23327709-dk1288-ch03

3Complexation of Metal IonsGREGORY R. CHOPPIN* Florida State University, Tallahassee, Florida,U.S.A.

3.1 METAL ION COMPLEXATION

Chapter 2 discussed the various forms of interaction between solute and thesolvent molecules (see section 2.3), which leads to a certain solubility of thesolute in the solvent phase. It was also described how the ratio of the solubilityof the solute between two immiscible solvents could be used to estimate distri-bution ratios (or constants) for the solute in the particular system (see section2.4). It was also pointed out that in the case of aqueous solute electrolytes,specific consideration had to be applied to the activity of the solute in the aque-ous phase, a consideration that also was extended to solutes in organic solvents.

However, in many solvent extraction systems, one of the two liquids be-tween which the solute distributes is an aqueous solution that contains one ormore electrolytes, consisting of positive and negative ions that may interact witheach other to form complexes with properties quite different from the ions fromwhich they are formed. Such complexation is important to the relative extractiveproperties of different metals and can provide a sufficient difference in extract-ability to allow separation of the metals.

In this chapter, the factors underlying the strength of metalligand interac-tion are reviewed. An understanding of how these factors work for differentmetals and different ligands in the aqueous and in the organic phases can be ofmajor value in choosing new extraction systems of greater promise for possibleimprovement in the separation of metals. The discussion in this chapter buildson the principles of solubility of Chapter 2 and provides additional theoretical

*Retired.

Copyright 2004 by Taylor & Francis Group, LLC

background for the material in the chapters that deal with the distribution equi-libria, kinetics, and practices of solvent extraction systems.

3.1.1 Stability Constants

The extent of metal ion complexation for any metalligand system is definedby the equilibrium constant that is termed the stability constant (or formationconstant) metalligand interaction. The term metal in metalligand systemssimply refers to the central metal ion (or cation), and the term ligand (fromLatin ligare, to bind) to the negative ion (anion) or to a neutral electron donormolecule, which binds to the central atom. Since most ligands bind to the metalion in a regular sequence, equilibria are established for the formation of 1:1, 1:2,1:3, etc., metal-to-ligand ratios. In some systems, polynuclear (i.e., polymetal)complexes such as 2:1, 2:2, 3:2, etc., form. In this chapter, the primary concernis with the more common mononuclear complexes in which a single metal atomhas one or more ligands bonded to it. These relatively simple complexes canserve to illustrate the principles and correlations of metal ion complexation thatapply also to the polynuclear species. Defining M as the metal and L as theligand (with charges omitted to keep the equations simpler), the successive com-plexation reactions can be written as:

M L ML

ML L ML

+ =+ =

( . )

( . )

3 1

3 12

a

b

Or, generally,

ML L MLn n + =i c( . )3 1

The equilibrium constants for these stepwise reactions are expressed generallyas Kn:

K ML ML Ln n n= [ ] /[ ][ ] ( . )1 3 2a

Sometimes a complexation reaction is considered to occur between M and anacidic ligand HL

M HL ML H+ = + ( . )3 1d

in which case the protonated stepwise formation constant is

* [ ][ ]/[ ][ ] ( . )K ML H M HLn = 3 2b

It is common to use the overall stability constant, pqr, where p = number ofmetal, q = number of hydrogens (for protonated species), and r = number ofligands. The value of q is negative for hydroxo species. For the reaction to formML,

M L ML ML M L K+ = = =; [ ] /[ ][ ] ( . )101 1 3 3


However, the formation of multiligand complexes is more complex: e.g.;

M L ML ML M L K K K+ + = =3 3 43 103 33

1 2 3; [ ] / [ ][ ] . ( . )

This can be generalized as:

M nL ML ML M L Kn n n ii

n

+ = = ==

; [ ] /[ ][ ] ( . )101

3 5n

The pqr is sometimes referred to as the complexity constant.Some ligands retain an ionizable proton. For example, depending on the

pH of the solution, metals may complex with HSO4 , SO24 or both. In the forma-

tion of MHSO4, the stability constant may be written as:

M M K M M+ = =HSO HSO HSO HSO a4 4 4 4; [ ] /[ ][ ] ( . )1 3 6

or

M M M M+ + = =H SO HSO HSO H][SO b4 4 4 4; [ ] /[ ][ ] ( . )111 3 6

where

111 111 2= K Ka/

and Ka2 is the dissociation acid constant for HSO4. Alternately, some complexes

are hydrolyzed and have one or more hydroxo ligands. For such complexes,usually in neutral or basic solutions, the reaction may be represented as:

M L M L+ + = +H O OH) H a2 ( ( . )3 7

and

1 11 3 7 = [ ( ]/[ ][ [ ] ( . )M L M LOH) H] b-1

or

* [ ( ][ ( . )111 3 7= M L M LOH) H] / [ ][ ] c

In general, we use n to represent 10n in this text.

3.1.2 Use of Stability Constants

If the concentration [L] of free (uncomplexed, unprotonated, etc.) ligand atequilibrium can be measured by spectrometry, a selective ion electrode, or someother method, the stability constant can provide direct insight into the relativeconcentrations of the species. This is achieved by rewriting Eq. (3.5) in theform:

[ ] /[ ] [ ] ( . )ML M Ln nn= 3 7d

For example, if 1 = 102 and [L] = 102 M, there are equal concentrations of Mand ML in the solution since 1 [L] = 102 102 = 1. This relationship is indepen-


dent of the amount of metal in the solution and the equality [M] = [ML] = 1 isvalid whether the total metal concentration is 109 M or is 1M as long as thefree ligand concentration [L] = 0.01M. For example, if the ligand is present onlyas L and ML, and if the total metal concentration, [M] + [ML], is 109 M, the totalligand concentration is [L] + ML = 0.01 + 0.5 109 = 0.01 M. However, if thetotal metal is 1.00 M and [M] = [ML], the total ligand is 0.01 + 0.50 = 0.51 M.

Consider a system in which 1 = 102, 2 = 103 and 3 = 2 103. The con-centrations of each complex can be calculated relative to that of the free (un-complexed) metal for any free ligand concentration. If [L] = 0.1 M,

[ ] /[ ] [ ]

[ ] /[ ] [ ]

[

ML M L

ML M L

M

= = =

= = =

1

2 1

2 22 3 2

10 10 10

10 10 10

LL M L3 33 3 32 10 10 2] /[ ] [ ]= = =

Thus, abbreviating the total metal concentration [MLn] = [MT], and definingthe mole fraction of each metal species (i.e., of M, ML, ML2, and ML3) asthe ratio of the concentration of that species to the total metal concentration byKML,i = [MLi]/[MT], then

K

K

K

M

ML

ML

= + + + == + + + == + +

1 1 10 10 2 0 43

10 1 10 10 2 0 43

10 1 10 1

/( ) .

/( ) .

/( 00 2 0 43

2 1 10 10 2 0 087

+ == + + + =

) .

/( ) .KML

Such calculations can be done for a series of free ligand concentrations togenerate a family of formation curves of concentration or mole fraction of metalcomplex species as a function of the concentration of the free ligand. Such curvesare shown in Figs. 3.1 and 3.2. These calculations are particularly useful for tracelevel values of metal as they require only knowledge of the free ligand concentra-tions and the n. Values of stability constants can be found in Refs. [1,2].

3.1.3 Stability Constants and Thermodynamics

The examples in section 3.1.2 of calculations using stability constants involveconcentrations of M, L, and MLn. Rigorously, a stability constant, as any thermo-dynamic equilibrium constant should be defined in terms of standard state con-ditions (see section 2.4). When the system has the properties of the standardstate conditions, the concentrations of the different species are equal to theiractivities. However, the standard state conditions relate to the ideal states de-scribed in Chapter 2, which can almost never be realized experimentally forsolutions of electrolytes, particularly with water as the solvent. For any condi-tions other than those of the standard state, the activities and concentrations arerelated by the activity coefficients as described in Chapter 2, and especially


Fig. 3.1 Formation curves of the fraction of Cd(II), Xi, in the species Cd(NH3)2i+, where

i = 0 to 4, as a function of the uncomplexed concentration of NH3.

as discussed in Chapter 6. Thus, for the thermodynamic constant, K 1, for thereaction

M L ML+ =one obtains

Ka

a a

ML y

M y L y

ML y

M L y yy y yML

M L

ML

M L

ML

M LML M L = = = = = 1 1 1 3 8

[ ]

[ ] [ ]

[ ]

[ ][ ]/ ( . )

Sometimes the activities are replaced by braces, e.g., aML = {ML}; here we preferthe former formality. The estimation of yi values by equations such as Eqs.(2.38) and (2.43) is unreliable for ionic strengths above about 0.5 M for univa-lent cations and anions and at even lower ionic strengths for polyvalent species.Consequently, values of i are rarely calculated, except for very exact purposes(see Chapter 6). Instead, measurements of equilibrium concentrations of thespecies involved in the reaction are used in a medium of fixed ionic strengthwhere the ionic strength, I, is defined as I = 12 ci z2i M [see Eq. (2.38)]. Asolution of fully ionized CaCl2 of 0.5 M concentration has an ionic strength I =12 0.5 22 + 2 0.5 (1)2 or 1.5 M. Stability constants are reported, then,as measured in solutions of 0.1 M, 0.5 M, 2.0 M, etc., ionic strength. In practice,


Fig. 3.2 Formation curves of the fraction of Eu(III), Xi, in the species Eu(OAc)i3i,

where i = 0 to 4, as a function of the uncomplexed acetate anion concentration.

the concentrations of the complexing metal and ligand may be so low (e.g., 0.01M) that if an inert (i.e., noncomplexing) electrolyte is added at higherconcentration (e.g., 1.00 M), it can be assumed that the ionic strength remainsconstant during the reaction. However, such a practice, referred to as a constantionic medium, is not always possible if the complexation is so weak that rela-tively high concentrations of metal and ligand are required.

Consider the complexation of a trivalent metal by a dinegative anion. As-sume M(ClO4)3 is 0.01 M and Na2SO4 is 0.05 M. To obtain an ionic strength of1.00 M, if no complexation occurs, requires a concentration of NaClO4 calcu-lated to be:

[ ] . / . ( ) . ( ) . ( )

. ( ) . . .

NaClO

M

4 = + +

+ = =

1 00 1 2 0 01 3 3 0 01 1 2 0 05 1

0 05 2 1 00 0 21 0 79

2 2 2

2

If all the M3+ is complexed,

[ ] .

] . . .

] . .

MSO M,

[SO M

[Na M,

[

4+

42

+

-

=

= =

= =

0 01

0 05 0 1 0 4

2 0 05 0 10

CClO M and

[NaClO4

4

- ] . .

] .

= ==3 0 01 0 3

0 79


The ionic strength would be:

I = + + +

+ + =

1 2 0 01 1 0 04 2 0 10 0 79 1

0 03 0 79 1 0 94

2 2 2

2

/ . ( ) . ( ) ( . . )( )

( . . )( ) . M

Therefore, a 6% error in the ionic strength arises from not adding additionalNaClO4 during the measurement of the stability constant. Such a change in theionic strength might result in significant changes in the yi values of Eq. (3.8). Ifthe ionic strength is maintained constant during the measurement, Eq. (2.43)indicates that the values of yi should remain constant. Thus, Eq. (3.8) can bewritten for constant ionic strength as:

= = n n ML M Ln ny y y C/ ( . )3 9Since C has a particular value for each value of ionic strength, I, the n valuescan only be used for solutions of that value of I. In fact, the problem can beeven more complicated. Equation (2.43) implies that yi is determined by thevalue of I and is not dependent on the electrolyte used to obtain the ionicstrength. For example, values have been measured in solutions with KNO3 asthe added inert electrolyte while other experimenters have used NaClO4, LiCl,NaCl, etc. In I 0.1 M solutions, the differences in values from these differentsolutions are small but when the ionic strength increases above 0.1 M, signifi-cant differences may arise. Therefore, both I, the ionic strength, and the salt thatis used to set the ionic strength should be specified for values. For furtherdetails see Chapter 6 and Ref. [3].

3.2 FACTORS IN STABILITY CONSTANTS

Many factors play a role in establishing the value of the stability constants of aparticular metalligand system. J. Bjerrum [4] considered such factors and theireffect on the successive stability constants. The ratio of two stepwise constantsis defined as:

log K K T Tn n n n/ / ( . )+ +=1 1 3 10

Bjerrum divided this Tn,n+1 value into two terms: Sn,n+1, which accounts for statis-tical effects and Ln,n+1, which accounts for all effects attributable to the nature ofthe ligand, including electrostatic effects.

3.2.1 Statistical Effect

When simply hydrated, the number of water molecules bonded to the metal(central) ion correspond to a value N, the coordination number, which is alsotermed the hydration number. In complexation, ligands displace the hydratewaters, although not necessarily on a 1:1 basis. Charge, steric, and other effectsmay cause the maximum number of ligands to be less than N. For example, in


aqueous solutions Co2+ is an octahedral hexahydrate, Co(H2O)26

+, but complexeswith chloride to form the tetrahedral species CoCl24

. Trivalent actinides havelarge hydration numbersusually 8 or 9but may form complexes with N 0.73

configuration (square planar) is associated with complexes with more covalentnature than the tetrahedral complexes of sp3 configuration. However, neutralligands such as H2O and NH3 can form octahedral structures Ni(H2O)

26

+ andNi(NH3)

26

+. Figure 3.8 shows examples of these geometric structures.In summary, the geometry of transition metal complexes is determined by

the necessity (1) to group the ligands about the metal to minimize electrostaticrepulsions and (2) to allow overlap of the metal and ligand orbitals. The first

Fig. 3.7 Common stereochemistries of the elements. (After Ref. 4.)


Fig. 3.8 Geometric structures of tetrahedral NiCl24, planar Ni(CN)24

and octahedralNi(H2O)

26

+.

requirement favors a tetrahedral configuration for coordination number 4, as theligands are farther apart than in the square planar geometry. However, if overlapof orbitals is a stronger requirement, and a d orbital can be included in thehybridization, the dsp2 square planar geometry gives the more stable complex.In the octahedral complexes of coordination number 6, secondary structural ef-fects can be observed that can be attributed to differences in the electron distri-bution among the metal d orbitals. Such effect can be deduced from Fig. 3.9 forthe divalent transition metals. The metal ion radius would be expected to de-crease smoothly between Mn2+ and Zn2+, resulting in a regular increase in logas shown by the dashed lines connecting the Mn2+ and Zn2+ values for 103(en).However, the electrostatic field of the ligand anions (or ligand dipoles) causesan asymmetric pattern of electron distribution in the d orbitals of the metals,which results in increased stability of the complexes. Mn2+ with five electronsin d orbitals has a half-filled set of 3d orbitals while Zn2+ with 10 d electronshas a completely filled set of 3d orbitals. Neither of these configurations allowsasymmetric distribution, so no extra complex stability is present. The increased


Fig. 3.9 Variation of log 101 for complexation by ammonia (NH3) and ethylenediamine(en) of some first-row divalent transition metal. The electron occupations of the 3d orbit-als are listed for each metal.

complex stability between Mn and Zn due to the asymetric electron distributionis known as ligand field stabilization and is a maximum for metals with d3 andd8 configurations.

Notice in Fig. 3.9 that the expected maximum at the d8 configuration(Ni2+) is not present inasmuch as the d9(Cu2+) complexes are more stable. Thisextra stability is due to the JahnTeller effect by which d9 systems have excep-tional stability when only two or four of the six coordinate sites of the metal


are occupied by the ligand. These sites are in the square plane of the octahedron.A loss of this extra stabilization is shown for Cu(en)23

+ formation when the threeethylenediamine (a bidentate ligand) molecules occupy all six coordination sites.As expected, the ligand field stabilization (the difference between log 103 andthe dashed line between Mn2+ and Zn2+) is greater for Ni(en)23

+ than for Cu(en)23+.

3.2.4 The Chelate Effect

Figure 3.9 also reflects the chelate effect. Ligands that can bind to a metal inmore than one site are said to form chelates. If a ligand binds in two sites, it istermed bidentate, if three, terdentate, etc. Ethylenediamine, H2NC2H4NH2,(often abbreviated en) is a bidentate ligand inasmuch as it can bind through thetwo nitrogen atoms; see Fig. 3.10. Ethylenediaminetetraacetate (EDTA) is ahexadentate ligand [(OOCCH2)2 NC2H4N(CH2COO)2]

4 binding through twonitrogens and an oxygen of each of the 4 carboxylate groups.

Chelates are commonly stronger than analogous, nonchelate complexes.Ammonia and ethylenediamine both bind via nitrogen atoms and log 2 forM(NH3)

22

+ formation can be compared with log 1 for M(en)2+ formation whilelog 4 for M(NH3)24+ and log 2 for M(en)22+ can be similarly compared, to ascer-tain the stabilizing effect of chelate formation. In Fig. 3.9, the curves forCu(NH3)

22

+ and Cu(en)2+ are roughly parallel, with Cu(en)2+ being more stableby about 2 units of log . The increase in stability for double chelation is seento be almost 6 units from the values of log 104 for Cu(NH3)24+ and log 102 forCu(en)22

+. The extra JahnTeller stabilization for Cu2+ complexation is roughlyindependent of whether the complex is a chelate or not.

Chelate complexes are very useful in many solvent extraction systems.Most often, chelating ligands are organic compounds that provide the possibilityof solubility in the organic phase. When a metal ion forms an octahedral com-plex with three bidentate organic ligands, it is surrounded by an outer skin oforganic structure that favors solubility in an organic solvent, and, hence, extrac-tion from the aqueous phase.

Fig. 3.10 Structures of Cd(NH3)24

+ and Cd(en)22+.


3.3 MODELS OF COMPLEX FORMATION

3.3.1 Early Models

A. Werner had clarified many of the structural aspects of complexes, includingchelates, in the early part of this century. A further major advance in developinga theory of how and why metal ions form complexes was made by N. V. Sidg-wick in 1927. He noted that the number of ligands that bond to a metal ioncould be explained by assuming the metal ion accepted an electron pair fromeach ligand until the metal ion completed a stable electronic configuration. Hecalled the metal the acceptor and the ligand the donor. A few years earlier,G. N. Lewis had introduced a generalized acid-base theory in which the basicsubstance furnishes a pair of electrons for chemical bond; the acid substanceaccepts such a pair [6]. Combining these views, the acceptor (metal) becomesan acid and the donor (ligand) is a base. In these models, complexation wasone class of the general acid-base reactions.

In the 1950s it was recognized that metal cations could be divided intotwo general classes. The first, or class a, cations behaved like H+ and theirstability constants in aqueous solution had the order:

F Cl>Br>I

O S>Se>Te

>>>>

The second, or class b, cations had stability constants that followed the reversesequence: i.e.,

I Br > Cl > F

Te Se S O

>>>>~ ~

Complexes of class a metals are more ionic, while those of the class bmetals are more covalent. Generally, the metals that form tetrahedral complexesby using sp3 hybrid orbitals are class a types. Those forming square planarcomplexes by using dsp2 hybrid orbitals are normally class b types.

3.3.2 Hard/Soft Acids and Bases (HSAB)

A popular model for predicting whether a metal and a ligand are likely to reactstrongly or not is the hard-soft acid-base principle [7]. In general, hard acidsare cations that are in the class a group and the log of their stability constantsshows a correlation with the pKa of the ligand base of the complex. Soft acidsare usually in class b and their log values correlate with the redox potential,E, or the ionization potential, IP, of the ligand base. Ligands that are hard basestend to have higher pKa values, while soft bases have large E or IP values. Theimportant HSAB principle states that hard acids react strongly with hard basesand soft acids react strongly with soft bases. This is only a general principle, as


some hard acid/hard base pairs do not interact strongly and neither do someof the soft acid/soft base pairs. The exceptions to the general rule have fac-tors other than inherent acidity and/or basicity, which are more important inthe interaction. Nevertheless, the HSAB principle has proven a very usefulmodel for a large variety of complexation reactions, partially because of itssimplicity.

Commonly, soft acids have low-lying acceptor levels while soft baseshave high-lying donor orbitals. As a consequence, the bond in the complexresults from sharing the electron pair. Softness is thus associated with a tendencyto covalency and soft species generally have large polarizabilities. In hard(metal) acids, the acceptor levels are high and in hard bases, the donor levelsare low. The large energy difference is so large that the cation acid cannot sharethe electron pair of the base. The lack of such covalent sharing results in astrongly electrostatic bond.

The principal features of these species can be listed as follows:

1. Hard species: difficult to oxidize (bases) or reduce (acids); low polarizabili-ties; small radii; higher oxidation states (acids); high pKa (bases); morepositive (acids) or more negative (bases) electronegativities; high chargedensities at acceptor (acid) or donor (base) sites.

2. Soft species: easy to oxidize (bases) or reduce (acids); high polarizability;large radii; small differences in electronegativities between the acceptor anddonor atoms; low charge densities at acceptor and donor sites; often havelow-lying empty orbitals (bases); often have a number of d electrons (acids).

Following these guidelines, cations of the same metal would be softer for loweroxidation states, harder for higher ones. In fact, Cu+ and Tl+ are soft while Cu2+

is borderline and Tl3+ is hard. Even though Cs+ has a large radius and lowcharge density, the low ionization potential is sufficient to give it hard acidcharacteristics. This illustrates that the properties listed may not be possessedby all hard (or soft) species, but can serve as guides as to what characteristicscan be used to predict the acid-base nature of species.

3.3.3 Qualitative Use of Acid-Base Model

Using these properties, a number of species have been placed in the hard, soft,or borderline categories in Table 3.2. This table can be used to predict, at leastqualitatively, the strength of complexation as measured by the stability con-stants. For example, Pu4+ is a hard acid, F, a hard base, and I, a soft base. Thisleads to the prediction that log 1(PuF3+) would be larger than log 1(PuI3+); theexperimental log 1 values are 6.8 and

Table 3.2 Partial List of Hard and Soft Acids and Bases

A. Acids:Hard

+1 ions H+, Li to Cs+2 ions Mg to Ba, Fe(II), Co, Mn+3 ions Fe(III), Cr(III), Ga, In, Sc, all Ln (III), all actinides (III)+4 ions Ti, Zr, Hf, all actinides (IV)y1 ions Cr (VI), VO, MoO3, AnO2, Mn(VII)

Borderline +2 ions Fe, Co, Ni, Cu, Zn, Sn, Pb+3 ions Sb, Bi, Rh, Ir, Ru, Os, R3C+, C6H5+

Soft BH3+1 ions Cu, Ag, Au, Hg, CH3Hg, l+2 ions Cd, Hg, Pd, Pt

B. Bases:Hard H2O, ROH, NH3, RNH2, N2H4, R2O, R3PO, (RO)3PO,

1 ions OH, RO, RCO2, NO3, ClO4, F, Cl,2 ions O, R(CO2)2, CO3, SO43 ions PO4

Borderline C6H5NH2, C5H5N1 ions N3, NO2, Br2 ions SO3,

Soft C2H4, C6H6, CO, R3P(RO)3P, R3As, R2S1 ions H, CN, SCN, RS, I.2 ions S2O3

Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ are borderline, and, therefore, their complexingtrends are less easily predicted. For F, we find the order of log 1 to be

Cu Zn Fe Mn Ni Co> > > >whereas for thiocyanate, SCN, it is

Cu Ni Co Fe Zn Mn>> > > > >For borderline metals and/or borderline ligands, the order is determined by otherfactors such as dehydration (removal of hydrate water), steric effects, etc.

Table 3.3 shows some stability constants for hard and soft types of metalligand complexes. The constants are experimental values [1,2] and, as such,contain some uncertainties. Nevertheless they support well the HSAB principle.

The HSAB principle is useful in solvent extraction, as it provides a guideto choosing ligands that react strongly (high log ) to give extractable com-plexes. For example, the actinide elements would be expected to, and do, com-plex strongly with the -diketonates, R3CCOCH2COCR3 (where R = H


Table 3.3 Stability Constants for Hard and Soft Types of Metal Complexesand Halide Ions

Hard type ion: In3+ Soft type ion: Hg2+

Liganda log K1 log K2 log K3 log K4 log K1 log K2 log K3 log K4

F (hardest) 3.70 2.56 2.34 1.10 1.03Cl 2.20 1.36 6.74 6.48 0.85 1.00Br 1.93 0.67 9.05 8.28 2.41 1.26I (softest) 1.00 1.26 12.87 10.95 3.78 2.23

aFor In3+ the ionic medium is 1M NaClO4 + F, Cl, and Br, and 2M NaClO4 + I. For Hg2+

the ionic medium is 0.5M Na(X,ClO4).

or an organic group), as the bonding is through the oxygens (hard base sites) ofthe enolate isomer anion. The formation of a chelate structure by the metalenolate complex results in a relatively strong complex, and if the R groups onthe -diketonates are hydrophobic, the complex would be expected to have goodsolubility in organic solvents. In fact, many -diketonate complexes show excel-lent solvent extraction properties.

The solvent extraction of the -diketonate system can be used to illustratethe importance of the high coordination numbers of the actinides and lanthan-ides (see section 3.2) in which hydrophobic adducts are involved. The chargeon a trivalent actinide or lanthanide cation is satisfied by three -diketonateligands (each is 1). However, the three -diketonate ligands would occupyonly six coordination sites of the metal while the coordination number of thesemetal cations can be 8 or 9. Thus, the neutral ML3 species can coordinate otherligand bases. The alkyl phosphates, (RO)3PO, are neutral hard bases that reactwith the ML3 species to form ML3Sn (n = 1 to 3). Tributyl phosphate is widelyused as such a neutral adduct-forming ligand of actinides and provides en-hanced extraction as the ML3Sn species is more hydrophobic than the hydratedML3 and, thus, more soluble in the organic phase. However, the role of coordina-tion sphere saturation by hydrophobic adducts is not limited to synergic systems.In the Purex process for processing irradiated nuclear fuel, uranium and pluto-nium are extracted from nitric acid solution into kerosene as UO2(NO3)2 (TBP)2and Pu(NO3)4 (TBP)2. In these compounds the nitrate can be bidentate and sofills four or fewer of the coordinate sites for the uranium and eight or fewer forthe plutonium. Uranium (U) in UO22

+ usually has a maximum coordination num-ber of 6, while that of Pu4+ can be 9 or even 10. The addition of the two TBPadduct molecules in each case causes the compound to be soluble and extract-able in the kerosene solvent.


3.3.4 Quantitative Models of Acid-Base Reaction

The major disadvantage of the HSAB principle is its qualitative nature. Severalmodels of acid-base reactions have been developed on a quantitative basis andhave application to solvent extraction. Once such model uses donor numbers[8], which were proposed to correlate the effect of an adduct on an acidic solutewith the basicity of the adduct (i.e., its ability to donate an electron pair to theacidic solute). The reference scale of donor numbers of the adduct bases isbased on the enthalpy of reaction, H, of the donor (designated as B) with SbCl5when they are dissolved in 1,2-dichloroethane solvent. The donor numbers, des-ignated DN, are a measure of the strength of the BSbCl5 bond. It is furtherassumed that the order of DN values for the SbCl5 interaction remains constantfor the interaction of the donor bases with all other solute acids. Thus, for anydonor base B and any acceptor acid A, the enthalpy of reaction to form B:A is:

H a bB:A B:SbCl5DN= + ( . )3 14

From Eq. (3.14), it is possible to calculate HB:A for a base B and an acid Aif HB:A has been measured for two other donors. For example, the interactionof UO2(HFA)2 (HFA = hexafluoroacetone) with pyridine and with benzonitrilehas been measured in CHCl3 solvent. The equilibrium constants were deter-mined to be log KB:A 0.88 in pyridine and 2.79 in benzonitrile, assuming thatlog KB:A HB:A. With the use of the donor number for these ligands in Table3.4, the values of a and b are calculated to be 0.04 and 4.85, respectively. Inturn, with these values and the donor number that is given for acetonitrile(AcN), 59.0 in Table 3.4, the value of log K for the reaction

Table 3.4 Donor Numbers (kJmol1)

Donor DonorDonor Number Donor Number

Benzene 0.42 Diphenyl phosphonic chloride 93.7Nitromethane 11.3 Tributylphosphate 99.2Benzonitrile 49.8 Dimethoxyethane 100.4Acetonitrile 59.0 Dimethylformamide 111.3Tetramethylene sulfone 61.9 Dimethylacetamide 116.3Dioxane 61.9 Trimethylsulfoxide 124.7Ethylene carbonate 63.6 Pyridine 138.5n-Butylnitrile 69.5 Hexamethyl phosphoramide 162.4Acetone 71.1 Ethylenediamine 230.2Water 75.3 t-Butylamine 240.6Diethylether 80.4 Ammonia 246.9Tetrahydrofuran 83.7 Triethylamine 255.3


UO (HFA) AcN UO (HFA) AcN2 2 2 2+ = in CHCl3 is estimated to be 3.3. Experimentally, it was measured to be 3.5.

The donor number model has been used for correlating a number of sys-tems. The success of this approach, to a large extent, is based on its applicationto hard systems. It is unreasonable to expect that a single order of reactionstrengths for donors would be applicable to all acidic solutes. Also, the assumptionof constant entropy, which is required if log B:A HB:A, would not be univer-sally valid. In general, it can be expected to have more limited value for softsystems than for hard ones. Nevertheless, for oxygen and nitrogen donors and,particularly, in nitrogen and oxygen solvents, it has proven to be very useful.

3.4 THERMODYNAMICS OF COMPLEXATION

The free energy of complexation reaction, Gn, is defined by (cf. section 2.4):

G G T ML M Ln n nn= o R ln a[ ] /[ ][ ] ( . )3 15

where

G Tn n = R ln ( . ) 3 15b

and n is the stability constant for the complexation. The deviation from equilib-rium conditions (defined by n) determines the direction of reaction that goesspontaneously in the direction of Gn < O. The free energy term is the differ-ence between the enthalpy of reaction, Hn, and the entropy changes for thereaction, Sn; that is

G H T Sn n n = ( . )3 16

The free energy is calculated from the stability constant, which can be deter-mined by a number of experimental methods that measure some quantity sensi-tive to a change in concentration of one of the reactants. Measurement of pH,spectroscopic absorption, redox potential, and distribution coefficient in a sol-vent extraction system are all common techniques.

The enthalpy of complexation can be measured directly by reacting themetal and ligand in a calorimeter. It can also be determined indirectly by mea-suring log n at different temperatures and applying the equation

d dT H Tn nln / / ( . ) = R 3 17

The temperature variation method is used often in solvent extraction studies. Itcan give reliable values of the enthalpy if care is taken to verify that the changein temperature is not causing new reactions, which perturb the system. Also, areasonable temperature range (e.g., T 50C) should be used so that it ispossible to ascertain the linearity of the ln n vs. 1/T plot upon which Eq. (3.17)is based.


3.4.1 EnthalpyEntropy Compensation

The thermodynamics of complexation between hard cations and hard (O, Ndonor) ligands often are characterized by positive values of both the enthalpyand entropy changes. A positive H value indicates that the products are morestable than the reactants, i.e., destabilizes the reaction, while a positive entropyfavors it. If TSn > Hn, Gn will be negative and thus logn positive, i.e., thereaction occurs spontaneously. Such reactions are termed entropy driven sincethe favorable entropy overcomes the unfavorable enthalpy.

Complexation results in a decrease in the hydration of the ions whichincreases the randomness of the system and provides a positive entropy change(Sdehyd > 0). The dehydration also causes an endothermic enthalpy (Hdehyd > 0)as a result of the disruption of the ionwater and waterwater bonding of thehydrated species. The interaction between the cation and the ligand has a nega-tive enthalpy contribution (Hreaction < 0) due to formation of the cationanionbonds. This bonding combines the cation and the anion to result in a decreasein the randomness of the system and gives a negative entropy contribution(Sreaction < 0). The observed overall changes reflect the sum of the contributionsof dehydration and cationligand combination. If the experimental values of Hand S are positive, the implication is that the dehydration is more significantin these terms than the combination step and vice versa. The reaction steps canbe written (with charges omitted and neglecting intermediates):

1. Dehydration: Hh, ShM L M L( ) ( ( ( ( ( . )H O H O) H O) H O) p q m s)H O a2 p 2 q 2 m 2 s 2+ = + + + 3 18

2. Combination: Hc, ScM L ML( ) ( ( ( . )H O H O)s H O) b2 m 2 2 m+s+ = 3 18

3. Net reaction: Hr, SrM L ML( ) ( ( ( ( . )H O H O) H O) p q m s) H O c2 p 2 q 2 m +s 2+ = + + 3 18

and, therefore:

H H H H

S S S Sr h c

r h c

= + = = + = ( . )3 19

It has been shown that for many of the hardhard complexation systems,there is a linear correlation between the experimental H and S values. Fig-ure 3.11 shows such a correlation for actinide complexes. These H and Sdata involve metal ions in the +3, +4, and +6 oxidation states and a variety ofboth inorganic and organic ligands. Such a correlation of H and S hasbeen termed the compensation effect. To illustrate this effect, reconsider the


Fig. 3.11 Correlation of H and S of formation of a series of 1:1 complexes atdifferent ionic strengths.

step reactions above for complexation. The net reaction has the thermodynamicrelations:

G G G H H T S Sr c h c h c h= + = + +( ) ( ) ( . )3 20

The compensation effect assumes Gh 0; the positive values of Hr (=Hc +Hh) and Sr (=Sc + Sh) mean *Hh* > *Hc* and *Sh* > *Sc*. So Eq. (3.20)can be rewritten:

G G H T S H T Sr c r r c c + ( . )3 21The complexation, interpreted in this fashion, implies that:

1. The free energy change of the total complexation reaction, G, is relatedprincipally to step 2 [Eq. (3.18b)], the combination subreaction;

2. The enthalpy and entropy changes of the total complexation reaction, Hand S, reflect, primarily, step 1 [Eq. (3.18a)], the dehydration subreaction.

This discussion is important to solvent extraction systems, as it provides furtherinsight into the aqueous phase complexation. It also has significance for the


organic phase reactions. In organic solvents, solvation generally is weaker thanfor aqueous solutions. As a consequence, the desolvation analogous to step 1would result in small values of H(solv) and S(solv) (note that we term the aqueousphase solvation hydration). Therefore, Hc = Hsolv and Sc = Ssolv, which meansthat H is more often negative, while S may be positive or negative butrelatively small.

3.4.2 Inner Versus Outer Sphere Complexation

Complexation reactions are assumed to proceed by a mechanism that involvesinitial formation of a species in which the cation and the ligand (anion) areseparated by one or more intervening molecules of water. The expulsion of thiswater leads to the formation of the inner sphere complex, in which the anionand cation are in direct contact. Some ligands cannot displace the water andcomplexation terminates with the formation of the outer sphere species, inwhich the cation and anion are separated by a molecule of water. Metal cationshave been found to form stable inner and outer sphere complexes and for someligands both forms of complexes may be present simultaneously.

Often, it is difficult to distinguish definitely between inner sphere andouter sphere complexes in the same system. Based on the preceding discussionof the thermodynamic parameters, H and S values can be used, with cation,to obtain insight into the outer vs. inner sphere nature of metal complexes. Forinner sphere complexation, the hydration sphere is disrupted more extensivelyand the net entropy and enthalpy changes are usually positive. In outer spherecomplexes, the dehydration sphere is less disrupted. The net enthalpy and en-tropy changes are negative due to the complexation with its decrease in random-ness without a compensatory disruption of the hydration spheres.

These considerations lead, for example, to the assignment of a predomi-nantly outer sphere character to Cl, Br, I, ClO3, NO

3, sulfonate, and trichloro-

acetate complexes and an inner sphere character to F, IO3, SO24

, and acetatecomplexes of trivalent actinides and lanthanides. The variation in H and Sof complexation of related ligands indicates that those whose pKa values are 2form predominantly inner sphere complexes with the trivalent lanthanides andactinides. As the pKa increases above 2, increasing predominance of inner spherecomplexation is expected for these metals.

3.4.3 Thermodynamics of Chelation

In the preceding section, the positive entropy change observed in many com-plexation reactions has been related to the release of a larger number of watermolecules than the number of bound ligands. As a result, the total degrees offreedom of the system are increased by complexation and results in a positive


Table 3.5 Thermodynamic Parameters of Reaction of Cadmium(II)-AmmoniaComplex with Ethylenediamine

Product log K H o(kJmol1) S o (JmK1)

Cd(en)+2 0.9 +0.4 5.4Cd(en)2

+2 2.2 3.4 +15.0

K nn

nn

= +[Cd(en) NH

[Cd(NH en

+23

3

][ ]

) [ ]

2

22

value of the entropy change. In many systems, a similar explanation can begiven for the enhanced stability of chelates. Consider the reaction of Cd(II) withammonia and with ethylenediamine to form Cd(NH3)

24

+ and Cd(en)22+, whose

structures are given in Fig. 3.10. Table 3.5 gives the values of log K, H, andTS for the reactions

Cd(NH en Cd(en) NH

Cd(NH en Cd(en) NH

3 ) ( . )

) ( . )

22 2

3

3 42

22

3

2 3 22

2 4 3 23

+ +

+ +

+ = +

+ = +

The enthalpy value of Eq. (3.23) is very small as might be expected if twoCdN bonds in Cd(NH3)2+2 are replaced by two CdN bonds in Cd(en)2+. Thefavorable equilibrium constants for reactions [Eqs. (3.22) and (3.23)] are due tothe positive entropy change. Note that in reaction, Eq. (3.23), two reactant mole-cules form three product molecules so chelation increases the net disorder (i.e.,increase the degrees of freedom) of the system, which contributes a positiveS change. In reaction Eq. (3.23), the H is more negative but, again, it is thelarge, positive entropy that causes the chelation to be so favored.

As the size of the chelating ligand increases, a maximum in stability isnormally obtained for 5 or 6 membered rings. For lanthanide complexes, oxalateforms a 5-membered ring and is more stable than the malonate complexes with6-membered rings. In turn, the latter are more stable than the 7-membered che-late rings formed by succinate anions.

3.5 SUMMARY

The important role of thermodynamics in complex formation, ionic mediumeffects, hydration, solvation, Lewis acid-base interactions, and chelation hasbeen presented in this chapter. Knowledge of these factors are of great value inunderstanding solvent extraction and designing new and better extraction sys-tems.


REFERENCES

1. Martell, A. E.; Smith, R. M.; Critical Stability Constants, Vol. 15, Plenum Press,New York, (19741982).

2. Hogfeldt, E. Stability Constants of Metal-Ion Complexes, Part A: Inorganic ligands.IUPAC Chemical Data Series No. 22, Pergamon Press, New York (1982).

3. Robinson, R. A.; Stokes, R. H.; Electrolyte Solutions, Second Revised Edition, But-terworth, London (1970).

4. Bjerrum, J.; Metal Amine Formation in Aqueous Solution, P. Haase and Son, Copen-hagen (1941).

5. Moeller, T.; Inorganic Chemistry, John Wiley and Sons, New York (1952).6. Lewis, G. N.; Valence and the Structures of Atoms and Molecules, The Chemical

Catalog Co., New York (1923).7. Pearson, R. G.; Ed. Hard and Soft Bases, Dowden, Huchinson and Ross, East

Stroudsburg, PA, (1973).8. Gutmann, V.; The Donor-Acceptor Approach to Molecular Interactions, Plenum

Press, New York (1980).


Solvent Extraction Principles and Practice-Second Edition, Revised and ExpandedTable of ContentsChapter 03: Complexation of Metal Ions3.1 METAL ION COMPLEXATION3.1.1 Stability Constants3.1.2 Use of Stability Constants3.1.3 Stability Constants and Thermodynamics

3.2 FACTORS IN STABILITY CONSTANTS3.2.1 Statistical Effect3.2.2 Electrostatic Effect3.2.3 Geometric Effects3.2.4 The Chelate Effect

3.3 MODELS OF COMPLEX FORMATION3.3.1 Early Models3.3.2 Hard/Soft Acids and Bases (HSAB)3.3.3 Qualitative Use of Acid-Base Model3.3.4 Quantitative Models of Acid-Base Reaction

3.4 THERMODYNAMICS OF COMPLEXATION3.4.1 EnthalpyEntropy Compensation3.4.2 Inner Versus Outer Sphere Complexation3.4.3 Thermodynamics of Chelation

3.5 SUMMARYREFERENCES

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