QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA By LARS GUNNAR SILL~N (DEPARTMENT OF INORGANIC CHEMISTRY ROYAL INSTITUTE OF TECHNOLOGY STOCKHOLM 70.) Introduction IF an iron(Ir1) salt say the nitrate or perchlorate is dissolved in water the solution has an acidic reaction. Thus reaction with the water a “hydro- lysis” has taken place:” xFe3+ + yH20 + Fex(OH),(3z-Y)+ + yH+ (1) Iron(II1) is by no means unique in this respect almost all cations undergo this reaction perceptibly in aqueous solution e.g. Be2+ AP+ UOZ2+ Cu2+. Many explanations have been offered but not always supported by suffi- cient experimental evidence. Some of the older textbooks for instance state that uncharged hydr- oxide is formed Fe3+ + 3H20 $ Fe(OH) + 3H+ This requires either microcrystals or a true solution of the hydroxide and both these explanations can be ruled out by applying the law of mass action even to rather crude measurements.It was suggested by Werner1 and by Pfeiffer2 that protons are split off from the water molecules bound to the cation (“aquo-acidity”) e.g. or more briefly Fe(H20),3+ + H 2 0 + Fe(H20),0H2+ + H,O+ Fe3+ + H20 + FeOH2+ + H+ (2) The equilibrium constant of this reaction would be the acidity constant K, of the Fe3+ ion. Niels Bjerr~m,~.~ who was the pioneer in this field as in many others determined K for Cr3+ as early as 1906. Bronsted and V~lqvartz,~ in 1928 from kinetic measurements of [H+] and solubility * Editor’s note As written in equation (1) this reaction appears to be fission (lysis) of water rather than fission by water the latter being the sense in which the term “hydrolysis” is generally used in other fields.The reaction however assumes the form of hydrolysis by water if it is written in the old (inadequate) non-ionic form such as FeCl + H20 3 FeC12.0H + HCl The word “hydrolysis” is used in this Review for any such reactions in which water takes part as is customary in other publications in this field. A. Werner Ber. 1907 40 272; “Neuere Anschaungen auf dem Gebiete der anorganischen Chemie” Vieweg and Son Braunschweig 2nd edn. 1909 p. 238. P Pfeiffer Ber. 1907 40 4036. N. Bjerrum Kgl. danske Videnskab. Selskub. Skrifter Nat.-mat. Afd. 1906 4 1; 2. phys. Chem. 1907,59 336; 1910,73 724. J. N. Bronsted and K. Volqvartz Z . phys. Chem. 1928 134,97 N. Bjerrum Thesis 1908 Copenhagen pp. 110-117. 146 SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 147 data calculated K for AP+ Fe3+ and six other cations.As a result and perhaps also under the influence of the success of the Bronsted-Lowry acid-base concept in other fields it was thereafter often assumed that reactions such as (2) are the general explanation of cation hydrolysis. If this were so it would provide an extremely simple picture of the be- haviour of elemental ions in aqueous solution. Consider for instance the series of ions with 2s2p6 structure Na+ Mg2+ AP+ Si4+ P5+ S6+ C17+. The electrostatic field close to the ions increases strongly from Na+ to C17+ since the radius decreases and the charge increases; thus it would be increasingly hard for protons to remain near the central ion. The field of Na+ barely suffices to direct the surrounding water dipoles whereas Mg2+ and APf hold 6 water molecules strongly enough to bring them into the lattice when a salt crystallises.The increased repulsion of protons is illustrated by the species that may reasonably be assumed to exist in acidic and alkaline solution at pH = 0 Mg(H20)62+ Al(H20)63+ PO(OH), SO,-OH- c104- at pH = 14 Mg(H,O),OH+ A1(H2O),(OH),- Si02(OH)22- P043- Obviously the simple electrostatic picture goes a long way towards explaining the facts. However it is certainly an oversimplification. Already in 1908 Niels B j e r r ~ m ~ ~ had found that the hydrolysis of Cr3+ also gives polynuclear complexes i.e. complexes with several metal atoms Cr2(OH)24+ etc. This work was however for a long time not the centre of attention. Jander,5 by diffusion measurements later gave qualitative evidence for polynuclear complexes of many cations.Nevertheless and in spite of the fact that polynuclear complexes have long been recognised among the hydrolysis products from anions such as molybdate and silicate the idea of aquo-acidity with mononuclear products predominated for many years Previous work on hydrolytic equilibria of cations and anions is listed in the recent Tables of Stability Constants for inorganic ligands,g Tables 1-4 (ligand OH-); anionic hydrolyses will be found in Tables 5,6,7 8 and 50. The present Review deals mainly with work carried out in Stockholm in the last 10 years. Symbols and Equations.-The basis of all the work to be described is the law of mass action. Consider two reagents A and B (omitting the charges) which can form one or several complexes A,B, each with a formation constant Bpg.Let a be the concentration of free A and b the concentra- tion of free B. If the activity factors are kept constant for instance by using a concentrated ionic medium we may choose the standard states so For a review see G. Jander and K. F. Jahr Kolloid-Beih. 1936 43 295. J. Bjerrum G . Schwarzenbach and L. G. SillCn “Stability Constants Part 11 Inorganic Ligands” Chem. SOC. Special Publ. No. 7,1958 published under the auspices of I.U.P.A.C. Sod2- C104- 148 QUARTERLY REVIEWS that they are equal to unity and then use concentrations in place of activities. The law of mass action then gives [A,Bq] = JS,,[A]P[B]Q = ppqapbq . . . . (3) If B is the total concentration of B and 2 the average number of A atoms bound per B atom we have B = [B] + Cq[A,B,] = b + Cq/Ipqa”bq .. . . (4) BZ= Cp[A,B,] = ZpPpqapbq . . . . . . . . ( 5 ) We shall moreover define a convenient variable q 9 = log(B/b) = log(1 + Cq/3pqa~bq-1) . . . . . . .(6) For the special case of hydrolysis let A be OH- and B the metal ion; here however we shall still often leave out the charges of complexes. The general formula of a complex may conventionally be written as B,(OH),; it must be stressed at once that equilibrium measurements cannot distinguish between species which differ only in the number of solvent molecules or ions of the ionic medium. For instance it is not possible to distinguish from equilibrium measurements in a perchlorate medium alone between Fe2(OH)24+ Fe,04+ Fe2(OH)2C10,3+ or a mixture of these and similar species such as Fe2(OH),(H20).(C104-),4-~.To conform with the published Tables6 we shall denote by *Paq the equilibrium constant for the reaction written with (H20 - H+) as a reagent rather than OH-:? where h is the concentration of H+ Equations (4) (5) and (6) then are changed to the forms The problem is to find the sets of numerals p q that correspond to complexes present in appreciable amounts and the equilibrium constants *ISDq for their formation. 7 In this Review as in ref. 6 /3, is the equilibrium constant for the formation of A,B from the reagents A (the ligand) and B (usually a metal ion cf. eqn. 3). For mononuclear complexes A,B q = 1 and the second subscript is usually left out p2 being written instead of Pz1 etc. The squilibrium constant for step-wise formation of a mononuclear complex Ap-IB + A f A,B is denoted by K,.An asterisk on a p or a K denotes that the reactions are written with HA-H* as ligand instead of A (for instance in the F-Fe3+ system * p 2 is the equilibrium constant for Fe3+ + 2HF + FeF,+ + 2Hf). For OH- complexes HA is of course water *P, is the equilibrium constant defined by eqn. (7) and *K1 *K2 etc. are the acidity constants as in equations (8) and (9). SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA Experimental methods To provide numerical values for p q and */I in equations (4a-6a) we have to measure B 2 b and h over as wide a range as possible. B (= the total concentration of B) is always known from the amount of component B added to the solution. h (= [H+]) may often be measured with a hydrogen or quinhydrone electrode and almost always with a glass electrode.2 (= the average number of OH groups bound per atom of B) is obtained from h and the simple argument that the number of protons in the solution should be the same as that originally added. In many cases b and thus 7 [= log (B/b)] may be obtained by using cells with a metal (Agf Hg22+) amalgam (Cd2+ Pb2+ Bi3+ In3+) or redox (Hg2+ TI3+ Fe3+) electrode. The experiments are conveniently carried out as “titrations” to say 100 ml. of a solution S are made successive additions of a solution T (for practical reasons sometimes of two different solutions TI and T2). The compositions of the solutions are so chosen that B the concentration of B in the mixture remains constant whereas 2 is varied by the addition of acid or base. Moreover the ionic medium is kept as constant as possible usually by the aid of sodium perchlorate.After each addition the equili- brium values for h and if possible b are measured by suitable electrodes. After a small correction for the liquid junction potential Ei which is proportional to h the e.m.f.s give the concentration directly and may be calibrated with solutions of known h and b. It seems for instance that with 3~-(sodium) perchlorate as medium one may replace as much as 0.6 mole per 1. of Na+ by H+ before deviations in the activity factors of metal cations correspond to more than h0.2 mv in the e.m.f.s.’ All the data used for the calculations refer to clear solutions (no colloid or precipitate may be present) where it has been proved that the same values are obtained from whichever direction the equilibrium between the dissolved species is approached e.g.from higher or from lower 2. To increase 2 a base is added often OH-. Sometimes however e.g. for Fe3+ a local excess of OH- gives rise to a local precipitate which dissolves very slowly. It has then been proved practicable to add HC03- instead it is proved that complex-formation by carbonate is negligible by bubbling carbon dioxide and nitrogen alternately through the solution and observing the effect on the e.m.f.s8 By such titrations at constant total concentration of B and in a constant ionic medium but with varying 2 values (first used by I. Leden9 in a study of a number of cadmium complexes) it is possible to obtain in a limited time a much larger number of experimental results than could be obtained in the same time by the older “point-wise” method.Moreover from the course of a titration curve it is possible to correct for small errors in the 149 7 G. Biedermann and L. G. Sillen Arkiv Kemi 1953,5 425. * B. 0. A. Hedstrom Arkiv Kemi 1953,6,- 1_._ 150 QUARTERLY REVIEWS analysis for instance to determine accurately the excess of acid concen- tration in a metal-salt solution.l* This incidentally gives the titration method an advantage over the time-honoured method of measuring the pH of a solution of a “pure salt” (see the case of Fe2+ belowll). Treatment of results For each system studied it is essential to obtain a series of measurements as accurate as possible and over as wide a range of concentrations (B h) as possible. The results are conveniently displayed as in many cases in this Review as graphs of 2 against log h (or as graphs of 7 against log h) for specified values of total concentration of reagent B.These families of curves will be represented in the text below by Z(1og h)B and y(log h)B. If a certain set of *PDq is to be acceptable as the final solution of the problem the curves Z(1og h)B calculated by use of these constants must within the experimental error agree with the experimental results over the whole range studied. It is important that the whole range rather than a limited part of it shall be covered. Even when the numerical equations derived give acceptable agreement with the experimental results over the whole range the question still remains whether the explanation in terms of chemical reactions is unique or not. Therefore it has been necessary to devise mathematical and graph- ical methods for treating the results that are free from preconceived opinions as to what the complexes should be and to apply as many such independent methods as possible.For details of the mathematical and graphical methods the original papers12 should be consulted. Sometimes the set of curves gives important information at a first glance. For instance if the data inZ(1og h) coincide for different values of B and thus are independent of B then only one value of q is represented. In that case all the complexes present in appreciable amounts are homonuclear ; then as a rule q = 1 and the complexes are mononuclear. [If 7(log h) is independent of B the complexes must be mononuclear.] This is exceptional with OH- but common with other ligands; for OH- the 2 and 9 curves generally change with B so that polynuclear complexes must also be present.If the curves are parallel with a constant spacing ( A log B)/ (A log h)Z = t then Z and 7 are functions of the single variable x = log B - t log h and it can be shown that all complexes present in appreciable amounts can be written in the form B((OH),B), the “core + links” formula.12a However it requires a more accurate analysis of the curves to find whether lo C. Berecki-Biedermann Arkiv Kemi 1956,9 175. l1 B. 0. A. Hedstrom Arkiv Kemi 1953,5,457. l2 L. G. Sillen Acta Gem. Scund 1954 8 (a) 299 (6) 318; S. Hietanen and L. G. Sillkn ibid. p. 1607; B. 0. A. Hedsiiorn ibid. 1955,9 613; G. Biedermann and L. G. Sillen ibid. 1956 10 1011; F. J. C. Rossotti and H. S. Rossotti ibid. 1955 9 1166; L.G. Sillhn ibid. 1956 10 186; F. J. C. Rossottl H. S. Rossotti and L. G. Siilen ibid. p. 203; L. G. Sillen ibid. p. 803. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 15 1 only one or two values of n are represented or whether there are several such perhaps a series of complexes.12* In the following pages our results for several systems will be discussed. The chemical picture will be stressed and for some systems the degree of agreement between experiment and theory will be indicated. Since the same species and equilibrium constants have been deduced by several independent mathematical approaches-often also several independent experimental methods-it seems that the main reactions are generally well established; it is however possible that species existing in minor amounts escaped detection.Cationic systems Mononuclear Species.-Mercury(i1) is one of the few ions which on hydrolysis fulfil the criterion for mononuclearity 2 and 7 are functions of log h only and independent of B. The two independent sets of data Z(1og h) obtained by use of a glass electrode and r(log h) obtained by use of a redox electrode may be explained by an acid dissociation in two steps; the same values are obtained for the acidity constants :13 HzOHgOHg2+ + HOHgOHz+ + H+; *Kl = */I1 (= */Ill) . (8) HOHgOHz+ + HOHgOH + H+; *Kz = *Pz/*/I1 (= */3zl/*/311) (9) The symbols given for the equilibrium constants are those used in the Tables of Stability Constants6 (cf. footnotet on p. 148). For other polyprotic acids such as H,PO and HzS04 the ratio between successive acidity constants is often around For PO(OH), for instance the logarithms of the constants are -2.1 -7.2 and -12.3.-This is easily understood it must become harder to pull protons from molecules of increasing negative charge PO(OH)3 P02(OH)z- P030H2-. By analogy one might perhaps expect that for mercury(r1) a proton would be more easily split from an ion of charge +2 than from one of charge + l . The first acidity constant *Kl (at 25"; in 0.5~-NaClO,) is lO3*' so the second might be expected to be of the order lo-*. In fact it is 10-2*6 and this is a case where the second dissociation constant of an acid is greater than the first. This means that the following disproportionation is favoured 2HgOH+ + Hg(OH)2 + Hg2+; K = *Kz/*K,=lO1*l . (10) Fig. 1 shows the distribution of HglI and for comparison Pv over various complexes for variations of log h.It is seen that the fraction of mercury(r1) present as the intermediate complex HgOH+ is at most about 14%. If we assume that there are N equivalent possible sites for OH groups on a HgU atom and that the probability that one of these is oc- cupied by an OH is independent of whether the other sites are occupied lS S. Hietanen and L. G. Sill& Actu Chem. Scund. 1952 6 747. 152 QUARTERLY REVIEWS or not then one niay derive the “statistical” value for the equilibrium constant K in equation (10). We have 5 0 - 0 - x - If we assume N = 2 we find that log Kstat. = log 1/4 = - 0.6; for higher values of N log Kstat. would have values between - 0.6 and - 0.3. 3 ‘ I I I 1 1 I I I 1 I 1 1 0 2 4 6 8 10 /2 14 PH FIG. 1. Distribution of Pv and HgII over diferent species in solutions of various pH.For each pH one can draw a vertical line; the section of this line falling within theJield of each species is proportional to the amount of that species present at equilibrium e.g. at pH = 3-0 we have 12% of H3POa and 88% of H2P042-; at the same pH we have 59 % of Hg2+ 12 % of Hg(OH)+ and 29 % of Hg(OH) 2. 1 Hg2+; 2 Hg(OH)+; 3 Hg(OH),; 4 H3P04; 5 H2P04-; 6 HPO,,-; 7 P043-. [Reproduced with permission from J. Inorg. Nuclear Chem. 1958 8 193.1 In fact although the electrostatic effects would have tended to decrease log K it is greater than the statistical value. (Our conclusion was in- cidentally later confirmed by work in Schwarzenbach’s school at Ziirich.l4) It appears at first sight possible to relate the high value for K with the sp-bonds in Hg(r1) complexes to consider that the two symmetrical species are favoured by mesomerism but this view cannot be maintained in face of the accumulated data.The Table (p. 167) is a survey of equilibrium constants for mono- and di-nuclear hydroxo-complexes studied at Stockholm. Some of the products are only secondary while in the available concentration range polynuclear complexes predominate. In other cases however the data have been accurate enough to afford *K and *K2 independently and so to give K in equation (10). It is true that TP+ and In3+ with electronic structures similar to Hg2+ also have log K greater than the statistical value; but so have Fe3+ and Sc3+ with very different l4 G. Anderegg G. Schwarzenbach M. Padmoyo and 0. F. Borg Helv.Chim. Acta 1958 41 988. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 153 electronic structures. It seems therefore that this behaviour is typical of OH2 acidity as distinguished from the OH acidity of say PO(OH)3 and S02(0H),. Perhaps the second complex is not M(OH)2 but rather MO FeO+ HgO InO+ etc. (cf V02+). One specific case that of the iron(rr) ion has general interest. An early inve~tigatorl~ very carefully applied what was then the standard method for cation hydrolysis. He prepared a very pure specimen of iron@) perchlorate recrystallising it many times in the absence of air and measured the pH of solutions of this salt in air-free water. He then calculated *K (the equilibrium constant for Fe2+ + H,O + FeOH+ + H+) as [Other workers,15" using pure solutions of iron (11) chloride found a value of 10-7.9.] The same reaction was studied by Bengt Hedstrom,ll by what has become our standard method.He prepared a solution containing iron(I1) and perchlorate ions and a small amount of H+ in excess. From the changes in log h on addition of increasing amounts of base he calculated accurately the amount of H+ in the solution; the part of the titration curve where Fe2+ and FeOH+ were both present gave *Kl namely 10-9*5 iron(rr) is thus a much weaker acid than was previously thought. It is not hard to explain the discrepancy it is difficult to avoid presence of small amounts of H+ and Fe3+ which may be adsorbed on the crystals of Fe(ClO,),; although the resulting solutions do not change their pH after a number of recrystallisations the acidity is then much too high.Unfortunately most older work and some more recent on cation hydrolysis is founded on measurements of pH in "pure salt" solutions. Dinuclear and polynuclear complexes Iron(IrI).-The hydrolysis of the iron(rrr) ion has been studied by many workers,6 who however have until recently usually tried to explain their results in terms of reaction (2) only with an equilibrium constant *Kl. Now by various methods it is possible to obtain approximately constant values for *Kr over limited ranges of h and total iron concentration. However accurate measurements over a wide concentration range show that the calculated *K varies by more than can be accounted for by activity factors or by a second mononuclear complex Fe(OH),+. From deviations in both spectrophotometric16 and magnetic rnea~urements~~ it was concluded that there must exist some other species presumably a polynuclear complex Fe2(OH)y(33C-Y)+.Bengt Hedstrom* in Stockholm studied the hydrolysis of iron(1rr) using glass and redox electrodes and deduced very straightforwardly from both sets of results that the main product in his experimental conditions [ 3 ~ (Na)ClO,; 25"] had the formula Fe,(OH),4+ and that two mononuclear l6 F. Lindstrand Diss. Lund 1939. 150 K. H. Gayer and L. Woontner J. Amer. Chem. SOC. 1956,78 3944. l6 T. H. Siddall tert. and W. C. Vosburgh J . Arner. Chem. SOC. 1951 73,4270. l7 P. W. Selwood personal communication (1952). 154 QUARTERLY REVIEWS complexes occurred as by-products becoming important at low concen- trations Fe3+ + H20 + FeOH2+ + H+; log “KI = -3.05 FeOH2+ + H20 + Fe(OH),+ + H+; log *K2 = -3.26 log *Bz2 = -2.91 2Fe3+ + 2H20 + Fe,(OH),4+ + 2H+; Once the formulae of the complexes and the approximate equilibrium constants were known it was possible to explain the magneticla and spectrophotornetric results,lg though it seems that these methods alone did not permit determination of x and y in Fe,(OH) with certainty.0.8 0- 6 ry 0.4 0.2 0 -2 -3 - 4 -5 -6 jog h Average number Z of OH bound per Be as a function of log h. All experimental points are given. Completely filled or open symbols represent points from diferent titrations half-filled symbols represent points from back-titrations (decreasing Z ) . A hydrogen electrode was used for and a quinhydrone for other symbols. Full curves are calculated by assuming Bes(OH)sa+ as the only complex with log * p33 = - 8-66.Broken curves are calculated with the constants given in the text by assuming Be20H3f Be(0H) 2 and Be3(OH)s3+ to be present. Total Be concentration; B; 1 48 m ~ ; 2 19 mM; 3 10mM; 4 5 m; 5 2.5 m ~ ; 6 1 mM. [Reproduced with permission from Acta Chem. Scand. 1956 10 990.1 The Table lists also a number of other ions where a complex B,(OH)2 or B 2 0 is formed either as main product or together with mono- or poly-nuclear species. The column “ t KZ2” gives the “dimerisation con- stant” of BOH to B,(OH)z. This often has a fairly high value in spite of L. N. Mulay and P. W. Selwood J. Amer. Clzem. SOC. 1954,76,6207; 1955,77,2693. FIG. 2. l@ R. M. Milburn and W. C. Vosburgh J. Amer. Chern. Soc. 1955,77 1352. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 155 the fact that the reaction is an association of two positive ions.The fact that strong forces are involved is demonstrated by Mulay and Selwood's discovery18 that the dinuclear Fe 2(OH) 24+ is diamagnetic whereas the mononuclear FeOH2+ is strongly paramagnetic like Fe3+. Beryllium.-It has been known since Berzelius's time that solutions of beryllium salts remain clear on the addition of up to 1 OH- per Be2+. Previous work on this reaction can be divided into two groups that20 in which the main product is held to be Be,(OH)22+ (or its equivalent Be202+) and that21 in which it is claimed as Be4(OH)44+ (or Be4024+). The hydrolysis of beryllium (in ~ M - N ~ C ~ O at 25") was studied by modern methods by Kakihana and whose results [in the form of Z(1og h)B curves] are reproduced in Fig.2. This Figure shows that Z increases (ie. more OH is bound per Be) with decreasing log h (Bconstant) and with in- creasing B(1og h constant). The first result must be so; the second indicates that there are polynuclear products. The detailed measurements are incom- patible with the assumption of either Be2(OH)2z+ or Be4(OH)44+ as the main product whereas mathematical analysis of them strongly indicates Be3(0H)33+. Assuming this as the single product gives fair agreement over a fairly wide range (full curves in Fig. 2) but deviations at the two ends of the curves lead to the formulae and formation constants of two further complexes present in minor amounts (but still not those assumed by pre- vious workers). The broken curves in Fig. 2 have been calculated by assuming the following equilibria :22 3Be2+ + 3H,O + Be,(OH),3+ + 3H+; log *p33 = -8.66 log *p12 = -3.24 log *p2 = -10.9 2Be2+ + H 2 0 + Be20H3+ + H+; Be2+ + 2H20 + Be(OH) + 2H+; Fig.3 is a distribution diagram like Fig. 1. For each species in the solution a field is given. If a vertical line is drawn at a specific value of log h the section of this line falling within each field denotes the fraction of total beryllium present as the corresponding complex at the log h in question. Since polynuclear complexes are formed the distribution depends also on the total concentration B diagrams are given for B = 1 10 and 100 milliniolar. The predominance of Be3(OH)33+ suggests that it contains a ring of 3Be and 30H with 6H20 to fill out the co-ordination tetrahedra of beryllium. The other two complexes have narrower fields of existence; it seems likely that other complexes might also appear presumably with still narrower ranges if more sensitive experimental methods were available.ao M. Prytz 2. anorg. Chem. 1929,180 355; 1931,197 103; R. A. Gilbert and A. B. Garrett J. Amer. Chem. Soc. 1956 78 5501. 21 R. Schaal and J . Faucherre Bull. SOC. chim. France 1947 927; J. Faucherre ibid. 1953 1117; 1954 253; P. Souchay ihid. 1948 143; M. Teyssidre and P. Souchay ibid. 195 1,545. 2 2 Ref. u of the Table p. 167. 5 156 QUARTERLY REVIEWS Tin(II).-In early work on the hydrolysis of Sn2+ it was assumed that either23Q the mononuclear SnOH+ the dinuclear Sn2(OH)2+ (or Sn202+) was formed. This system was studied by Tobias24 who measured h with glass electrodes and b (= [Sn2+]) with tin amalgam electrodes.The / 2 0.5 F 0 -2 -3 -4 -5 log h -6 -2 -3 -4 -5 -6 log h 100 2 F 0 -2 -3 - 4 -5 -6 log h Distribution of beryllium over complexes for total beryllium concentra- FIG. 3. tion B = 1 10 and 100 millimolar as a function of log h. 1 Be2+; 2 Be,0H3+; 3 Be3(OH),3+; 4 Be(OH),. [Reproduced with permission from Acta G e m . Scad. 1956,10 1002.1 two sets of data 2 (log h)B and 7 (log h)B (Figs. 4 and 5) independently gave the same set of species and equilibrium constants namely Older values 3Sn2+ + 4H20 + SII~(OH),~+ + 4H+; log *Pa3 = -6-77 - 2Sn2+ + 2H20 $ Sn,(OH),2+ + 2H+; log *pz2 = -4-45 *30 M. Gorman and P. A. Leighton,J. Amer. Cliem. SOC. 1939,61,3342; 1942,64,719; A. B. Garrett and R. E. Heiks ibid. 1941,63 562; C . E. Vanderzee and D. E. Rhodes ibid. 1952,74,3552,4806; (b) M.Prytz Z. arzorg. Chem. 1928,174,355. 84 Ref. fof the Table p. 167. --3 Sn2+ + H 2 0 + SnOH+ + H+; log *Kl = -3.9 -1.7 SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 157 The solid curves in Figs. 4 and 5 were calculated by assuming only Sn3(OH)42+ which suffices to account for a large part of the data fairly well. The broken curves were calculated by.assuming also the two secondary products. FIG. 4. Hydrolysis of tin@); glass electrode used for measurements. Average number Z of OH bound per Sn as a function of log h (molar scale); B as a para- meter. Full curves are calculated by assuming Sn,(OW)42+ as the only complex with ldg *j143 = - 6.69. Broken curves are calculated by also assuming the presence of Sn,(OH),2+ and SnOH+ and using equilibrium constants given in the text.Sna+ concn. 1,4040 mM; 2 20.00 mM; 3 10.00 mM; 4 5.00 mM; 5 2-50 mM. [Reproduced with permission from Acta Chem. Scand. 1958 12 205.1 The two minor products happened to be the same as those proposed earlier as main products. Knowing the species and the approximate equilibrium constants Tobias recalculated the old data. In most of the old work the tin@) solutions must have been much too acidic because of a rather high content of tin(rv) which is harder to avoid than might be expected. The purest tin(r1) solutions seem to have been those of Milda P r y t ~ ~ ~ ~ who concluded correctly that a polynuclear complex was formed; but because she used too narrow a concentration range she missed the correct formula. The fact that Tobias obtained the same reactions and the same equili- brium constants by two independent experimental methods24 justifies some confidence in his results.Bismuth(m).-The hydrolysis of bismuth(I1r) was studied by Olin25 who measured b(= [Bi3+]) and thus 7 using bismuth amalgam electrodes. as Ref. j of the Table p. 167. 158 QUARTERLY REVIEWS His results (Fig. 6) indicate that the main product is a hexanuclear complex of charge 6+ Bi6(0H)1z+ (or e.g. Bi6066+). The deviations at the lowest 1 2 3 4 5 0 - l o g h FIG. 5. Hydrolysis of tin@); amalgam electrode used for measurements. q = log B/b as a function of log h B as a parameter. Curves are calculated for the same sets of constants and same Sn2+ concns. as in Fig. 4. values of 7 give evidence for another species BiOH2+. The curves in Fig. 6 were calculated by assuming the equilibrium constants [25"; 3~-(Na)C104 [Reproduced with permission from Acta Chem.Scand. 1958 12 205.1 6Bi3+ + 12H20 + Bi6(OH)1:+ + 12H+; log *p12,6 = 0.33 Bi3+ + H20 + BiOH2+ + H+; log "K = -1.58 The agreement is as good as could be desired in a range of B 0.1-50 millimolar i.e. a ratio of 1500. Since the solutions are rather acidic Z is a difference between large numbers and is not very accurate; the agreement however is good within experimental error. For Z> 2.0 slightly larger complexes are formed probably26 with 9Bi atoms and charges 5+ 6+ and 7+. About twelve years ago Grankr and the Re~iewer,~' studying the hydro- lysis of Bi3+ concluded that a series of species Bi{ (OH)2Bi}n3+n was formed. This also seemed to give fair agreement with the experimental results though not as good as that in Fig.6. Two factors contributed to the shortcoming. Tn this early work the concentration B was varied only five- fold (from 10 to 50 millimolar). Secondly there was a systematic un- expected experimental error the quinhydrone electrode which was used 2B Unpublished work at Stockholm. 2i F. Graner and L. G. Sillkn Acta Chem. Scand. 1947 1 631. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 159 for certain standardisations deviates from the ideal formula at higher acidities because p-benzoquinone is a base and attracts a proton.28 The resulting error (maximum 1-2 mv) shifted the experirncntal points so that the distance between the 7 curves corresponded to the general formula Bi{ (OH)2.0Bi},3+n rather than Bi( (OH),.qBi)n3+0‘6n. log n FIG.6. Hydrolysis of bismuth(@. 77 = log B/b as a function of log h. The curves are calculated by assuming the presence of the complexes Bi,(OH),,6+ and BiOH2+ with equilibrium constants given in the text. For clarity not all of the experimental points are shown for low values of v. 1,O.l mM; 2,0.5 mM; 3 l mM; 4,25 mM; 5 5 mM; 6,lOmM; 7 5 0 m ~ . [Reproduced with permission from Acta Chem. Scand. 1957,11,1452.] This experience stresses the importance of using a broad concentration range. When Olin later studied Bi3+ over a wider range of B a deviation was found which was traced back to the basicity of quinone. It should be mentioned however that the mechanism which was first proposed for bismuth and was erroneous in that case sufficed to explain the results very well for a number bf other ions especially indium thorium uranyl and scandium.Series of complexes For the cations discussed above one or at most two polynuclear species have been found; if two one of them has had a much wider “range of existence” in distribution diagrams such as Fig. 3 { Be3(0H)32+ Sn,(OH),2+}. For a number of other systems the predominating com- plexes seem to have the general formula B((OH),B}, with t constant and there is no preferred value of y1. Good agreement with experiment is obtained 28 G. Biedermann Act0 Chem. Scand. 1956 10 1340. 160 QUARTERLY REVIEWS by assuming that complexes with all values for n = 1,2,3 . . . are formed and that the equilibrium constants for their formation vary with n in some regular manner usually linearly. For In3+ BiedermanP' deduced the following equilibrium constants (as well as those for the mononuclear complexes see Table) from two independent sets of measurements Z(1og h)B and $log h)B (glass or quin- hydrone and In-Hg electrodes) In3+ + 2H20 + In3+ $ In(OH),In4+ + 2H+; log = -5.21 In{(OH)21n),n+3 + 2H20 + In3+ + In{(OH)$n);:f + 2H+; log K = -4.69 for r~>0 or in general (n + l)In3+ + 2nH20 +- 1r1{(0H),In),~+~ + 2nH+; -0.52 - 4 .6 9 ~ ~ I 1% *P2n,n+1 - The following reactions have been deduced exclusively from Z(1og h)B curves (n + l)U022+ + 2nH20 $ U02((OH)2U02),2+ + 2nH+; (n + l)Sc3+ + 2nH20 (n + l)Th4+ + 3nH,O log*p2n,n+l = 0-30-635n ref. 30 log *p2?a,n+l = 0.70-6.87n ref 31 log *&@+I - -7050n ref. 32 + SC((OH),SC},@+~ + 2nH+; + Th((OH)3Th},4+n + 3nH+; - It should be mentioned that there is evidence for other complexes as well namely (U02),0H3+ Th2(OH) 26+ Th20H7+ScOH2+ Sc(0H) ,+(Table refs.g and k) and that the equations for the equilibrium constants /3tnn,+l must be understood as approximations only. This simple approximation in spite of its having only two arbitrary constants gives fairly good agreement with experiment; it might perhaps 'have been improved by introducing more than two adjustable constants. Structure of the complexes When one complex predominates it seems reasonable to assume a closed structure (cyclic tetrahedral or octahedral etc.) and attempts are being made to determine their crystal structures. For aluminium earlier equilibrium studies by Cyril1 B r o s ~ e t ~ ~ indicated rather larger complexes contrary to previous opinion. Alkali can be added to a solution of alumin- ium chloride up to a ratio of 2.50H- per A13+ without causing permanent Ref.h of the Table p. 167. The mononuclear complexes were also studied by a distribution method by F. J. C. Rossotti and H. S. Rossotti Acta Chem. Scand. 1956 * 10 779. 30 Ref. c of Table p. 167. 31 Ref. g of Table p. 167. 3a S. Hietanen Acta Chem. Scand. 1954 8 1626. s5 C. Brosset G. Biedermann and L. G. SillCn Acta Chem. Scand. 1954 8 1917. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 161 precipitation. Such solutions have important cosmetical uses. The alu- minium complex they contain has been conventionally written as Al,(OH),+; it is formed rather slowly but once it is formed one may precipitate well-crystallised salts with e.g. Se042- and C2042-. In the hope of finding the structure of the complex “A12(OH),+” some of these salts were studied by X-ray methods.They were found26 to contain also alkali metal; a typical formula is NaA1,3(0H)32(S04)4(H20)z. The crystal structure of a corresponding selenate has been studied thoroughly by Georg Johansson.26 Aluminium was found to form separate groups with 13 A1 and charge +7; the formula conventionally Al13(OH)327+ is really A1130POH487+ and the structure is remini~cent~~ of that of dodecahetero- tungstates such as PW120403-. The equilibria in AP+ solutions are now under study by Biedermann and it seems probable that these large All ions will form a part of the final picture. In crystal structures units U604(OH)412+ and Ce6O4(0H),l2+ have been found35 as separate building-stones they contained an octahedron of U (or Ce) and a cube of 0 atoms.Recent X-ray of solutions seem to indicate that the “Bi6(OH)126+” complex may have a similar structure Bi604(0H)4“+. However no direct evidence has yet been found for existence of the Ce and U complexes in solution. n = l n =2 n-3 n - 4 0 0. 0.0 0 0 0 0 0 0 0 0 0 0 . 0 0 . 0 0. 0.0 0 0 0 n-5 0.0 0 0 0 . 00.00 0 0 0 . n - 6 a O . 0.0. O . O . O 0 0 0 0 0 0 0 FIG. 7. Possible structures of complexes U02[(OH)2U02],2+ with n = 1 to 6 shown as increasing fragments of a sheet from a- UO (OH),. @ uranyl groups with U in the plane of the paper and the two uranyl0 (not shown here) above and below perpendicular to the paper 0 oxygen atoms above (thick) and below (thin) the plane of the paper. [Reproduced with permission from Acta Chem. Scand. 1954,8 1914.1 In those cases where a series of complexes is formed it seems reasonable to assume open structures chains or sheets so that addition of each new “link” has approximately the same equilibrium constant.It is tempting to make comparisons with crystal structures of compounds which are known to be precipitated from such solutions. For instance Fig. 7 shows the geometry of the sheets in the crystal structure26 of cc-U02(OH)2. 34 J. F. Keggin Proc. Roy. SOC. 1934 A 144 75. 36 G. Lundgren Arkiv Kemi 1953,5 349; 1956,10 183. 36 H. Levy and K. A. Kraus 1958 personal communication. 162 QUARTERLY REVIEWS The black dots are the U atoms of UOZ2+ groups; the two oxygen atoms are one above and one below the plane of the paper. The open circles are OH groups in two layers one above and one below the level of the U atoms.If well-rounded fragments are cut from such a sheet their formulae will be (UO,),+,(OH),, as seen for n = 1-6 in‘Fig. 7. From the e.m.f. data the same formula was deduced for the complexes in solution and it is attractive to regard them as fragments of the UO,(OH) crystal structure pre-formed in the solution. Similarly the series of indium and thorium complexes may be related to the chains that have been found in the crystal structures of “basic” thorium3’ and indium Their composition would then be In(OIn),n+3 and Th(ogTh),n+4; by equilibrium measurements in aqueous medium one cannot distinguish between species with 20H- and lo2-. The assumption that Th4+ on hydrolysis forms chain-like complexes is supported by recent work on colloidal thorium hydr~xide,~ especially electron-microscopy which shows the particles to be threadlike.Anionic hydrolysis General.-Borates. It has long been known that polynuclear species are formed in certain anionic hydrolytic systems examples are borates germanates tellurates chromates molybdates tungstates and vanad- ates. There is no fundamental difference between anionic and cationic systems. The same graphical and mathematical approaches can be used for both and the experimental methods are similar except that in anionic systems as a rule it is necessary to work at higher pH and there are some extra experimental dficulties (e.g. exclusion of carbonate). In some systems with polyions both cations and anions are formed in the ordinary pH range for example with aluminium vanadium(v) and molybdenum(m).One of the first systems studied by our methods was the b o r a t e ~ . ~ ~ Besides the mononuclear species B(OH) and B(OH)g polyborate ions are known to exist especially at high total concentrations; they have previously been described in general as B40,2-. From the Z(1og h)B curves it was however deduced that in the more acidic range the predominant polynuclear species is a triborate of charge - 1 presumably B303(OH)4- a 6-membered ring compound. For higher 2 the accuracy of the equili- brium measurements in ref. 40 did not permit distinction with certainty between B303(OH)52- and Bp05(OH)42-; it is possible that both exist in solution and both have been claimed to exist in crystal lattices.41 Recent work by a “self-medium” method26 indicates that the tetraborate ion of ’ 37 G.Lundgren and L. G. Sillen Arkiv Kemi 1949,1,277; G. Lundgren ibid. 1950 2 535. 38 H. E. Forsberg Actu Chem. Scund. 1956 10 1287; 1957 11 676. 3B A. Dobry S. Guinand and A. Mathieu-Sicaud J. Chim. phys. 1953 50 501. 40 N. Ingri G. Lagerstrom M. Frydman and L. G. SillCn Acru Chem. Scund. 4 1 C. L. Christ and J. R. Clark Actu Cryst. 1956,9 830; N. Morimoto Mineralog 1957,11 1034. J.,J956 2 1. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 163 charge -2 and the triborate ion of charge - 1 are the two predominating polyions . measured by Sa~aki,~ [25"; 3hl-NaC1O4]. In this case it was practicable to let 2 be the average number of H+ bound per [A = H+ B = in equations (3-6)]. A related quantity is z = 2 - 2 the average charge per Mo atom. Molybdates. Fig. 8 gives Z(1og h)B curves for hydrolysis of -7 -6 -5 -4 -3 /oY[H'] Hydrolysis of molybdate ions.Average charge per Mo atom (z) plotted against log h. Points are for diferent total concentrations B of Mo. Circles with crosses in them (curve 2) refer to back-tritations. The curves are calculated by assuming the species and equilibrium constants given in the text. 7 2.5 mM; 8 1.2 m ~ ; 9 0.6 mM. [Mo] total 1 160 mM; 2 80 mM; 3 40 mM; 4 20 mM; 5 10 mM; 6 5 mM; [Reproduced with permission from J. Inorg. Nuclear Chem. 1959 9 94.1 At low log h 250 (z = - 2) at all values of B since is the pre- dominant species. The shape and spacing of the curves show conclusively that the first polynuclear complex formed is one with 7Mo and a charge of 6-. It is reasonable to identify this species with Mo@246- the para- molybdate ion which exists42a as a separate unit in the crystal structure of and Mo ,O 246-.Deviations at low concentrations of molybdenum indicate the presence of HMoO,- and at higher Z that of HMO,O,,~- The curves in 42 Y. Sasaki I. Lindqvist and L. G. SillCn J. Inorg. Nuclear Chem. 1959,9,93. d2a I. Lindqvist Arkiv Kemi 1950 2 325; Nova Acta Regiae SOC. Sci. Upsaliensis (NH4)6Mo,02dH20)4* Most of the results in Fig. 8 require only the two species 1950 C1. IV 15,l. 1 64 QUARTERLY REVIEWS Fig. 8 were calculated by assuming the following equilibrium constants (there is as yet no standard symbolism for such constants) + H+ + HMo04-; log K = 4.08 7M0042- + 8H+ + + 4H20; log K = 57.7 MO7Oz4'- + H+ $ HM0702g5-; log K = 4.33 HM0702g5- + H+ $ H2M070244-; l o g K = -3.7 Agreement is quite good.The species HMo702a- is well supported; some doubt may be expressed about H2M07024P in spite of the very good agreement since at the end of the range there must anyhow be some un- known species.42a 2 3 4 6 - / O g b FIG. 9. Hydrolysis of vanadium(v). Average number of hydroxyl groups 2 bound to each VO,+ ion as a function of log h for different total concentrations B and vanadium. The curves are calculated by assuming the presence of the species and equilibrium constants given in the text. [V] total 1 0.0200 M; 2 0.0100 M (+ reverse titration); 3 0.0050 M ; 4 0.0025 M. [Reproduced with permission from Acta Chem. Scand. 1956 10 964.1 Vanadium(v). Fig. 9 gives curves for vanadium(v) hydroly~is;~~ Z is the average number of OH- bound per V02+ ion. In highly acidic solutions VO,+ seems to be the only species (2 = 0); increasing the acidity from 0.05 to ~M-H+ does not change the vanadium absorption spectrum.With decreasing h 2 increases up to -1.4 and the solution becomes orange-coloured. An uncharged species corresponding to Z = 1 (V020H or HV03 or V205 etc.) might have been expected but there has been no evidence of its presence. The data indicate that the main reaction is the formation of a single polynuclear species namely an anion with 10 vanadium atoms. Assuming a complex with 11 vanadium atoms gives 43 F. J. C. Rossotti and H. Rossotti J. Inorg. Nuclear Chem. 1956 2 201; Acta Chem. Scand. 1956,10,957. STLLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUTLIBRIA 165 acceptable agreement for 2 = 0--1-1 but deviations at higher 2 values. With V or‘Vlz complexes neither the spacing between the curves nor their shape gives acceptable agreement with experiment.Moreover X-ray studies4* of orange vanadates crystallised from similar solutions indicate a multiple of 10 V per unit cell. The full curves of Fig. 9 were calculated by assuming the following equilibrium constants [ lw(Na)Cl O4 ; 25’1 lOVO2+ + 8H20 f H2Vlo02,4- + 14H+; log */114,10 = -6.75 H2V100284- f HV100285- + H+; HV100285- + V,,0286- + H+; log K = -3.6 log K = -5.8 The agreement is satisfactory. The formulae are written in the conventional way with as little water as possible. Structural studies may show them to contain more water. From a study26 of the alkali side of vanadate equilibria the following equilibrium constants have been deduced [0*5~-NaC1; 25’1 V04” + H+ + HVO,”; HV042- + H+ + H2V07-; log K = 12.6“ log K = 7*7b 2HV042- + H+ + HV2073- + H20; log K = 1 0 ~ 6 ~ 3HV0,2- + 3H+ S V30g3- + 3H2O; log K = 3007~ a By spectrophotometry.By e.m.f. measurements. Fig. 10 gives a schematic survey of all the vanadate equilibria the average charge z per V is plotted as a function of log h for different total concentrations of vanadium. We may neglect the difference in ionic medium between different parts of the diagram. In each of the ranges z = + 1 to - 0.6 and - 1 to - 3 there are rapid reversible equilibria. As long as the solution is kept within one of these regions equilibrium is obtained practically instantaneously on change of composition. If however a solution or a part of it has once been brought into the region z between - 0.6 and - 1.0 it requires a long time to attain equilibrium.This “instability range” may be one reason for difficulties that some pre- vious authors have experienced with vanadate equilibria. Similar instability ranges have been observed also for silicate equilibria.26 It is pertinent to ask why vo43- HV042- HV2073- and V30g3- pre- dominate of all the conceivable species. It may be these formulae seem arbitrary because they are written on the pattern of ortho- pyro- and meta-phosphates. It is true that some vanadates are isomorphous with phosphates indicating a tetrahedral V043- ion. However the more common co-ordination number of vanadium(v) seems to be 5 two oxygen atoms being bound in a linear group OVO and three more lying in the equatorial 44 I. Lindqvist personal communication; H. T.Evans jun. M E. Mrose and R. Marvin Arner. Min. 1955 40 314. 166 QUARTERLY REVIEWS v,o,3- FIG. 10. Schematic survey of the hydrolysis of vanadium(v). Average charge per V atom z plottedagainst log h. The lower leff part corresponds to Fig. 9 the upper right part to unpublished measurements by Ingri and Brito.26 Between them is an “instability range” with slow equilibria. plane. One may then imagine the following structures for the three species that predominate between z = - 1 and -2 (B = V02+ A = OH-) A A A A B A B V02(OH)32- = HV042- AB A (V02)2(OW,3- = HV,O,~- A A A B A A A B A B The equilibrium data as usual give only the average charge of a species and the number of vanadium atoms but not the amount of water. So there is no way of distinguishing between say HV042- and V02(OH)32- by equilibrium data alone.There is however no proof for these formulae. SILLEN QUANTITATIVE STUDIES OF HYDROLYTIC EQUILIBRIA 167 Conclusion In the systems discussed above it seems that the e.m.f. methods when applied over a wide concentration range and with a constant ionic medium have been able to give independently of other data sufficient information Logarithms of equilibrium constants for cations with mono- and di-nuclear Ion "K "K2 *P22 "K2I"K tK22 Other p q Ref. hydrolysis products. Be2+ vo2+ uo,2+ Fe2+ CU2f Cd2+ Hg22+ Hg2+ Sn2+ sc3+ Fe3+ 1n3+ TP+ Bi3+ Th4+ u4+ ("P2 - 6.0 -9.5 -9.0 - 5.0 -3.70 - 3.9 -5.1 -3.05 -4.4 -1.14 -1.58 -2.0 - (-8) I - 10.9) - - - - - - -2.60 I -5.1 -3.26 -3.9 -1.49 - - I - - 6.9 - 6.05 - - 10.6 - - - -4.45 - 6.2 -2.91 - 5.2 - - -4.7 - 3,3; 1,2 2n,n+ 1 - - - - - - 473 2n,n+ 1 2n,n+ 1 12,6 3n,n + 1 3n,n + 1 - - a b 11 10 d e 13 f g 8 h i j k 1 C The medium is usually 3~-(Na)clO, and the temperature 25" ; 1M-(Na)C1O4 for UOZ2+ Fez+ and Sc3+; 0.5~-(Na)C10 for Hg,2+ and Hg2+.For UOz2+ the temperature was 20". (a) H . Kakihana and L. G. Sillen Acta Chem. Scand. 1956 10 985. (b) F. J. C. Rossotti and H. S. Rossotti ibid. 1955 9 1177. (c) S. Ahrland S. Hietanen and L. G. SillCn ibid. 1954 8 1907. ( d ) Y . Marcus ibid. 1957 11 690. (e) W. Fording S. Hietanen and L. G. SillCn ibid. 1952 6 901. ( f ) R. S. Tobias ibid. 1958 12 198. (g) G. Biedermann M. Kilpatrick L. Pokras and L. G. Sillen ibid. 1956 10 1327. (h) G. Biedermann Arkiv Kemi 1956,9,277; Rec. Trav. chim. 1956 75 716. (i) Idem Arkzv Kemi 1953 5 441; Rec. Trav.chim. 1956 75 716. ( j ) A. Olin Acta Chem. Scand. 1957,11 1445; F. GranCr A. O h and L. G. SillCn ibid. 1956 10 476. (k) S. Hietanen and L. G. Sillen unpublished work. (I) S. Hietanen Acta Chem. Scand. 1956 10 1531; Rec. Trav. chim. 1956,75,711. to allow reliable conclusions about the species present and the equilibrium constants. Even if the e.m.f. method is perhaps the most versatile single method there is every reason to supplement it wherever possible by other equilibrium methods such as solubility and distribution studies and by spectral "finger-print" methods. With the last one may check the results obtained with e.m.f. data and also extend the measurements in the ranges where the accuracy of the e.m.f. data is unsuflicient. K z z = *pzz*Kl-z 2BOH+B,(OH)z. 168 QUARTERLY REVIEWS The structure of the polynuclear complexes formed on hydrolysis is of considerable interest Much remains to be done by diffraction work both on crystals and solutions.The equilibrium work gives only the dG of the reaction whereas it would be desirable to know the AH and AS components. It seems that the accuracy that may be obtained from the variation of equilibrium con- stants with temperature is rather low so an attack with calorimetric methods seems more promising. Acknowledgements. The research work described in the present Review has been supported in various ways by the Swedish Natural Science Research Council the Swedish Council of Technical Research and the Swedish Atomic Energy Commission. Recently very valuable support has been given by the Air Research and Development Command United States Air Force through its European Office.