J. CHEM. SOC. DALTON TRANS. 1983 31The Hydrolysis of Metal Ions. Part 5.' Thorium(1v)Paul L. Brown and John EllisUniversity of Wollongong, PO Box 1144, Wollongong, N.S. W. 2500, AustraliaRonald N. Sylva *Australian Atomic Energy Commission Research Establishment, Lucas Heights Research Laboratories,N.S. W. 2232, AustraliaThe hydrolysis of thorium(iv) in 0.10 mol dm-3 potassium nitrate has been investigated bypotentiometric titration at 25 "C. Numerical analysis by our version of MINIQUAD has indicated thatthe only acceptable model involves the species [Th(OH)I3+, [Th4(0H)12]4+, and [Th,(OH),,]9+, forwhich the overall formation constants, expressed as -log ppg, are 2.98 (0.007), 30.55 (0.03), and34.41 (0.03), the estimated standard deviations being given in parentheses.The hydrolysis of thorium(1v) has been investigated for morethan 20 years.2-8 The hydrolytic behaviour has been shownto be extremely complex because of the presence of extensivepolymerisation reactions which occur in a narrow pH range(about 0.5 units) before the onset of additional, slow hydro-lytic and/or precipitation reactions.Indeed, none of thesestudies has obtained a definitive result. Accordingly, weinvestigated the system (0.10 mol dm-3 KN03, at 25.0 "C)and herein present the results.ExperimentalReagents.-Unless otherwise stated, all reagents wereMerck Suprapur grade. The source of thorium was thorium(1v)nitrate 5-hydrate (Merck G.R.); the base used was potassiumhydrogencarbonate (Fluka-Garantie reagent). Thorium analy-sis of the stock solution was carried out spectrophotometric-ally using 3,6-bis(o-arsonophenylazo)-4,5-dihydroxynapth-alene-2,7-disulphonic acid (Arsenazo III).9Procedure.-The previously described procedure * was used.In the expression [H+] = 10-PH/h the value of h was found bynumerical analysis to be 0.768 (for the ' best ' model).Alltitrations were carried out in a solvent of 0.10 rnol dm-3KNO, at 25.0 f 0.1 "C. A summary of the titrations is givenin Table 1 ; full details are available on request.ResultsThe stoicheiometric equilibrium constants for the formationof the hydrolysis products by the (hypothetical) reactions (1)are defined by (2), in accord with the previously adoptedEach species is represented by either a(p,q) pair or its formula.pTh4+ + qH2O + [Thp(OH),]'4p-''+ + qH+ ( I )Our version of MINIQUAD l3 is an augmented version ofthe original 14~15 and has, among other things, the followingfeatures : (i) numerical refinement of the analytical protonexcess at the beginning of a titration, allowing a titration to becommenced at any pH value irrespective of the extent ofreaction ; (ii) optional numerical refinement of the relationshipbetween pH values and hydrogen ion concentrations (seeExperimental section and refs.10-12); (iii) optional refine-ment of negative formation constants; and (iv) two auto-mated model (as opposed to species) selection procedures inaddition to the ' manual ' method as given by Gans et a1.l'Table 1. Summary of titrations of thorium(1v) at 25 "C and in 0.1mol dm-3 KNO,Total initialthorium(1v)concentration Number ofmol dm-3) pH range points1.960 3.138-3.501 1110.980 3.355-3.794 960.490 3.530-3.91 1 1210.196 3 .4 0 M . 0 3 3 148A preliminary examination of the data, largely by trial anderror, indicated the likely presence of the species (l,l), (4,12),and (6,15). This model, indeed, satisfies our acceptancecriteria,'O-12 namely estimated standard deviations of p,values of less than 10% and an agreement factor R of less than0.002 (see Table 2). This, of course, does not demonstrate theuniqueness of this model. Accordingly, further, very extensivecalculations were carried out using a systematic approach.Noting the various claims made in the earlier literature z-8*16for a variety of species and models (the distinction betweenwhich is often confused), the following ' species list ' wasconsidered: (1 21, (2,1), (W, (2,3), (2,4), (3,3), (3,4), (3,5),(3,6), (4,4), (43, (4,6), (4,7), (4,8), (4,9), (4,10), (491 I), (5,10),(5,11), (5,12), (6,14), and (6,16).It was used in two ways,namely : (a) to the base model of (1, l), (4,12), and (6,15), eachspecies was added singly, and in pairs (253 models); (b) to thebase model (1'1) and (6,15) was added each species bothsingly and in pairs [with the inclusion of the (4,12) species 276models; 23 models are common to calculations (a) and (6)l.tThis model selection procedure was carried out by means ofthe subroutine NEXSET which is a completely generalmethod of selecting combinational subsets from a given set(i.e.species list) according to any requirements, as specifiedby the user. The initial estimates of the formation constants ofthe added species were obtained from the extended Sylva-Davidson equation.I2 In both computer runs, all unknownparameters (formation constants, h, in the proton mass-balance equation, and the initial proton excess values) wereallowed to refine simultaneously.Since an examination of models rather than species wasrequired, values of the formation constants were allowed tobecome, and remain, negative throughout the refinement.Obviously, a negative formation constant for a species is ast In group (6) calculations, seven models containing the (1 ,l), (1,2),and (6,15) species, together with a fourth species, failed to converge32 J.CHEM. SOC. DALTON TRANS. 1983physically meaningless as a model which contains a negativeconstant. But it does not necessarily follow that such a speciesis non-existent ; deficiencies in the model (species presentand/or the estimated formation constants) may cause anegative value to be assumed at some stage in the refinementprocess. Both LETAGROP l7 and MINIQUAD l 4 9 l 5 caneliminate such species from a model (formation constant setto zero). However, our experience with MINIQUAD hasdemonstrated that this elimination can be premature orinappropriate; thus, a given model cannot always be examinedafter numerical convergence if one (or more) species has beenrejected because the model has been altered.In addition,before final convergence, the sign of a formation constant canchange several times such that the convergent model containspositive constants only. The permitted use of negative con-stants also often allows greater latitude in the choice of initialestimates for the constants.None of the models so obtained was satisfactory, largelybecause of the presence of negative constants or, in a minorityof instances, because of failure to meet our acceptancecriteria (see above). Thus, our data indicate that under theexperimental conditions used the three species [Th(0H)l3 +,[Th4(0H)12]4+, and [Th6(OH)15]9+ are the only ones that existin detectable concentrations. Extension of the calculations toinclude this model and all members of the species list, takenthree at a time (1 540 models), seems to us to be unwarranted.Earlier ~ o r k , ~ * ~ together with the present results, demon-strates that the onset of further, slow polymerisation and/orprecipitation reactions in the thorium(rv) system can be aserious problem because of non-equilibrium effects.Indeed,Baes et aL5 observed localised precipitation on the addition ofbase (NaOH) to their test solutions, which often disappearedon stirring, and hysteresis effects have also been ob~erved,~.~Efforts in the present work to eliminate such problemsinclude: ( i ) the use of low ionic strength, low total (initial)metal ion concentrations, and low pH values; and (ii) the useof 0.01 mol dm-3 base as titrant in the form of potassiumhydrogencarbonate.The presence of hysteresis effects is readily demonstratedunder certain conditions but we believed it was imperativeto examine the data actually used in the analysis for possibleinterference from this source.Accordingly, (a) 20 and (6) 40data points were removed from the high-pH region of eachtitration curve and the numerical analysis was repeated withthe following results: (a) -log Sl,l = 3.00 (0.01), -log p4.12 =30.64 (0.04), -log = 34.42 (0.03), h = 0.771, R ==0.0018; (b) -log p1.1 = 3.02 (O.O2), -log p4,12 = 30.71 (0.05),-log p6,15 = 34.46 (0.03), h = 0.769, R == 0.0018. Corn-parison of these results with those obtained from the full dataset (Table 2) thus demonstrates that these slow reactions madeno significant contribution over the time period of theexperiments.DiscussionThe present results are compared with some previouslyreported investigations in Table 2.This comparison is oflimited significance because, in addition to differences inionic strength and medium, the work cited appears to haveeither poorly defined or undefined species or model acceptancecriteria. We also find aspects of this earlier work disconcertingfor the following reasons.( i ) The choice of high total thorium(1v) concentrations (upto 500 mmol dm-3) would invoke significant compositionalchanges (and hence errors) throughout a titration.I6 Such highconcentrations rarely serve any useful purpose, and do notfacilitate easier detection of higher polymeric species, as hasbeen demonstrated in systems such as copper(u),1°uranium(vr)," and lead(ri),12 and in the present work.(ii) The use of very high ionic strengths might be seen tooffset the criticism of (i) above. This, however, is illusory sincehigh ionic strengths militate against the attainment of highpH values in titrations because of the increased ease ofprecipitation reactions under such conditions.16 This is wellborne out in the work of MiliC where the maximum averageOH/Th ratio (ii) obtained is about 0.6 (in 3.0 mol dm-3lithium, potassium, and magnesium nitrate media: models10, 12, and 14 in Table 2).In the present work, fi values of upto about 2.5 have been obtained. Thus, despite the very highprecision of the data of MiliC,8*16 any conclusions that can bedrawn from this work are very uncertain.(iii) It appears that a somewhat cavalier attitude has beenadopted towards species and/or model selection in earlierwork.Thus, for example, Hietanen and Sil16n3 propose anumber of models in attempts to explain their data and, in theabsence of stated or established acceptance criteria, nounequivocal choice could be made. Two of these models eachcontain nine species and common to both models is thespecies [Th3(0H)I1*+; we consider such models to be un-realistic.In the work of Baes et aL5 numerical differences betweenmany models is slight and the chosen model is based solelyon a goodness-of-fit parameter [see (iu) below]. Also, in thework of Danesi et al.,7 the criteria for model selection are notgiven.(iu) In an attempt to rationalise some of the earlier ~ o r k , ~ * ~ ~ Baes and Mesmer l6 have carried out further analysis of thedata.They arrive at the two schemes: [Th2(OH)2]6+, [Th4-(OH),$+, and [Th6(OH)ls]9 + (in perchlorate and nitratemedia) ; and [Th2(OH)2]6+, [Th2(OH)3]5 + , and [Th6(OH)14]10+(in chloride media). The choice of these schemes is basedsolely on the goodness-of-fit parameter, ~ ( i i ) (estimatedstandard deviation based on the hydroxide number, fi), whenthe present and earlier work 1*10-12 clearly shows that thisparameter, alone, cannot provide even an approximatelysatisfactory criterion of acceptability.(u) All previous work on the hydrolysis of thorium(1v) (andthe majority of other metal ions) has relied, for data analysis,on either graphical methods or, more recently, on non-linear least-squares analysis by computer.Of the latter, thebest-known programs are LETAGROP," the ORNL programof Rush et al.," and MINIQUAD.l4.l5 The first two programshave been used, for comparative purposes, to analyse thethorium(1v) hydrolysis data of Baes et al.' The excellentagreement obtained l9 suggests that no significant differencesexist between the programs. If, however, MINIQUAD iscompared to these programs, a very significant differencebecomes apparent. In LETAGROP and the ORNL programthe numerical refinement is based on minimising the quantity(fi& - ijcalc.)*, as defined in equations (3) and (4). Here(3)[HIT and [MIT are total proton and metal-ion concentrations,[HI and [MI are free proton and metal-ion concentrations, andthe other symbols have their usual meaning.The MINIQUADprogram, in contrast, separately and independently minimisesas defined by the mass-balance equations and experimentalobservations. Thus, whereas LETAGROP and the ORNLprogram require only one numerical relationship to beobeyed, MINIQUAD requires two such relationships to be60th {[H]T(obs.) - [H]T(calc.))* and {[MlT(obs.) - [M]T(cal~.))~J. CHEM. SOC. DALTON TRANS. 1983 33Table 2. Survey of potentiometric investigations of the hydrolysis of thorium(iv)Modelnumber Medium1 " NaCl(3 mol dm-3)2 b NaCl(3 mol dm-')34 '567891011NaC104(1 mol dm-7NaCIOI(1 mol dm-3)NaC104(1 mol dm-3)LiN03(3 mol dm-3)NaC104(4 mol dm-3)NaN03(4 mol dm-3)KN03(0.10 mol dm-7Total thorium(rv)Temperature concentration("C)252502595252s25252525mol dm-70.10-100.00.10- 100.01.58-20.60.25-1 5.02.15-20.02.5-121.03.0-1 26.01.31-121.054.2-50010.0-5000.196-1.96- log B,,5.144.788.7217.161 S O6.8636.424.974.768.9416.991.366.8321.1136.5863.354.328.485.6022.7943.844.157.704.6119.0136.762.292.5510.4920.635.1414.73> 7.735.108.98>9.6740.955.1714.2943.202.7210.4912.4219.236.25.517.9237.22.9830.5534.41Standarddeviation in(relativeper cent)16.93.16.110.817.710.82.312.33.115.48.413.810.016.97.716.14.66.94.64.64.69.26.94.64.64.64.66.96.94.60.84.62.36.15.40.85.46.16.81 .o3.48.59.73.15.04.91.78.06.2BPqRef.3355 , h58887This work" Model IIIB of Hietanen and SillCn for which p < 6, and systematic error in q / p ratio is refined.Model IVB of Hietanen and SillCn;3 asfor model 1 with value of p unrestricted. Recalculation of data of Kraus and Holmberg by Baes et aL5 Present work: R = 0.001 805.The total thorium(1v) concentration range involves the initial concentrations. Estimated standard deviations (log units) are: (1, l), 0.007 ;(4,12), 0.03; and (6,15), 0.03. Calculations using present data with models in Table 2 gave unsatisfactory results (negative constants, poorgoodness-of-fit, or poor standard-deviation estimates).obeyed independently and, as such, is inherently more The present work indicates that, for the concentrationpowerful.ranges studied, [Th(0H)l3+ is the most important species atAttempts at accommodating the various models in Table 2 low pH values. At higher pH values the tetrameric (4,12)with the present data gave unsatisfactory results. This lack of species becomes dominant. The (6,15) polymer is a relativelycompatibility makes any further comparisons of doubtful value. minor species even at high pH and metal-ion concentrations34 J. CHEM. S O C . DALTON TRANS. 1983Figure. Percentage concentration of thorium(1v) hydrolysis pro-ducts at total [Th4+] = 2 x 10-3 mol dm-3 assuming [H+] =1 0 - p H (A = 1)The Figure illustrates the species concentrations for a totalmetal-ion concentration of 2.0 x lo-’ mol dm-’ in the rangeOf the hydrolysis products of thorium(1v) previouslydocumented,2-8 the species [Th2(0H)J + , and one or otherof the hexamers, [Th,(OH)14]10+ and [Th6(oH),,]9+, havebeen postulated either singly or together in the presence ofother species.The present work does not indicate any sig-nificant formation of a dimeric species; the reasons for thisare not apparent but it has been suggested l6 that its formationmay be inhibited at low ionic strength.Danesi ef al.’ proposed the formation of the (4,12) speciesin 4.0 mol dm-3 nitrate medium (but not in 4.0 mol dm-’perchlorate) in common with the present work.Furtherevidence for this species in the thorium(1v) system is notavailable. However, a recalculation of the data of Hietanen *Oby Baes and Mesmer l6 for the uranium(iv) system suggestedthe presence of the (1,l) and (6,15) species (q/p values of 1.0and 2.5, respectively) together with an additional specieshaving q/p > 2.5. Of all the species examined here, only three,namely (4,l l), (4,12), and (6,16), meet this condition. FurtherpH 3-4.work at our laboratories on the uranium(1v) and relatedsystems might thus provide substantial evidence for theexistence of tetramers of this stoicheiometry in metal(1v)systems.AcknowledgementsOne of us (P. L. B.) acknowledges the Australian Institute ofNuclear Science and Engineering (A.I.N.S.E.) for the awardof a Postgraduate Research Studentship.We wish to thankMr. Ivan Traverso, Melbourne University, for carrying outsome exploratory titrations (with financial assistance fromA.T.N.S.E.). We are grateful to Dr. J. P. Pollard, AppliedMathematics and Computing Division, Australian AtomicEnergy Commission for writing the NEXSET subroutine.References1 Part 4, P. L. Brown, J. Ellis, and R. N. Sylva, J. Chem. SOC.,2 S. Hietanen and L. G. SillCn, Acla Chem. Scand., 1964, 18, 1018.3 S. Hietanen and L. G. SillCn, Acta Chem. Scand., 1968,22, 265.4 S. Hietanen, Acta Chem. Scand., 1954, 8, 1626.5 C. F. Baes, N. J. Meyer, and C. E. Roberts, Znorg. Chem., 1965,6 K. A. Kraus and R. W. Holmberg, J. Phys. Chem., 1954,58,325.7 P. R. Danesi, M. Magini, S. Margherita, and G. D’Alessandro,8 N. A. Milid, Acta Chem. Scand., 1971, 25, 2487.9 S. B. Savvin and V. B. Bagreev, Zuod. Lab., 1960, 26, 412.Dalton Trans., 1982, 191 1.4, 518.Energ. Nucl. (Milan), 1968, 15, 335.10 R. N. Sylva and M. R. Davidson, J. Chem. SOC., Dalton Trans.,11 R. N. Sylva and M. R. Davidson, J . Chem. SOC., Dalton Trans.,12 R. N. Sylva and P. L. Brown, J. Chem. SOC., Dalton Trans., 1980,13 P. L. Brown and R. N. Sylva, to be published.14 A. Sabatini, A. Vacca, and P. Gans, Talanta, 1974, 21, 5 3 .15 P. Gans, A. Sabatini, and A. Vacca, Znorg. Chim. Acta, 1976, 18,16 C. F. Baes,jun., and R. E. Mesmer, ‘ The Hydrolysis of Cations,’17 N. Ingri and L. G. SillCn, Ark. Kemi, 1964,22,253.18 R. M. Rush, J. S. Johnson, and K. A. Kraus, ORNL-3278,1963.19 L. G. SillCn, Pure Appl. Chem., 1969, 18, 55.20 S . Hietanen, Actu Chem. Scand., 1956, 10, 1531.1979,232.1979,465.1577.237.Wiley-Interscience, New York, 1976.Received 10th May 1982; Paper 2176