rare earths. Thus the ionic radii of Pr+3 and Am+3 are both 163 ° 14 6 1.00 A, as determined from isomorphous compounds. 145 A. F. Wells, Structural Inorganic Chemistry, Second Edition, Oxford University Press, (1950), p. 661. Because of the lanthanide and the actinide contractions, the aquo-acidity of the ions should increase with the atomic number. It Is further postulated that even though the "ionic potentials" of the lanthanides and the heavier actinides are almost identical, the trivalent actinide ions should be stronger aquo-acids, since the bond between the central ion and the water in the hydration sphere is not purely electrostatic in origin. It has been proposed by Seaborg and Street-*-^® that bonding involving 5f orbitals 146 G. T. Seaborg and K. Street Jr., J. Am. Chem. Soc. , 72, 2790 (1950). occurs in chloride complexes of the tri-valent ions of americium and curium. This was proposed to explain the fact that 13 M hydrochloric acid was found to effect a good separation of americium and curium, in the form of their tri-valent ions, from the tri-valent rare earth ions, when used as an eluting agent in an ion exchange column. As has been discussed, the tri-valent rare earth ions show negligible complexing in the presence of chloride ion. The participation of the 5f orbitals in bonding in the complexes of the heavier of the transuranium elements 164 is postulated to result in the coordination of as many as 6 chloride ions through the formation of bonds with a small amount of covalent character. There are no reliable data with which to compare the values for the hydrolysis of the rare earths determined in this work. Although there have been several deter minations of the hydrolysis of Nd+3 , these have been done by measuring the pH of aqueous solutions of various neo dymium salts. There are many inherent errors in work of this type that render the results highly inaccurate. Fre quently there is significant complexing of the cation by the anion present, preparation of salts completely free of occluded acid is difficult giving uncertain stoichiometry, the effects of atmospheric carbon dioxide are difficult to avoid in the case of weakly hydrolyzed solutions, and fre quently variations in the ionic strength give concentration effects as great as those due to hydrolysis. Because of these difficulties in the older work, little will be said of the data of Bodlander^4^ (1915), Bodlander, inagural dissertation, Berlin (1915). Neish and Bur n s ^ ^ (1921) , or Kleinheksel and Kremers'^®(1928). G. Neish and J. W. Burns, Can. Chem. Met., 5, 69 (1921). 149j . jj. Kleinheksel and H. C. Kremers, J. Am. Chem. Soc., 50, 959 (1928). 165 1 SO The most recent work is that of Moeller on the 150 T. Moeller, J_. Phys. Chem., 50, 242 (1946). hydrolysis of the rare earth sulfates. The data was ob tained by measurement of the pH of aqueous solutions of the sulfates with a glass electrode at various concentrations of the rare earth sulfate. This work is thus subject to all of the above criticism. Also, since it has been shown that solutions of the rare earth sulfates contain, pri marily, the ionic species MS04+, these hydrolysis data reflect the reaction [m (OH) (H20)nf]| and not as assumed, M(0H)(H20 Widely varying values were obtained for the hydrolysis constant which were attributed to the use of concentrations instead of activities. An approximate value of 1 x 10“^ was given. In view of the complex formation with sulfate ion, this should be smaller .than the true value. CONCLUSIONS From the large negative value of the standard free energy change for the reaction of neodymium hydroxide with hydrogen ion, it is evident that this hydroxide is a strong base. This datum together with the very slight hydrolysis exhibited by the trivalent ion in aqueous solution and the slight reaction with hydroxide ion place neodymium hydroxide with the hydroxides of magnesium, calcium, stron tium, barium, and the alkali metal hydroxides as the strong est of the bases. This indicates that the Nd+^-hydroxide ion bond is weak, being formed by electrostatic attraction alone. The high coordination number of the neodymium ion with respect to hydroxide ion, 9 gives rise to a high lattice energy for the solid hydroxide, however, and the hydroxide is only very slightly soluble in water. By analogy, the heavier of the transuranium elements should form bases about as strong as neodymium hydroxide, although the possibility of a small degree of covalent bonding in the compounds of the transuranium elements will probably cause these to be slightly less basic. Solutions of neodymium halides, nitrate, and per chlorate should approach the behavior of Ideal 3:1 electro- lyter in the sense of the Debye-Huckel treatment, i.e., only electrostatic forces are significant and that the energy of these electrostatic attractions is small with 166 167 respect to the thermal energy. Reactions of anions with Nd+3 giving penetration of the hydration sphere and the formation of directed bonds appear to be negligible, and it is probable that forces other than purely electrostatic ones are less important in these solutions than in solutions of any other of the tripositive ions, including the heavier transuranium elements. The hydrolysis measurements show + 3 that reaction of Nd, . with water to give species contain- (aq) ing hydroxide ion is extremely slight, and that the hydro lysis of the lighter of the rare earth elements is probably less than that of any other of the tri-valent cations. The solubility measurements indicate that species other than + 3 Nd, x can exist only in very small amounts in equilibrium (aq) with the solid hydroxide at pH values as high as 7.5. These results should be interpretable in terms of the strength of the bond between the neodymium ion and the water molecules in the first coordination sphere, or between the neodymium ion and the hydroxyl ion. Thus the hydro lysis reaction may be pictured as + 3 V t t 7 + K .+ * h 30 There is no accurate information on the number of water molecules coordinated, so it is assumed that n remains constant. The bond between the water molecules and the 168 neodymium ion must be essentially of the ion dipole type, since almost no cases have been found where neodymium forms 151 directed covalent bonds. Mattock has attempted to Mattock, Acta Chem. Scand. , 8, 771 (1954). estimate the effect of the cation-water bond energy on the hydrolysis constant by plotting K-hydrolysis versus factors such as the ionic heat of hydration divided by the average coordination number, the "ionic potential", etc. These rough data indicate that neodymium forms a very weak bond with water and should be only very slightly hydrolyzed in aqueous solution. Neodymium hydroxide dissolves in distilled water to give a basic solution with pH = 9.1. The very low solu bility of the hydroxide prevents the preparation of highly basic solutions even though the hydroxide is a strong base. The data do indicate that the dissolved hydroxide is only partially dissociated under these conditions, probably with the formation of univalent ions. This is not at. all surprising if the ability of the hydroxide ion to bond with the neodymium ion is examined. On the basis of the ionic charge and size, the bonding ability of the anions should decrease in the order, sulfate, hydroxide, chloride, nitrate, and perchlorate. The last three anions give solu tions with very little complexing of the Nd+3 ion. In 169 sulfate solutions, the Nd+^ ions are almost completely in + the form of NdSO^. sulfato complexes, which have an insta- —4 bility constant of 2.3 x 10 . From the hydrolysis data, I O a value for the instability constant of Nd(OH) may be calculated. Thus K-instability = K-water/K-hydrolysis= 3 x 10”®. This very small value of K-instability is explainable as the metallic hydroxides are observed to act as much weaker electrolytes than would be expected on the basis of the ionic radius and charge, because of the lack of protection afforded by the coordinated water molecules. The decrease in ionic radius from Cl” to OH- is also critical in the effect on the lattice energy of the solids compared to the energy of hydration of the ions. Thus Nd(OH)^ and NdClg are isomorphous, but Nd(0H)g is only very slightly soluble while NdClg is very soluble. Neodymium hydroxide shows a slight tendency to dis solve in concentrated base solutions. No accurate identi fication of the ionic species present in these solutions could be made, and hence no determination of the reaction(s) occurring could be made either. The data do indicate the formation of an ion with a charge of -2. Since the solu bility in basic solutions is so slight, there seems little validity in attributing acidic properties to Nd(OH)^. 170 As discussed by Wells,there is no more reason to con- 1 rip A. F. Wells, Structural Inorganic Chemistry, Second Edition, Oxford University Press, (1950), p. 411. ■sider the formation of compounds such as KNdOg, KPr(0H)4 , 1 G. Beck, Angew. Chem., 52, 536 (1939). 1 S4. NaLaOp, and rare earth analogs of CaAlOp by interaction 154 E. Zintl and W. Morawietz, Z. anorg. allgem. Chem., 245, 26 (1940). of the oxides at temperatures as high as 1500°C. as evidence of the amphoteric nature of the oxides, than there is to consider the spinel MgAl204 as the salt of an acid HgAlgOg. These substances are ionic crystals, and frequently they have structures closely related to the simple oxides. Table 55 SUMMARY OF DATA ON NEODYMIUM HYDROXIDE Nd(0H)3(g)+ 3H(aq^ Nd^ q ) + 3H2°(D’ K=8.7±4.7x lol8^ F298“ "25*9-0-3 kcal Nd(s)+ 3/202(g)+ 3/2H2(g)^ N d ( 0 H ) 3(s), AF ° gs= -299.6±0.3 kcal Nd(OH),, v ^ N d t 3 x+ 3(0H)“, K=8.7±4.7 x 10**24, £F° = 31.5±0.3 kcal 3is; (aq) 298 Nd(g)+ 3(OH)" Nd(OH)3 ^gj+ 3e~ , Potential in basic solution Eb=2.701±0.004V MaU q ) + H g O ^ H d { O H ) ^ q)t H|aq), pK=8.5t0.4 P r (aq)+ “(aq) ’ pK= 8 -6t° - 4 171 AUTOBIOGRAPHY I, Russell Stuart Tobias, was born in Columbus, Ohio, September 11, 1930. I received my primary and secondary education in the public schools of Grandview Heights, Columbus, Ohio. My undergraduate training was obtained at The Ohio State University, Columbus, Ohio. In June, 1952, I received the degree of Bachelor of Science summa — cum laude and with high distinction in chemistry. During the academic year 1951-1952, I was the recipient of the Phi Beta Kappa fellowship. I entered the graduate school of The Ohio State University in the autumn quarter of 1952, and was a member of the junior staff of the Department of Chemistry during the academic years 1952-1953 and 1953-1954. I was awarded the Visking Corporation Fellowship for 1954- 1955, and the General Electric Corporation Fellowship for 1955-1956. While completing the requirements for the degree Doctor of Philosophy, I received additional grants of one quarter duration each from E. I. du Pont de Nemours and Company and from the Allied Chemical and Dye Corpora- ti on. 172