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THERMODYNAMICS OF SOLVENT EXTRACTION a

G. R. Choppin & A. Morgenstern

a

a

Florida State University, Tallahassee, FL-32306-4390, USA Published online: 10 May 2007.

To cite this article: G. R. Choppin & A. Morgenstern (2000) THERMODYNAMICS OF SOLVENT EXTRACTION, Solvent Extraction and Ion Exchange, 18:6, 1029-1049, DOI: 10.1080/07366290008934721 To link to this article: http://dx.doi.org/10.1080/07366290008934721

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SOLVENT EXTRACTION AND IONEXCHANGE, 18(6), 1029-1049(2000)

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THERMODYNAMICS OF SOLVENT EXTRACTION

G. R. Choppin and A. Morgenstern Florida State University, Tallahassee, FL-32306-4390, USA

ABSTRACT The fundamental thermodynamic characteristics of aqueous electrolyte solutions and organic solutions which affect solvent extraction are summarized and the influence of metal complexation and hydration on the distribution ratios is discussed. The thermodynamics of extraction systems, including synergistic systems, is reviewed. The influence of structural aspects of the complexing extractant agents on these thermodynamic parameters is also reviewed.

THERMODYNAMICS OF AOUEOUS ELECTROLYTE SOLUTIONS AND ORGANIC SOLUTIONS

In solvent extraction systems, the interaction of the extracted solute with both aqueous and organic solvent molecules plays a significant role in the distribution of the solute between the phases. Thus, an understanding of the physico-chemical properties of aqueous electrolyte and of organic solutions as they determine the role of the interactions with the solute is necessary for successful design of solvent extraction systems. An extensive review of the thermodynamics of aqueous and organic solutions is beyond the scope of this paper and can be found in textbooks on physical chemistry and solvent

1029 Copyright IJ:> 2000 by Marcel Dekker, Inc.

www.dekker.com

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CHOPPINAND MORGENSTERN

extraction [1-4). Here we restrict the discussion to the fundamental concepts of molecular interactions in aqueous and organic solutions. Commonly in solvent extraction systems, one of the phases between which the solute distributes is an aqueous solution that contains one or more electrolytes The ions

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of the solute are likely to have associated waters of hydration, in the aqueous phases and associated solvent molecules in the non-aqueous phase. At sufficiently high concentrations, the ions can interact with one another, repulsively if of the same charge sign, attractively if of opposite sign. A fundamental principle of electrolyte solutions is that of the electroneutrality of the solution. Another useful concept, related to the activities of electrolytes, is that of the ionic strength, I, of the solution where I = 1/2 ~ CiZ? (the summation extends over the concentration and charge of all cations and anions present in the solution). Debye and Huckel (5) used electrostatic and statistical mechanical theories to obtain an equation for calculation of the mean ionic activity coefficient of a dilute electrolyte solution. When two or more electrolytes are present in the same solution, and one is at a significantly higher concentration, the activity coefficient of the secondary electrolytes are a function of the high concentration component. This is the basis of the ionic medium method in which an electrolyte (e.g. sodium perchlorate) is present at a fixed, high concentration (e.g., ;>: 1 mol L") which allows variation of lower concentrations of reactive electrolytes within certain limits without significant change in their activity coefficients [1). Solutions in organic solvents or in mixed aqueous-organic solvents may behave similarly to purely aqueous solutions. In particular, if the relative permittivity (E) of the solvent is greater than about 40, electrolytes at lower concentrations are, more or less, completely dissociated into ions. However, for solvents of E < 10, ionic dissociation is insignificant and the behavior is likely to differ significantly from aqueous systems. It must also be noted that mixed solutions of aqueous-organic nature usually have major disruption of the three-dimensional, cooperative hydrogen-bonded network that characterizes the water structures in aqueous solutions. Many "anomalous" properties of aqueous solutions that depend on this structured nature of water are absent in organic solvents. The presence of an organic solvent, even at low concentrations, in a solvent mixture affects the activity coefficient of an electrolyte relative to its value in water.

THERMODYNAMICS OF SOLVENT EXTRACTION

1031

Accordingly, in mixed aqueous-organic solvents there is a primary medium effect on the activity coefficient which reflects the interactions of the ions with their mixed-solvent surroundings as it differs from their interactions with a purely aqueous environment. Anion - cation attraction to form "ion-pairs" occurs readily in organic and mixed

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aqueous-organic solvents. It also occurs in aqueous solutions, notably with higher valence type electrolytes at higher concentrations. Ion pairing, generally, is weaker than normal complex formation involving covalent bonding between metal cations and anionic ligands. A useful concept to describe the association of a cation and an anion to form an ion pair is Bjerrum's theory [I]. Electrostatic interactions also must include ion-dipole and dipole-dipole bonding. Dipole-dipole interactions between polar solute particles in organic solvents may be either repulsive "head-head" interactions or attractive "head-tail interactions. Such attractive dipole interactions can lead to solute aggregation, of dimers, (in which the "head" of each of the two partners is near the "tail" of the other), and of chainlike and cyclic aggregates (oligomers). Tertiary amine salts in hydrocarbon solvents are typical examples of such aggregated solutes. Hydrogen bonding between solute particles also leads to aggregation. Typical of such solutes are carboxylic acids and acidic phosphate esters and cyclic dimers. Noncyclic aggregates can form which result in an increase in the viscosity of the solution with increasing concentrations. Another kind of solute-solute interaction, donor-acceptor adduct formation, forms I: I species between molecules of two different kinds of solute. Adduct formation results when one partner (the donor) has a pair of unbonded electrons, (e.g. the nitrogen atom in trioctylamine), and the acceptor has an empty orbital that can accept the pair of electrons. These effects play varying roles in the extraction of the solute between the aqueous and the organic solvent phases

METAL ION COMPLEXATION AND HYDRATION

The complexation of metal ions can have an important influence on the relative affinity of different metals for the solvent phases and can provide a sufficient difference in extractability to allow separation of the metals. In this section, the thermodynamics of metal complexation relevant to solvent extraction are described briefly with attention to

CHOPPIN ANDMORGENSTERN

1032

the parameters influencing complexation and to models of complex formation. For more extensive discussions, references 1- 4 are recommended. For any metal-ligand system, the equilibrium constant (i.e., the stability constant) is a quantitative measure of the metal ion complexation, and is expressed as the stepwise

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reaction constants K, for the reaction MLn.I+L=MLn, or as the overall constant, Bn, for

,

the net reaction M+nL=ML, (~, = n K,). These overall constants are also written with ..I

several subscripts; e.g., ~pq, where p=number of metal ions, q=number of protons (or, if negative, to the number of OH) and r=number of ligands. The ratio of complexed and free species is expressed by the equation: [ML,l = f3 [M]

. [L)'

(I)

n

Rigorously, a thermodynamic stability constant is defined in terms of standard state conditions where the constant is defined by the activities of the different species. However, the conditions of measurements of ions and complexes provide their concentrations are related by the activity coefficients. Activity coefficients at ionic strengths below ca. 2 mol kg" can generally be modeled with acceptable accuracy using the SIT approach [6], while systems at higher ionic strengths are better treated by the Pitzer model [7].

FACTORS IN STABILITY CONSTANTS

Many factors, among them statistical, electronic, geometric (bonding and steric), chelation, and the nature of the metal and ligands are reviewed for their effects on the stability constrants.

Statistical Effects

In complexation, ligands displace hydrate waters, although not necessarily on a I: I basis. Charge, steric, etc. effects determine the number of displaced waters and of bonded ligands. For example, Co" is an octahedral hexahydrate, Co(H 20)62+, but with chloride forms complexes with 1-4 Cl' anions (CoCl;' is tetrahedral). Trivalent actinides have large hydration numbers - usually 8 or 9 - but may form complexes with N<8 with

THERMODYNAMICS OF SOLVENT EXTRACTION

1033

bulky anionic ligands. In his treatment of the statistical effect, Bjerrum assumed that the total coordination, N, remained constant as hydration was replaced by complexation. If a ligand with a single binding site approaches the metal, its probabilitiy of interacting is proportional to the number of available bonding sites on the metal, N. The probability of

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dissociating the complex is proportional to the number of ligands present; i.e., I for ML. Therefore, statistically the stepwise stability constant, K, should be proportional to the ratio of the probabilities ofML formation and ofML dissociation; i.e., K,

oe

Nil [2].

Similarly, for the ML, formation by ML + L, only N-I sites are avialable on the M since one site is already occupied but the probability of dissociation of L from ML, is proportional to 2, i.e., K,

ee

(N-l )/2. In general, for MLn.1+L=ML n Kn~

[N-Cn-I)]/[n]

(2)

and the ratio of successive stability constants would be (assuming other factors play no role): Kn+1 K,

=::

n N-n N-(n+l) n+1

Thus, for a hypothetical systems in which

~,=IOO

(3)

and N=6, we can calculate K,0"42,

(~,=4.2 x \03) while K3=21, C~3=8.8 x \04), etc. The experimental (8) values reported for

cadmium complexation by chloride are ~1=\OO, ~,=400, ~3=50. Obviously, factors other than the statistical effect reduce K" K3, etc., in the Cd + Cl complexation system. Nevertheless, such statistical calculations can be used for an upper limit on the Kn+,lK n ratio and the difference in the calculated values and the experimental values can offer a measure of the ligand and steric effects which lower the constants.

Electrostatic Effect The Born equation, which describes the electrostatic interactions between an anion and a cation in a solvent, has the form: Ll.G.1=-A'Iz,z./Er where A'l is a constant, z, and

z,

(4)

are the cationic and anionic charges, E is the dielectric

constant and r is the distance between the charge centers (i.e., the sum of the radii of the cation and anionic bonding group). Ionic radii for a number of cations and anions are listed in [8]. Although Equation (4) has the theoretical form to calculate Ll.G,\, the proper values of E are uncertain and empirical values of E or of E/r are obtained from experimental values of Ll.G'1 for use in calculation of related systems.

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CHOPPIN AND MORGENSTERN

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cE.. 4.00 Cl

.2

2.00

0.00 ""_-'-..L>*'*,,-_'----_.-"';-------'_----,."""--' 0.00

Figure 1. Correlation of log 13 of fluoride complexation vs. ~r, of the metal.

Equation (4) indicates that for complexation systems with ligands in which the bonding is strongly electrostatic and steric effects are very similar, the stability constant should be related to the charge of the cation divided by r. For a particular ligand (constant anionic radius), log 13 could be expected to correlate with

~r,

(r,= cationic radius).

Figure I shows such a correlation for a number of metals complexcd with the fluoride anion; the linearity of this correlation confirms the dominance of electrostatic bonding in these I: I flouride complexes. Another useful correlation can be derived from Eq. (4). Proton association with ligands is electrostatic so the equation should be applicable to proton association. Moreover, if both HL and ML are ionic, log 131 should correlate with log K. (or, with pKa), assuming no structural changes in the metal complex. Figure 2 shows the excellent correlation found for log 131 for samarium (1II) with pKaof a series of monocarboxylate ligands. Such correlations can be very useful in estimating the role of unknown stability constants of new complexing/extractant ligands being considered for use in solvent extraction separations.

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THERMODYNAMICSOF SOLVENT EXTRACTION

1035

di 2 .O Dl

..2

pKa Figure 2. Relationship between the stability constant, ~IO" for formation of SmL2+ and the acid constant, pK", of HL: (I) propionic; (2) acetic acid; (3) iodoacetic; (4) chloroacetic acid; (5) benzoic acid, (6) 4-flurobenzoic acid; (7) 3-flurobenzoic acid; (8) 3-nitrobenzoic acid.

Geometric Effects The geometry of the complex can playa significant role in the strength of many complexes. The relative sizes of the cations and anions is very important in determining the geometrical pattern in ionic crystals and, for such cation-anion pairs, steric effects can be expected to be found in their complexes. In Table 1, the coordination number and the geometric pattern are listed for various ratios of the radius of the metal cation to that of the anionic ligand. Co'+ and H,O have a radius ratio of about 0.5 and, as predicted octahedral Co(H,O)6'+ is the hydrated species; Co'+ and Cl' have a radius radio close to 0.3 and, as predicted, the CoC!.- complex has a tetrahedral structure. Factors important in the geometry of metal complexes are: (a) arrangement of the ligands about the metal to minimize electrostatic repulsions (predominant in ionic complexes) and (b) overlap of the metal and ligand orbitals (important in covalent compounds). The first requirement (a) favors a tetrahedral configuration for CN=4 as the

1036

CHOPPIN AND MORGENSTERN

ligands are father apart than in the square planar geometry. However, if overlap of orbitals is a stronger requirement, and a d orbital can be included in the hybridization, the dsp2square planar geometry gives the more stable complex. In the octahedral complexes of CN=6, secondary structural effects can be observed that can be attributed to

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differences in ligand field effects related to the electron distribution among the metal d orbitals.

The Chelate Effect This effect involves binding of the metal to more than a single donor site of the ligand. Ethylenediamine, H2N-C2H.-NH2, is a bidentate ligand which binds through the two nitrogen atoms. Ethylenediaminetetraacetate, EDT A, is a hexadentate ligand [(OOC·CH2h NC2H.N(CH2·COO)2]'", binding through the 2 nitrogens 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 for M(NH3h 2+ can be compared with log ~, for M(en)2+ while log ~. for M(NH3)P and log ~2 for M(enh 2+ can be similarly compared to ascertain the stabilizing effect of chelate formation. Cu(en) 2+ is more stable than CU(NH 3)22+ by about 2 units of log ~, Cu(enh 2+ is almost 6 units more stable than Cu(NH 3).'+. Chelate complexes are used in many solvent extraction systems. In such systems, the chelating ligands are organic compounds which provide solubility in the organic phase. The metal binds to the polar charged donor sites, leaving an outer organic structure about the metal which favors solubility in an organic solvent, and, hence, extraction from the aqueous phase.

MODELS OF COMPLEX FORMAnON

A major advance in developing a theory of how and why metal ions form complexes was made by N. V. Sidgwick in 1927 who proposed that the number of ligands that bond to a metal ion was determined by the number of electron pairs (one per bound ligand donor site) accepted by the metal ion to achieve a stable inert gas electronic configuration. The metal is the electron pair "acceptor" and the ligand, the electron pair

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THERMODYNAMICS OF SOLVENT EXTRACTION

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Table I Cation/Anion Radius Ratio Values for Cation Coordination Numbers

Coordination number

Geometric pattern

Radius ratio (rc/ra)

2

Linear

SO.15

3

Triangular

0.15-0.22

4

Tetrahedral

0.22-0.41

4

Planar

0.41-0.73

6

Octahedral

0.41-0.73

8

Cubic

>0.73

"donor". A few years earlier, G. N. Lewis had introduced a generalized acid-base theory in which a base was a substance which furnished a pair of electrons for a chemical bond and an acid was a substance accepted such the electron pair. In this model, complexation is a class of acid-base reactions. This relationship was developed further in the next model described.

Hard/Soft Acids and Bases (HSAB) The strength of interaction of metal and a ligand is predicted qualitatively by the hard-soft, acid-base principle [9]. In general, hard acids are cations which favor ionic bonding and their log

~n

values correlate linearly with the pK. of the ligand acid. By

contrast, soft acid cations favor covalent bonds and their log

~

values correlate with the

redox potential, EO, or the ionization potential of the ligand. Ligands which are hard bases tend to have higher pK, values in their acid form while ligands which are soft bases have large EO or IP values. The important principle of the HSAB model is that hard acids react strongly with hard bases and soft acids with soft bases. There are exceptions to this principle due to factors more important in the interaction than the inherent acidity and/or

CHOPPIN AND MORGENSTERN

1038

basicity. Nevertheless, the simple HSAB principle has proven a very useful model for a large variety of complexation reactions. The bond in soft acid-soft base complexes results from sharing an electron pair, and soft species generally have large polarizabilities. In hard (metal) acids, the energy

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difference between the acceptor and donor orbital levels is so large that they do not share the electron pair, and the bonding is strongly electrostatic. The characteristic features of these species are as follows: I.

hard species are difficult to oxidize (bases) or reduce (acids), and have low polarizabilities, small radii, higher oxidation states (acids), high pK. (bases), more positive (for the acids) or more negative (for the bases) electronegativities, and high charge densities at acceptor (acid) or donor (base) sites;

ii. soft species are relatively easy to oxidize (bases), or reduce (acids), and have high polarizability, large radii, small differences in electronegativities between the acceptor and donor atoms, low charge densities at acceptor and donor sites, and also often have low-lying empty orbitals (bases), and a number of d electrons (acids). Following these guidelines, cations of the same metal would be softer for lower oxidation states, harder for higher ones. Thus, Cu+ and rr' are soft acids; Cu" is borderline and Tl 3+ is hard. Even though Cs" has a large radius and low charge density, its low ionization potential makes it a hard acid. This illustrates that the properties listed above may not be possessed by all hard (or soft) species, but indicate the characteristics useful to predict the acid-base nature of cations and anions.

Qualitative Use of Acid-Base Model A number of species are listed in the hard, soft, or borderline categories in Table 2 which can be used to predict the strength of complexation. For example, Pu4+ is a hard acid, F-, a hard base and

r,

a soft base. This leads to the prediction that log ~1(PuF3'J

would be larger than log ~1(PuI3+); the experimental values are 6.8 and <1.0, respectively. By contrast, since Cd2+ is a soft acid, log ~1(CdF+) could be expected to be smaller than log ~1(CdI). The respective values are 0.46 and 1.89 (8). For the borderline metals such as Fe'+,

ce",

Ni'+, Cu", and Zn" the complexing trends are less easily

predicted. For F-, a hard base, the order oflog

~I

is:

Cu> Zn- Fe> Mn> Ni >Co

TIlERMODYNAMICS OF SOLVENT EXTRACTION

1039

Table 2 List of Some Hard and Soft Acids and Bases

A. Acids

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Hard.

H, Li to Cs

+1 ions +2 ions +3 ions +4 ions -yl ions

Mg to Ba, Fe, Co, Mn Fe, Cr, Ga, In, Sc, Y, Ln, An Ti, z-, Hf, Ln, An VO'+, MoO" AnO" Mn(VIl)O,"

ii. Borderline.

+2 ions +3 ions

Fe, Co, Ni, Cu, In, Sn, Pb Sb, Bi, Rh, Ir, Ru, Os

iii. Soft.

Neutral +1 ions +2 ions

BH) Cu, Ag, Au, Hg, CH)Hg, Cd, Hg, Pd, Pt

1.

B. Bases

i. Hard.

Neutral -1 ions -2 ions -3 ions

H,O, ROH, NH), RNH" N,H., R,O, R)PO, (RO»)PO OH, RO, RCO" NO), CIO., F, CI 0, R(CO,)" CO), SO. PO.

ii. Borderline.

Neutral -I ions -2 ions

C6H,NH" C,H,N N), NO" Br SO)

Soft.

Neutral -1 ions -2 ions

C,H" C6Ho, CO, R)P, (RO»)P, R)As, R,S H, CN, SCN, RS, I S,O)

111.

whereas for SCN', a soft base, it is:

Cu» Ni > Co > Fe > In> Mn In solvent extraction, the HSAB principle can be used to indicate ligands which react strongly with metal ions to form extractable complexes. For example, the actinide elements would be predicted to complex strongly with the ~-diketonates, R)C-CO-CH,· CO-CR) (where R ; H or an organic group) as the bonding is through the oxygens (hard base) of the enolate anion. The formation of a chelate structure by the metal-enolate

1040

CHOPPIN AND MORGENSTERN

complex results in a relatively strong complex which combines with the hydrophobic nature of the R groups on the ~.diketonates to produce high solubility in organic solvents.

Coordination Numbers

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The solvent extraction of the

~-diketonate

system can be used to illustrate the

importance of the high coordination numbers of the actinides and lanthanides which allows coordination of neutral hydrophobic adducts. The

~-diketonate

ligands balance

the cation ionic charge while occupying 2n coordination sites of the metal cations. Since the trivalent f-element cations have total coordination numbers of 8 or 9, the metal in the neutral MLl has residual hydration. Alkyl phosphates, (RO)l PO, can coordinate through an oxygen donor by replacing these water molecules to form MLm·Sn (n=1 to 3). This MLm·S n species is more hydrophobic than the more hydrated MLm·(H20)n and, thus, more soluble in an organic solvent. In the Purex process for processing irradiated nuclear fuel, uranium and plutonium are extracted from nitric acid solution into a kerosene solution of tributyl phosphate, TBP, as U02(NOl)dTBP)2 and Pu(NOlk(TBPh. U in UO/+ usually has a maximum coordination number of 6 while that of Pu'+ can be 8 to

10. The addition of two TBP adduct molecules in each molecule (indicating that NOl· is bidentate) causes the compound to be soluble (and, hence, extractable) in the kerosene solvent.

THERMODYNAMICS OF COMPLEXATION The standard free energy of a complexation reaction, is defined by: LlGo" = -RT In ~n where

~n

(5)

is the stability constant for the complexation. The enthalpy of complexation

LlH n can be measured directly by reacting the metal and ligand in a calorimeter or, indirectly, by measuring log

~n

at different temperatures and applying the equation:

d In ~n /dT = -LlHn/R

(6)

The temperature variation method is used often in solvent extraction studies. It can give reliable values of the enthalpy over the temperature range for which the graph of ln~n vs

I IT is linear.

1041

THERMODYNAMICS OF SOLVENT EXTRACTION

Enthalpy-Entropy Compensation Interaction of hard cations and hard (0, N donor) ligands to form complexes are often characterized by positive values of both the enthalpy and entropy changes. In such cases, if T~So >~Ho, (~Go = ~Ho - T~So), log ~o is positive. These "entropy driven"

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reactions are due to a decrease in the hydration of the ions, which increases the randomness of the system, resulting in a positive entropy contribution. Such dehydration results in an endothermic enthalpy contribution

(~Hh

> 0) since the metal-water bonds of

the hydrated species must be broken. The interaction between the cation and the ligand provides a negative enthalpy contribution

(~H, <

0) due to formation of the cation-anion

bonds. This bonding decreases the randomness of the system, resulting in negative entropy contribution

(~S,

< 0). The observed overall enthalpy reflects the sum of the

contributions of dehydration and cation-ligand combination. Positive values of ~Ho and ~So imply that the dehydration is more significant in these terms than the combination

step. Many hard-hard complexation systems, have a linear correlation between the ~H

experimental

and

~S

values (Figure 3), which has been termed the compensation

effect. In the compensation effect, the positive values of ~Ho (=~H,+~Hh) and +~Sh)

mean

I~Hhl>I~HoI

and

I~Shl>I~S,

Iand ~Go = ~G,.

~So (=~S,

This suggest the following:

a. the free energy change of the total complexation reaction,

~Go,

is related principally to

the combination subreaction; b. the enthalpy and entropy changes of the total complexation reaction,

~Ho

and

~ So,

reflect, primarily, the dehydration subreaction. These trends are important in solvent extraction systems as they provide insight into the aqueous phase complexation and, also, have significance for the organic phase reactions.

In organic solvents, solvation generally is weaker than for aqueous solutions. As a consequence, the desolvation analogous to step I would result in small values of ~H(solv)

and

~S(solv).

Therefore,

more often negative while

~So

~H,

;::

~Hsolv

and

~S,

;::

~Ssolv

which ineans

~H

is

may be positive or negative and relatively small.

Thermodynamics of Chelation The positive entropy change observed in many complexation reactions has been related to the release of a larger number of water molecules than the number of bound

CHOPPIN AND MORGENSTERN

1042

40 30 ;:' 20

10

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E

14

• 10

~

16

~

:I:
0 -10

~

691 11

5

-20

8

3/

1 2' ~ 4 5 6 7 8 9 10 11

12 13 14 15 16

CfF+2 CmF+2 AmF+2 U0 2 F+ 1

PuCI+2 U02 C1+1 PUN0 3+3 NpS04+2 AmS04+1 CmS04+ 1 U02S04 US04+2 AmSCN+2 Am (Glycinate)+2 Am (Acetate)+2 Am (Glycolate)+2

Figure 3. Correlation of ~H and ~s of formation of a series of hard-hard, J: I complexes at different ionic strengths.

ligands.

As a result the total degrees of freedom of the system are increased by

complexation and results in a positive value of the entropy change. In many systems, a similar explanation can be given for the enhanced stability of ehelates. Consider the reaction of Cd(II) with ammonia and with ethylenediamine to form Cd(NH 3)l+ and Cd(en),'+ whose structures are given in Figure 4. Table 3 gives the values of log K, ~H and T~S for the reactions: Cd(NH3),2+ + en ; Cd(en)2+ + 2NH3

(14a)

Cd(NH3)l+ + Zen > Cd(en)/+ + 4NH3

(I4b)

The enthalpy value of Eq.(14a) is very small as might be expected if two Cd-N bonds in Cd(NH3),'+ are replaced by two Cd-N bonds in Cd(en)'+. The favorable equilibrium constants for the two reactions are due to the positive entropy change. Note that in the reaction of Eq. (l4a), two reactant molecules form three product molecules so chelation increases the net disorder (i.e., increased the degrees of freedom) of the system which

THERMODYNAMICS OF SOLVENT EXTRACTION

1043

H2 H2C-N,

I

H2 /N-CH2 Cd

H2C_N/ H2

I

'N-C H2 H2

Cd (NH2C2H4NH2)22+

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Figure 4. Structures ofCd(NHJ)l+ and Cd(en)/+.

Table 3 Thermodynamic Parameters of Reaction of Cadmiurn(ll)-Ammonia Complex with Ethylenediamine

Complex

Cd(ent

n

Z

Cd(en):z

2

ss: (J·m·K·

LogK:

Mi" (klmor l )

0.9

+0.4

5.4

2.2

-3.4

+ 15

1 )

• K = [Cd(en);z][NH,]z, n

[Cd(NH,);~][en]'

contributes a positive 6.S change). Such chelation effects playa role in many extraction reactions in which the extractant ligand forms chelate bonds to the metal.

THERMODYNAMICS OF SYNERGISM

Synergism is an important factor in the degree of extraction and of separation factors in many extraction systems (10). The major factor in synergism is an increase in hydrophobic character of the extracted metal complex upon addition of the adduct. Three mechanisms have been proposed to explain the synergism for metal + chelant + adduct. The first involves an opening of one or more of the chelate rings and occupation by the

CHOPPIN AND MORGENSTERN

1044

adduct molecule(s) of the vacated metal coordination site(s). In a second mechanism, the metal ion is not coordinately saturated by the ligand and, hence, retains residual water(s) in the coordination sphere which can be replaced by adduct molecules.

The third

mechanism involves expansion of the coordination sphere of the metal ion to allow

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bonding of adduct molecules. From the extraction constants, it is rarely possible to choose between these alternative mechanisms but enthalpy and entropy data of the synergistic reactions can be used to provide more definitive arguments. The overall extraction reaction for metal extraction by HITA and TBP is written as: Mn\aq) + n HITA(org) + pTBP(org) = M(ITA)n (TBP)p(org) + pH+(aq) The extraction equation for TTA is, Mn+ + n HITA(org) = M(ITAln(org) + nll''(aq)

(15)

(16)

The adduct formation reaction in the organic phase (the "synergistic reaction") is obtained by subtracting Eq. (16) from Eq. (15): M(TTAln(org) + pTBP(org) = M(ITAln(TBP)p(org)

(17)

Direct calorimetric measurements of the reaction to form U02·(ITA)n·TBP(org), gave log K = 5.10, llH = -9.3 kl-mol', TIlS = 20.0kJ·mor'·K"'. The formation of Th(ITA).(org) + TBP(org) = Th(ITA).-TBP(org) gave values oflog K =4.94, llH= -14.4 kl-mol", TllS= 13.7 krmol'.

It was ascertained that both U02(ITAh and

Th(TTA). have two molecules of hydrate water when extracted in the benzene and these are released when TBP is added. Since two reactant molecules (e.g., U02(ITAh'2H20 and TBP) formed three product molecules (e.g., U02(ITAh·TBP and 2H20), llS is positive. TBP is more basic than H20 and forms stronger adduct bonds resulting in, the enthalpy being exothermic. Hence, both the enthalpy and entropy changes favor the reaction, resulting in relatively large values oflog K. These equations do not provide complete definition of the reactions which may be of significance in a particular system. For example, HITA can exist as a keto, an enol, and a keto-hydrate species. The metal combines with the enol form which usually is dominant in "organic" solvents (e.g. K=[HTTAle/[HTTAlk -6 in wet benzene). The kinetics of the keto - enol reaction are not fast, but, apparently, are catalyzed by the presence of reagents such as TBP or TOPO. Such reagents react with the enol form in drier solvents but cannot compete with water in wetter ones. HTTATBP and TBP'H20

THERMODYNAMICS OF SOLVENT EXTRACTION

1045

species also form readily. However, for extractions into the same solvent (e.g., benzene), these effects and need not be considered in a simple analysis of comparative extractions. For trivalent lanthanides and actinides, the data suggest a reaction in which addition

of TBP

displaces

some

or

all

of the

hydrate

molecules;

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An(TIA)3(H,O)3 ~An(TIA)3(TBP)(H,O)1-2~An(TIA)3(TBP)l-3 (I 8) This scheme of steps reflects the ability of the trivalent actinides and lanthanides to vary their coordination number in different species. Th(TIA). can be dissolved in dry benzene with no residual hydration. Values for the formation of Th(TTA)•. TBP from Th(TT A). + TBP in this dry system are log K = 5.46, 6W = -39.2 kJ mol", T6S o

= -8.0 kJ mol" x'.

The negative entropy and enthalpy

values reflect a decrease in the net degrees of freedom (2 reactant molecules combine to form I product molecule).

CORRELAnON BETWEEN

&. AND EXTRACTANT

STRUCTURE

In the hard-soft model of complexation reactions, hard-hard and soft-soft combinations lead to larger equilibrium constants than for hard-soft interactions. Since the lanthanides belong to the hard acids and oxygen to the hard bases, the HSAB theory helps to explain the data in Table 4 which shows K.x for the extraction reaction M"+ (aq) + n HR(org) ~ MR,,(org) + n H+(aq)

(19)

for M2+ and M 3+ cations. The increasing charge density from LaJ+ to Lu3+ (due to decreasing ionic radii) results in increasing stability constants for formation of LnR 3. Since K,x is proportional to the stability constants, K,x should also increase. Further, since the "hardness" of the extractant increases from RPS,H to RPO,H (soft S being replaced by hard 0) 133 (and, hence, K.x) also increases in this order. These trends may be compared with the data for three soft metals, with the same extractants in Table 4. For these soft-hard systems the extraction constant decreases with increase in charge density; and, also with increasing hardness of the ligand which is in agreement with the HSAB theory. The complexation of UO/+ with diamide extractants can be used to show the effect of ring size in chelation. TBOA (C.H9)zNCO" TBMA [(C.H9),NCO,],CH" TBSA [(C.H9)2NC02],(CH2)z form complexes with UO;' of 5,6 and 7-membered rings,

t046

CHOPPINAND MORGENSTERN

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Table 4 Comparison of the Extraction Constants K" for Metal Cations and Sulfur or Oxygen Dialkyl Phosphoric Acids

Zn2+

Cd 2+

Hg2+

La'+

Eu'+

LuJ+

5.4

4.1

3.6

7.83

8.74

9.68

log K" for R,'POOH'

-1.20

-1.80

-2.20

-2.52

-0.44

2.9

log K" for R"POSHb

0.70

3.70

5.40

-4.78

-4.23

0.34

log K" for R2'PSSH'

2.40

3.49

4.40

Charge density

Z; /r,

-8.28

R' ~ C4H,O; R" ~ C4H,CH(C2HS)CH2O a. R ~ R' for M2+, ~ R" for MJ+ b. R ~ R' for M2+, ~ R" for M'+ c. R~ R" for M2+ and M'+

respectively. The data {(log 1(",

~

0.005 (TBOA), 10.6 (TBMA), 9.3 (TBSA)) show that

the best extraction (i.e., largest 1(", value) is obtained for the 6-membered ring. Steric hindrance plays an important role in the interaction with the metal. The extraction constants log I("x for U022+ with the organophosphorous extractants, TBP and the more branched TiBP are 28 and 26, respectively. The relatively small difference indicates that the branching in TiBP has only a small effect because of the free rotation of the substituents around the phosphorous atom. For the amide, DOBA, and its branched isomer, DOiBA,log

K,,~

5.75 and 0.55, respectively. In these ligands, the nature ofR,

R' and R" in R"R'NCOR is important due to the molecular rigidity of the amide group.

SYSTEMATICS OF ADDUCT FORMATION CONSTANTS

Many common neutral extractants are able to replace solvated water at the metal complex, e.g.:

THERMODYNAMICS OF SOLVENT EXTRACTION

1047

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Table 5 Effect of Charge Density on the Adduct Formation Constants

M

ZJr,

Ligand

Adduct

Solvent

log K. d1

log K. d2

Ca(II)

3.4

ITA

TBP

CCl,

4.11

8.22

Sr(II)

3.0

ITA

TBP

CCI,

3.76

7.52

Ba(II)

2.6

ITA

TBP

CCI,

2.62

5.84

Eu(III)

8.74

ITA

TBP

CCI,

5.36

8.96

MAz(H20)w (org) + bB(org) ~ MAzBb(org) + H20(org)

K.d

(20)

The interaction of these adduct molecules with metallic ions depends strongly on the organic function in which the donor atom, resides (i.e., on the charge density of the donor). For oxygen donors, a sequence can be established based on the order in which they are able to displace each other in the complex: RCHO < R2CO < ROH < H20 = (RO)lPO < R"R'NCOR = (RO)2RPO < RlPO

(21)

A large adduct formation constant means greater extraction which is referred to commonly as a synergistic effect. Table 5 lists formation constants, (K.dx for the alkaline earth complexes M(TTA)z(TBP)x in carbon tetrachloride [II]. In the alkaline earth metals, when x=2, the TBP molecules bond perpendicular to the plane of the two ITA rings producing an octahedral complex. Since the coordination radius increases in the order Ca, Sr, Ba (1.00, 1.18 and 1.35 A, respectively), the charge density decreases, in that order, which leads to weaker bonding as the sequence progresses from Ca to Ba. The consequence is a decreased synergistic effect for the extraction. Table 6 lists constants for the formation to Eu(ITA)lB x complexes in chloroform, or carbon tetrachloride, where B is a series of different donor molecules, arranged in order of increasing K.d values. In Eu(ITA)l the ITA molecules occupy only 6 of the 9 coordination positions available; the 3 empty positions have been shown to be occupied

1048

CHOPPIN AND MORGENSTERN Table 6 Adduct constants for formation of Eu(TTA)lBb

Chloroform

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Adduct log KOJ!! HTTA(self-adduct)

0.56

Hcxone

1.16

Quinoline

3.29

TBP

3.63

Tapa

5.40

Carbon tetrachloride

!l!lLK.d2

log K,dl

log K,d2

>0.5 1.52

1.71

2.34

3.48

5.16

5.40

5.36

8.96

7.60

7.49

12.26

by three water molecules. The order of increasing K.dl and K.d2, is the same as that of increasing basicity of the donor molecules.

Thus, the order of magnitude of the

formation constant for adducts whose relative position in the basicity sequence or their relative donor strength can be predicted, provided steric hindrance does not interfere. In this system CHCIl solvates the Eu complex to some extent, while CC4 is inert. This has two effects, the K DC value increases due to the solvation by CHCb (not shown in the Table), while the adduct formation constants K.d decreases as the solvation hinders the adduct formation. The more inert solvent CCI. causes an opposite effect, a lower Koc and a larger K ad•

SUMMARY The important role of thermodynamics in complex formation, ionic medium effects, hydration, solvation, Lewis acid-base interactions, and chelation, has been discussed in this paper. An understanding of the factors are of value in assessing solvent the design of new, improved extraction systems for metal ion separation and purification.

THERMODYNAMICS OF SOLVENT EXTRACTION

1049

Preparation of this paper was assisted by a contract with the USDOE-OBES Division of Chemical Sciences.

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REFERENCES

1. H.S. Harned and R.A. Robinson. "Multicornponent Electrolyte Solutions." Pergamon Press, Oxford, 1968. 2. M.M. Jones, "Elementary Coordination Chemistry", Prentice-Hall, Englewood Cliffs, N. J., 1964. 3. Y. Marcus, " Ion Solvation", John Wiley and Sons, N.Y., 1985. 4. 1. Rydberg, C. Musikas, and G.R. Choppin, Marcel Dekker, "Principles and Practices of Solvent Extraction", eds. N.Y., 1992. 5. 1.N. Levine, "Physical Chemistry" 3'd Ed., McGraw Hill Co., New York, 1998. 6. Grenthe, et aI., "Chemical Thermodynamics of Uranium" Nucl. Ener. Agency Tech. Data Base, OECD, Paris, 1991. 7. K.S. Pitzer, J. Phys. Chern., 7.L 268 (1973); K.S. Pitzer and J.J. Kim, J. Am. Chern. Soc.,2Q, 5701 (1974). 8. R.D. Shannon, Acta Crystallogr., A32, 751 (1976). 9. R. G. Pearson, Ed., "Hard and Soft Bases", Dowden, Huchinson and Ross, East Strouburg, Pa., (1973). 10. G.R. Choppin, " Complexation of Metal Ions", Ch.3. in ref. 4. 11.B. Allard, G. Choppin, C. Musikas and 1. Rydberg, "Systematic of Solvent Extraction:, Ch. 6 in ref 4.

Received by Editor 2, 2000

June