4. Reaction principles and s-block Elements

Transcription

1 Chemistry 2810 Lecture otes Dr R T Boeré Page28 4 Reaction principles and s-block Elements 41 Lewis acids and bases Text: -A-L, Chapter Lewis acid/base theory The Arrhenius model required an acidic or basic species to posses ionizable or ions Br nsted-lowry theory requires only the transfer of a proton from an acid to a base, which broadens the available bases to include ammonia and other species that not have hydroxide groups Thus pyridine, alkyl amines and of course all the "bases" of living cells, eg the acid/base pairs of DA can be understood under this rubric But consider now the Lewis definition: A Lewis acid is any species possessing a vacant orbital capable of accepting an electron pair A Lewis base is any species capable of donating an electron pair into a vacant orbital in a Lewis acid Lewis thus extends the theory to include acids other than proton sources, breaking the second barrier to a broader definition of acidic and basic compounds owever, in doing so Lewis ignored the true uniqueness of the proton, which is the only cation which is a bare nucleus Although Lewis concept is genuinely useful, it has not completely replaced the Br nsted-lowry interpretation Thus typically when chemists refer to "acid" and "base" in ordinary parlance, they mean those species which fit the Br nsted-lowry definition When the Lewis definition is meant, we must specifically call the species "a Lewis acid" or a Lewis base ote that most Lewis bases are also Br nsted-lowry bases, though a good Lewis base can be a very poor Br nsted-lowry base, and vice versa owever only the ion is both a Lewis and a Br nsted-lowry acid 412 Examples of Lewis acids rom the definition of Lewis theory it will be clear that a full discussion of these reactions involves a detailed molecular orbital analysis from which the lone pair donor and empty acceptor orbitals can be obtained owever, in practice it is worth simply learning the types of ions and molecules that are Lewis acids and Lewis bases Just as in Br nsted-lowry theory some substances can be amphiprotic, some compounds are able to act as either Lewis acids or Lewis bases o special name is given to such compounds The Lewis of this theory is the same G Lewis that developed Lewis diagrams, and it should therefore come as no surprise that Lewis diagrams are an integral part of working with his theory of acids and bases Throughout this section we will use species for which you should be able to write out a Lewis diagram if required As we go on to survey the chemical compounds of the elements, you should always write out the Lewis diagrams of the molecules we discuss, and consider whether they may act as Lewis acids or as Lewis bases (If at the same time you remember to classify their point group symmetry, you will have a very effective running review of the main ideas in this course!) a) Electron-deficient compounds ome compounds are defined to be electron-deficient by Lewis theory, ie those for which the central atom cannot achieve a stable octet structure It is found in practice that such species readily react with Lewis bases (lone-pair sources) to give quite stable adducts ne common example of such electronically unsaturated molecules are the boron halides Thus for example consider the reaction of B 3 with ammonia, a common undergraduate experiment using a vacuum line to safely combine the two gaseous reagents The product is a stable white powder which may be handled in air In this reaction, shown below, the donor orbital is a lone pair on the and the acceptor is the empty p orbital left over in B 3 from the sp 2 hybridization at boron Generally you will not be identifying the nature of the acceptor orbitals, but in this case it is a well known bonding situation otice that the result is an ethane-like covalent bond between the and the B, and the bond has a reasonably high bond energy b) Coordinatively-unsaturated species B B Many inorganic molecules of the elements of the 3 rd period onward have large central atoms that can achieve high coordination numbers such as five, six and sometimes even seven These are said to be coordinatively unsaturated when the coordination number is not the maximum possible Consider the following three reactions which may be classified as reactions of the coordinatively-unsaturated acids P 5, Al 3, and b 5 The bases are thus, and 4 4 ote that the

2 Chemistry 2810 Lecture otes Dr R T Boeré Page29 latter, 4 4, has lone pairs on all the sulfur and nitrogen atoms nly a single lone pair from a atom is used in the interaction with the Lewis acid Also note that the second example is different in that the base is transferred from the acid Te 3 to the acid Al 3 urthermore, this reaction could just as well be classed with the electron deficient acids, since Al 3 is both electron deficient and coordinatively unsaturated - P P Al Te Al - Te b Another example of this general class of reaction is the catalysis step in riedel-crafts electrophilic aromatic substitution, where Lewis acids such as ebr 3 are employed to induce reaction of, for example, benzene with bromine: b ebr 3 Br Br ebr - 4 Br c) Metal cations: alkali or alkaline-earth elements Metal ions are extremely electron deficient, often having lost all their valence electrons when they ionize ot surprisingly, they are the largest single class of Lewis acids Much of the chemistry of metal ions involves their reaction with a wide variety of Lewis bases rganic chemists perform reactions involving active metals such as Li or a, eg BuLi or K t Bu, ether or T Why? Because these coordinating ether solvents can stabilize the metal ion in non-protic solvents Li Li complexed by oxygen lone pairs of tetrahydrofuran, a cyclic ether An even more powerful example of this kind of complexation is the use of crown ethers, such as dibenzo-18-crown-6 to solubilize all kinds of alkali salts in totally non-complexing solvents like benzene or hexanes The so-called cryptand ligands such as 2,2,2-crypt react with metal ions with greater selectivity than crown ethers, completely encasing the metals in an environment of multiple donor atoms dibenzo-{18}-crown-6 2,2,2-crypt

3 Chemistry 2810 Lecture otes Dr R T Boeré Page30 d) Metal cations: transition metal elements Consider the following reaction: Cu 2 (aq) 3? What explains the initial blue ppt? What about the purple solution? 1 Cu 2 (aq) - Cu() 2 (where the hydroxide comes from: ) 2 Cu() 2 excess 3 [Cu( 3 ) 4 ] 2 We call this last species, [Cu( 3 ) 4 ] 2, a complex ion It is a well-defined molecule built up from a Lewis acid cation and multiple Lewis base donor atoms, which are normally called ligands 413 ummary of basic concepts Lewis base, donor or ligand means much the same thing When transition metal adducts are considered, the term ligand is used most commonly The organic chemist would call most of these nucleophiles Lewis acid, acceptor or electrophile means much the same thing The resulting bonds are called coordinate covalent bonds, or dative bonds, in which both electrons are contributed by the Lewis base Many coordinate bonds are easily reversible, a measure T of the weakness of these bonds, which can be quite strong, but of the excellent leaving-group character of most Lewis bases ence there are many displacement reactions to consider The resulting compound is called a Lewis acid/base adduct, a coordination complex, a coordination compound, or a complex ion (if it is ionic) 414 ome reaction classifications It is important to be able to recognize different types of reactions using Lewis acids and bases, and one approach to this is to classify them by some common reaction types You have most likely already encountered some of these a) Adduct or Complex formation reactions The most fundamental reaction type, and one which occurs also in (b) and (c) is complex formation Consider again the first reaction we considered between ammonia and boron trifluoride: 3 B : 3 3 B 3 b) Displacement reactions These are reactions which involve the displacement of one Lewis base by another, such the reaction: Et 2 B 3 :(C 2 5 ) 3 Et 2 3 B (C 2 5 ) 3 In this case, the base trimethylamine displaces the base diethyl ether from the acid boron trifluoride It is therefore a base displacement reaction It is also possible for one acid to displace another acid from a common base, and these are called acid displacement reactions In both types of reaction, a previously formed adduct is broken down and replaced by a new adduct c) Metathesis or "double displacement" reactions When two Lewis acid/base adducts react and switch partners, the reaction is called a metathesis reaction There are many examples of such reactions The following is easily recognized as a metathesis reaction: 5 b: 2 (C 2 ) 2 Me 3 In:C b:c 5 5 Me 3 In: 2 (C 2 ) 2 The acids and bases involved, antimony pentachloride, dioxane, trimethyl indium and pyridine are listed in the table of Drago- Wayland parameters further along in these notes 42 ard/soft acid-base theory There are several reasons that the Lewis theory has not displaced the Br nsted-lowry model for protic acids ne of these is certainly that no acceptable way has been found to make the strength of a general Lewis acid quantitative It remains a largely qualitative theory Even when we try to qualitatively classify the strength of Lewis acids by comparing their reactions with a common base, we find that it is impossible to come up with a single scale that encompasses all possible Lewis acids ome Lewis acids (eg Al 3, B 3 ) act very much like when reacted with a base Thus for example we could use reactions with Al 3 to set up a scale of pk a 's very similar to that using But other Lewis acids, eg g 2, give an entirely different series of base strengths if the same procedure is followed for them The origin of this phenomenon is believed to lie in the fact that the origin of protic acid strength is primarily electrostatic But when all Lewis acids are considered, a pure

4 Chemistry 2810 Lecture otes Dr R T Boeré Page31 electrostatic model cannot be used Many species react with bases using a significant amount of covalent bonding, and these cannot be directly related to the others which are compatible with an electrostatic model In response to this discovery a simple, but extremely useful, qualitative scheme which divides Lewis acids and bases into two groups (along with a less-welldefined borderline category) has been developed This is called the Pearson hard-soft acid base, or AB, theory This model has found extensive application in the categorization of the chemical properties of the elements relative to their place in the periodic table, and is perhaps the single most important organizational scheme in use The origin of the AB scheme came from a consideration of the thermodynamic strength of the interaction of acids with halides The halide ions, -, -, Br -, I -, form adducts with most of the elements in the periodic table, and they are relatively simple monatomic ions They vary extensively in chemical properties, with being a small, dense ion with a highly focused negative charge, and I being a large diffuse ion, with a charge that is readily polarized This difference in polarizability is seen in terms of the relative order of reactivity of the Lewis acids with the halides Indeed, one finds two classes: "ass A" - ard acids - bond in the order I - > Br - > - >> - "ass B" - oft acids - bond in the order - >> - > Br - > I - The hard acids include and those acids that behave like : Al 3, B 3, Cr 3 etc This type of acid is found to prefer a whole range of bases as follows (stronger interaction): - >> - > Br - > I - R 2 >> R 2 R 3 >> R 3 P oft acids include g 2, Au, Pt 2, Cd 2, Pb 2 This type of metal ion prefers to bind to bases as follows (stronger interaction): I - > Br - > - >> - R 2 >> R 2 R 3 P >> R 3 The AB classification can be extended using the two groups of acids to group the bases into hard and soft categories as well, using the principle that hard acids tend to bind hard bases; soft acids tend to bind soft bases Thus -, R 2 : an R 3 : are harder bases; -, Br -, I -, R 2 and R 3 P are softer bases The bonding between hard acids and bases is dominated by electrostatic interactions This is shown by the fact that a strong interaction correlates with (1) small size and (2) high electronegativity of the base These are purely electrostatic parameters, and this implies that the bonding is essentially ionic The bonding between soft acids and bases seems to be primarily covalent in nature Thus a strong interaction occurs between large metal ions with high electronegativity (for example, Pt, Au and Pb, which have χ-values similar to that of boron and carbon) and the most polarizable bases The AB classification scheme is presented on the periodic table shown here ote that for some of the metals, different oxidation states belong to different groups The softest acids have the highest electronegativity of all the metals, while the softest bases have the lowest electronegativity of the non-metals Compare this table to the one featuring electronegativities of the elements that is given earlier in the notes Pearson ard and oft Acids and Bases LEWI BAE oft bases Borderline bases Li Be LEWI ACID B C ard a Mg ard acids Borderline acids Al i P Bases K Ca c Ti V Cr Mn e3 Co3 e2 Co2 Rb r Y Zr b Mo Tc Ru Rh3 Rh1 i Pd oft Cu1 Cu2 Ag Acids Zn Ga Ge As e Br oft Cd In3 In1 n4 n2 b Te I bases Cs Ba La- Lu r Ra Ac- Lr f Ta W Re s Ir3 ard acids Ir1 Pt Au g Tl Pb Bi Borderline acids La Ce Pr d Pm m Eu Gd Tb Dy o Er Tm Yb Lu Ac Th Pa U p Pu Am Cm Bk Cf Es m Md o Lr

5 Chemistry 2810 Lecture otes Dr R T Boeré Page ummary of the AB classification We can summarize the AB scheme by considering the properties of the hard and soft acids and base This is done in the following table Property ard Acid oft Acid oft Base ard Base χ ionic radius small large large small charge high low /A /A 422 Using AB theory to predict the course of reactions Consider the following chemical equilibria or each reaction, we can compare the AB character of the donor and acceptor atoms, and thus predict which adducts will have greater stability, using the principle that hard acids tend to bind hard bases; soft acids tend to bind soft bases This will usually allow us to predict whether the products or the reactants will be favored in each reaction ee that you can rationalize each prediction (ie by identifying the correct donor and acceptor atoms: b g b g (right) La 2 (C) 3 Tl 2 3 La 2 3 Tl 2 (C 3 ) 3 (left) 2 C 3 Mg g 2 (C 3 ) 2 g 3 Mg 2 (right) 423 Interpretation of the qualitative analysis scheme The Chemistry 2810 laboratory contains a small scale version of the qualitative analysis scheme for some representative cations from the periodic table This experiment is part of a classical analysis scheme developed by chemists of past generations to identify unknowns In commercial practice the qual-scheme, as it is affectionately known, has large been surpassed by automated analysis instrumentation But the scheme retains real value in teaching many of the chemical attributes of the elements, and for this reason we have retained it in the 2810 laboratory or background references on the qual scheme, you may consult the books by Wisner, Qualitative analysis and ionic equilibria, and ogness, Qualitative analysis and chemical equilibrium A flow chart is provided to indicate the separation scheme, and a rationale using AB and other principles is given for each separation The full qualitative analysis scheme for the element is presented in periodic table format below Group 1 The silver group Ag, g 2 2, Tl, Pb 2 These ions precipitate (as the chlorides) from 03 M solution Rationale: oftest acids react strongly enough with a borderline base to precipitate in acid solution Group 2 The copper group g 2, Bi 3, Cu 2, n 2, n 4 These ions precipitate as the sulfides from 03 M containing 2 Rationale: oft acids react with a very soft base Group 3 Zinc-aluminum group Zn 2, e 2, e 3, i 2, Cr 3, Al 3 These ions precipitate from an alkaline solution of 2 ome tend to form sulfides, some the hydroxides urther discrimination is possible, because e, Cr() 3 and Al() 3 will redissolve if the precipitate is layered with 10-2 M acid, but i and Zn will not Rationale (1): Zn, i, e as sulfides, ie borderline acids bind to a very soft base, when the p is adjusted so as to weaken the M( 2 ) m n hydrated cation A flow chart for the separation of cations in qualitative analysis olution containing ions of all cation groups olution containing ions of remaining groups 2 olution containing ions of remaining groups a olution containing ions of remaining groups a 2 C 3 olution contains ions of Group 5 (a, K, and 4 ) iltration iltration iltration iltration Group 1 precipitates Ag, g 2 2, Pb 2 Group 2 precipitates Cu, Cd, n, Bi 2 3 Group 3 precipitates Co, e, Mn, i, Zn, Al() 3, Cr() 3 Group 4 precipitates BaC 3, CaC 3, rc 3

6 Chemistry 2810 Lecture otes Dr R T Boeré Page33 Rationale (2): e() 3, Cr() 3, Al() 3 precipitate because these are hard acids reacting with the hard base - As acidic cations, they will tend to precipitate when the p is equal to the pk a These are all hard cation, and therefore prefer the hard base Group 4 Alkaline earths Ca 2, r 2, Ba 2 Precipitate from basic solution on the addition of C 3 2- in the form of sodium carbonate The carbonates are the insoluble products formed Rationale: These are weakly acidic (Br nsted definition) cations The carbonates are insoluble because of the favorable lattice energy when the weakly basic carbonate ion reacts with these cations, since the cation and anion are both doubly charged and similar in size Group 5 Alkali elements a, K and 4 These have soluble hydroxides and carbonates They do not precipitate from the qualitative analysis scheme Rationale: Lattice energy for carbonates is unfavorable, since the cations are small, and bear a 1 charge The hydroxides are soluble because the cations are non-basic, while hydroxide is strongly basic They are therefore likely to be soluble by the "cross-terms" rule Qualitative Analysis cheme for the Cations on-metals Li Be B C a Mg Group 3 Al i P K Ca c Ti V Cr Mn e Co i Cu d Rb r Y Zr b Mo Tc Ru Rh Pd Ag Cd In n Group Cs Ba La- f Ta W Re s Ir Pt Au g Tl Lu G R U P 5 r Ra Ac- Lr G R U P 4 Group 3 Group 2 Zn Ga Ge As e Br Group 1 b 2 Te Pb Bi Po La Ce Pr d Pm m Eu Gd Tb Dy o Er Tm Yb Lu Ac Th Pa U p Pu Am Cm Bk Cf Es m Md o Lr I 424 Goldschmidt classification of minerals As a final example of the use of AB theory we will briefly consider its application to Geology Goldschmidt independently developed his own scheme for the mineralogical classification of the elements ote however how closely his categories match the predicted ard-soft acid-base properties discussed above The common minerals of the elements as found on earth have been classified by Goldschmidt as follows: iderophiles: elements which are alloyed with the molten iron in the core, including i, Co, Pd, Pt, Rh and Ir Chalcophiles: found predominantly in sulfide ores Lithophiles: found in nature as parts of alumino-silicate minerals (ie as cations towards complex i y- w- x and Al z anions) Most rocks are minerals of this type Atmophiles: found in nature as gases AB theory rationalizes the middle two categories: the soft acid metals preferentially form sulfide minerals; the hard acid metals prefer the oxygen donors in aluminosilicates Goldschmidt's classification of the elements Eric Reardon Department of Earth ciences University of Waterloo Waterloo 2L 3GI (This article is reprinted from What on Earth, published by the Department of Earth ciences at the University of Waterloo)

7 Chemistry 2810 Lecture otes Dr R T Boeré Page34 Within the first two weeks of an introductory geochemistry course, a student usually learns the meaning of the words 'lithophile', 'siderophile', 'chalcophile', and 'atmophile' These terms were introduced in the early 1920s by a remarkable scientist is name was V M Goldschmidt and it was his way of classifying the elements according to their affinities (philos, a Greek word for love) for various earth materials Thus a siderophile element would be one with an affinity for iron metal Before discussing this classification scheme in detail, let's learn more about its developer Victor Moritz Goldschmidt was born in Zurich, 1888 By the time his family moved to slo when he was thirteen, he had also lived in Amsterdam and eidelburg The move to slo was so that his father could take up the Chair of Chemistry at what is now the University of slo Up until 1905, slo was part of weden and called 'Kristiania' rom his own interest in Earth ciences and likely because of his father's chemistry influence on him, Goldschmidt carved out a research area that fused together both of these disciplines Even though the word 'Geochemistry' was coined a century earlier by C honbein, another wiss-born chemist and inventor of gun cotton, most geochemists today recognize Goldschmidt as the ounder of this modern field of Earth ciences Goldschmidt completed his PhD thesis in 1911 at the age of 23; was appointed Director of the Mineralogic Institute of the University of slo three years later; and at the age of 29, was appointed Chair of the orwegian government's Commission on Raw Materials as well as the Director of its laboratory This meteoric rise to prominence within the orwegian scientific community simply reflected Goldschmidt's unbounded passion, ability and prodigiousness in his research discipline Goldschmidt made many important scientific contributions during his lifetime Perhaps the most important was in providing an understanding of the geochemical behaviour of rare earth elements and the factors which control their distribution in mineral phases during magma crystallisation It was Goldschmidt who first estimated the ionic sizes of the rare earth elements and discovered the somewhat paradoxical decrease in their ionic size with increasing atomic number - the now familiar 'Lanthanide Contraction', a term which he coined owever, as intimated in the opening line of this article, the most noted of Goldschmidt's contributions was his division of the periodic table into siderophile (iron-loving), lithophile (rock-loving), chalcophile (chalco indicates copper but Goldschmidt wanted to imply sulphur-loving), and atmophile (atmosphere-loving) elements This classification scheme, first suggested by Goldschmidt in 1922, is illustrated in the accompanying periodic table It represents the results of careful study of the elemental compositions of phases within two seemingly dissimilar materials: meteorites and sulphide ore smelting products 1 Geochemical classification of the elements 18 based on the ideas of Goldschmidt e Li Be B C e a Mg Al i P Ar K Ca c Ti V Cr Mn e Co i Cu Zn Ga Ge As e Br Kr Rb r Y Zr b Mo Ru Rh Pd Ag Cd In n b Te I Xe Cs Ba La- Lu r Ra Ac- Lr f Ta W Re s Ir Pt Au g Tl Pb Bi Po At Rn (ote: cells without entries are elements that are not naturally occurring) Lanthanides La Ce Pr d m Eu Gd Tb Dy o Er Tm Yb Lu Actinides Th U LEGED El iderophile El Chalcophile El Lithophile El Atmophile In most meteorites, there are three principle phases present: an iron-nickel metal alloy, a troilite or iron sulphide phase, and a silicate phase The silicate phase has a mineral assemblage that closely resembles mafic igneous rock on earth In some meteorites, there is evidence that all three phases originally existed as immiscible liquids at a higher temperature Goldschmidt thus reasoned that an analysis of these phases should indicate the relative preference of these phases for individual elements, which would provide a general basis for classifying elements Goldschmidt also had recourse to a large amount of analytical data on solid material produced from the smelting of the copper shale ore (Kupferschiefer) at Mansfeld, Germany During the smelting operation, three immiscible liquids develop and solidify: the iron melt; the copper sulphide matte; and the silicate slag Detailed analyses of the composition of these materials by Goldschmidt, and also by Ida and Walter oddack from Berlin, confirmed the similar affinities of meteorite and smelter product phases for a wide range of elements

8 Chemistry 2810 Lecture otes Dr R T Boeré Page35 Goldschmidt had a modern view of meteorites e considered them derived from the asteroid belt and represented material that had failed to coalesce into a planet, rather than as material produced from the breakup of a larger planet The close association of iron, sulphur and silicate phases in meteorites, unlike any terrestrial rock, was clear evidence to him of this e ascribed the fact that similar rocks are not found on Earth to a period of heating, partial melting, and elemental fractionation that occurred soon after the Earth was formed e envisioned the Earth to be originally composed of meteoritic material with a uniform composition eating would first result in the melting and sinking of the lowest melting point and highest density phase (iron-nickel alloy) This process formed the core of the earth With continued heating, the sulphide phase would melt and sink Thus a sulphide layer would mantle the core, leaving behind a residual outer silicate layer (slag) Today, there is no geophysical evidence for a sulphide layer as Goldschmidt proposed At the time, he overestimated the abundance of sulphur in his conjectured primordial Earth material Evidently, the actual lower amounts of sulphur present were easily accommodated in the iron and silicate phases during heating, such that a separate immiscible sulphide phase did not form Interpretation of Goldschmidt's classification scheme is straightforward Given a system where all three melts are in equilibrium (ie, molten e-i, sulphide and silica magma), a lithophile element, such as potassium, will be in highest concentration in the silica magma; a siderophile element, on the other hand, such as one of the precious metals - platinum, palladium or gold - will be most enriched in the e-i melt We would thus expect metals in the core of the earth The strong clustering of elements with particular affinity that is evident in the accompanying table is no coincidence It merely reflects an element's bonding characteristics and thus its electron configuration iderophile elements are mostly confined to Groups 8-10 of the periodic table - elements characterised by a mostly complete outer d electron shell and by this shell's strong attraction for any outer s electrons This makes the outer bonding shell of electrons of these elements generally unavailable for any type of bonding except metallic Lithophile elements tends to have an outer bonding shell that contains s and/or p subshells, but no d, whereas the outer bonding shell of chalcophile elements contains a d subshell As with all attempts to divide up a continuum of behaviour into several simple categories, there will be exceptions, crossovers and examples of dual behaviour The chief property not factored into Goldschmidts classification is elemental valence e was aware that many elements can occur in two or more valence states and when they do, they may exhibit different affinities or example, in reducing environments Cr3 is strongly chalcophile, whereas under oxidizing conditions Cr6 is distinctly lithophile Another example is that phosphorus has an affinity for iron metal only in the reduced form In the oxidized form it has lithophile character and occurs as phosphates in crustal rocks Different valence forms of the same element can behave chemically as differently as different elements Although not shown in the periodic table in this article, Goldschmidt indicated the elements with such secondary affinities Anyone interested in reading other treatments of this topic can consult any of the following references There is also a very informative writeup of the life and accomplishments of Goldschmidt by K Wedepohl or example, you can find out about his 1942 arrest in occupied orway and his rescue by the orwegian resistance This can be accessed on the Internet at: http-ilwwwuni-geochemgwdgdeldocsleascilvmgoldshtm References 1 Brownlow, Geochemistry, Prentice-all, Inc, ew Jersey, aure, Principles and Applications of Inorganic Geochemistry, MacMillian Publishing Co, ew York, Goldschmidt, Geochemistry, A Muir, ed, xford University Press, London, Mason and C B Moore, Principles of Geochemistry, 4th ed, John Wiley & ons, Inc, ew York, Wedepohl, Geochimica et Cosmochimica Acta, volume 59, 1217 (1995)