Stability constants of complexes
This article provides insufficient context for those unfamiliar with the subject.(February 2015) |
In
History
Jannik Bjerrum (son of
Hence by following the hydrogen ion concentration during a titration of a mixture of M and HL with base, and knowing the acid dissociation constant of HL, the stability constant for the formation of ML could be determined. Bjerrum went on to determine the stability constants for systems in which many complexes may be formed.
The following twenty years saw a veritable explosion in the number of stability constants that were determined. Relationships, such as the
Theory
The formation of a complex between a metal ion, M, and a ligand, L, is in fact usually a substitution reaction. For example, in aqueous solutions, metal ions will be present as aqua ions, so the reaction for the formation of the first complex could be written as
The equilibrium constant for this reaction is given by
[L] should be read as "the concentration of L" and likewise for the other terms in square brackets. The expression can be greatly simplified by removing those terms which are constant. The number of water molecules attached to each metal ion is constant. In dilute solutions the concentration of water is effectively constant. The expression becomes
Following this simplification a general definition can be given, for the general equilibrium
The definition can easily be extended to include any number of reagents. The reagents need not always be a metal and a ligand but can be any species which form a complex. Stability constants defined in this way, are association constants. This can lead to some confusion as pKa values are dissociation constants. In general purpose computer programs it is customary to define all constants as association constants. The relationship between the two types of constant is given in association and dissociation constants.
Stepwise and cumulative constants
A cumulative or overall constant, given the symbol β, is the constant for the formation of a complex from reagents. For example, the cumulative constant for the formation of ML2 is given by
- ;
The stepwise constants, K1 and K2 refer to the formation of the complexes one step at a time.
- ;
- ;
It follows that
A cumulative constant can always be expressed as the product of stepwise constants. Conversely, any stepwise constant can be expressed as a quotient of two or more overall constants. There is no agreed notation for stepwise constants, though a symbol such as KL
ML is sometimes found in the literature. It is good practice to specify each stability constant explicitly, as illustrated above.
Hydrolysis products
The formation of a hydroxo complex is a typical example of a hydrolysis reaction. A hydrolysis reaction is one in which a substrate reacts with water, splitting a water molecule into hydroxide and hydrogen ions. In this case the hydroxide ion then forms a complex with the substrate.
- ;
In water the concentration of hydroxide is related to the concentration of hydrogen ions by the self-ionization constant, Kw.
The expression for hydroxide concentration is substituted into the formation constant expression
In general, for the reaction
In the older literature the value of log K is usually cited for an hydrolysis constant. The log β* value is usually cited for an hydrolysed complex with the generic chemical formula MpLq(OH)r.
Acid–base complexes
A
There are three major theories relating to the strength of Lewis acids and bases and the interactions between them.
- Hard and soft acid–base theory (HSAB).[10]This is used mainly for qualitative purposes.
- Drago and Wayland proposed a two-parameter equation which predicts the standard enthalpy of formation of a very large number of adducts quite accurately. −ΔH⊖ (A − B) = EAEB + CACB. Values of the E and C parameters are available.[11]
- Guttmann donor numbers: for bases the number is derived from the enthalpy of reaction of the base with antimony pentachloride in 1,2-Dichloroethane as solvent. For acids, an acceptor number is derived from the enthalpy of reaction of the acid with triphenylphosphine oxide.[12]
For more details see: acid–base reaction, acid catalysis, Extraction (chemistry)
Thermodynamics
The thermodynamics of metal ion complex formation provides much significant information.[13] In particular it is useful in distinguishing between enthalpic and entropic effects. Enthalpic effects depend on bond strengths and entropic effects have to do with changes in the order/disorder of the solution as a whole. The chelate effect, below, is best explained in terms of thermodynamics.
An equilibrium constant is related to the standard Gibbs free energy change for the reaction
R is the gas constant and T is the absolute temperature. At 25 °C, ΔG⊖ = (−5.708 kJ mol−1) ⋅ log β. Free energy is made up of an enthalpy term and an entropy term.
The standard enthalpy change can be determined by calorimetry or by using the Van 't Hoff equation, though the calorimetric method is preferable. When both the standard enthalpy change and stability constant have been determined, the standard entropy change is easily calculated from the equation above.
The fact that stepwise formation constants of complexes of the type MLn decrease in magnitude as n increases may be partly explained in terms of the entropy factor. Take the case of the formation of
For the first step m = 6, n = 1 and the ligand can go into one of 6 sites. For the second step m = 5 and the second ligand can go into one of only 5 sites. This means that there is more randomness in the first step than the second one; ΔS⊖ is more positive, so ΔG⊖ is more negative and . The ratio of the stepwise stability constants can be calculated on this basis, but experimental ratios are not exactly the same because ΔH⊖ is not necessarily the same for each step.[14] Exceptions to this rule are discussed below, in #chelate effect and #Geometrical factors.
Ionic strength dependence
The thermodynamic equilibrium constant, K⊖, for the equilibrium
can be defined[15] as
where {ML} is the
Since activity is the product of concentration and activity coefficient (γ) the definition could also be written as
where [ML] represents the concentration of ML and Γ is a quotient of activity coefficients. This expression can be generalized as
To avoid the complications involved in using activities, stability constants are determined, where possible, in a medium consisting of a solution of a background electrolyte at high ionic strength, that is, under conditions in which Γ can be assumed to be always constant.[15] For example, the medium might be a solution of 0.1 mol dm−3 sodium nitrate or 3 mol dm−3 sodium perchlorate. When Γ is constant it may be ignored and the general expression in theory, above, is obtained.
All published stability constant values refer to the specific ionic medium used in their determination and different values are obtained with different conditions, as illustrated for the complex CuL (L =
When published constants refer to an ionic strength other than the one required for a particular application, they may be adjusted by means of specific ion theory (SIT) and other theories.[17]
Temperature dependence
All equilibrium constants vary with temperature according to the Van 't Hoff equation[18]
Alternatively
R is the
Factors affecting the stability constants of complexes
The chelate effect
Consider the two equilibria, in aqueous solution, between the copper(II) ion, Cu2+ and ethylenediamine (en) on the one hand and methylamine, MeNH2 on the other.
In the first reaction the
The thermodynamic approach to explaining the chelate effect considers the equilibrium constant for the reaction: the larger the equilibrium constant, the higher the concentration of the complex.
When the
The difference between the two stability constants is mainly due to the difference in the standard entropy change, ΔS⊖. In the reaction with the chelating ligand there are two particles on the left and one on the right, whereas in equation with the monodentate ligand there are three particles on the left and one on the right. This means that less entropy of disorder is lost when the chelate complex is formed than when the complex with monodentate ligands is formed. This is one of the factors contributing to the entropy difference. Other factors include solvation changes and ring formation. Some experimental data to illustrate the effect are shown in the following table.[19]
Equilibrium log β ΔG⊖ /kJ mol−1 ΔH⊖ /kJ mol−1 −TΔS⊖ /kJ mol−1 Cd2+ + 4 MeNH2 ⇌ Cd(MeNH
2)2+
46.55 −37.4 −57.3 19.9 Cd2+ + 2 en ⇌ Cd(en)2+
210.62 −60.67 −56.48 −4.19
These data show that the standard enthalpy changes are indeed approximately equal for the two reactions and that the main reason why the chelate complex is so much more stable is that the standard entropy term is much less unfavourable, indeed, it is favourable in this instance. In general it is difficult to account precisely for thermodynamic values in terms of changes in solution at the molecular level, but it is clear that the chelate effect is predominantly an effect of entropy. Other explanations, including that of Schwarzenbach,[20] are discussed in Greenwood and Earnshaw.[19]
The chelate effect increases as the number of chelate rings increases. For example, the complex [Ni(dien)2)]2+ is more stable than the complex [Ni(en)3)]2+; both complexes are octahedral with six nitrogen atoms around the nickel ion, but dien (
Deprotonation of aliphatic –OH groups
Removal of a
An important example occurs with the molecule tris. This molecule should be used with caution as a buffering agent as it will form chelate complexes with ions such as Fe3+ and Cu2+.
The macrocyclic effect
It was found that the stability of the complex of copper(II) with the
An important difference between macrocyclic ligands and open-chain (chelating) ligands is that they have selectivity for metal ions, based on the size of the cavity into which the metal ion is inserted when a complex is formed. For example, the
In
Cyclam | Porphine, the simplest porphyrin. |
Structures of common 18-crown-6, dibenzo-18-crown-6, and an aza-crown ether
|
Geometrical factors
Successive stepwise formation constants Kn in a series such as MLn (n = 1, 2, ...) usually decrease as n increases. Exceptions to this rule occur when the geometry of the MLn complexes is not the same for all members of the series. The classic example is the formation of the diamminesilver(I) complex [Ag(NH3)2]+ in aqueous solution.
In this case, K2 > K1. The reason for this is that, in aqueous solution, the ion written as Ag+ actually exists as the four-coordinate tetrahedral aqua species [Ag(H2O)4]+. The first step is then a substitution reaction involving the displacement of a bound water molecule by ammonia forming the tetrahedral complex [Ag(NH3)(H2O)3]+. In the second step, all the aqua ligands are lost and a linear, two-coordinate product [H3N–Ag–NH3]+ is formed. Examination of the thermodynamic data[25] shows that the difference in entropy change is the main contributor to the difference in stability constants for the two complexation reactions.
equilibrium | ΔH⊖ /kJ mol−1 | ΔS⊖ /J K−1 mol−1 |
---|---|---|
Ag+ + NH3 ⇌ [Ag(NH3)]+ | −21.4 | 8.66 |
[Ag(NH3)]+ + NH3 ⇌ [Ag(NH3)2]+ | −35.2 | −61.26 |
Other examples exist where the change is from octahedral to tetrahedral, as in the formation of [CoCl4]2− from [Co(H2O)6]2+.
Classification of metal ions
Ahrland, Chatt and Davies proposed that metal ions could be described as class A if they formed stronger complexes with ligands whose donor atoms are
The hardness of a metal ion increases with oxidation state. An example of this effect is given by the fact that Fe2+ tends to form stronger complexes with N-donor ligands than with O-donor ligands, but the opposite is true for Fe3+.
Effect of ionic radius
The Irving–Williams series refers to high-spin, octahedral, divalent metal ion of the first transition series. It places the stabilities of complexes in the order
- Mn < Fe < Co < Ni < Cu > Zn
This order was found to hold for a wide variety of ligands.[29] There are three strands to the explanation of the series.
- The ionic radius is expected to decrease regularly for Mn2+ to Zn2+. This would be the normal periodic trend and would account for the general increase in stability.
- The crystal field stabilisation energy (CFSE) increases from zero for manganese(II) to a maximum at nickel(II). This makes the complexes increasingly stable. CFSE returns to zero for zinc(II).
- Although the CFSE for copper(II) is less than for nickel(II), octahedral copper(II) complexes are subject to the Jahn–Teller effect which results in a complex having extra stability.
Another example of the effect of ionic radius the steady increase in stability of complexes with a given ligand along the series of trivalent lanthanide ions, an effect of the well-known lanthanide contraction.
Applications
Stability constant values are exploited in a wide variety of applications.
DTPA is also used as a complexing agent for
The selectivity of macrocyclic ligands can be used as a basis for the construction of an
Deferiprone | Penicillamine | triethylenetetramine, TETA | Ethylenediaminetetraacetic acid, EDTA |
Diethylenetriaminepentaacetic acid , DTPA
|
Valinomycin | Tri-n-butyl phosphate |
An
In all these examples, the ligand is chosen on the basis of the stability constants of the complexes formed. For example, TBP is used in nuclear fuel reprocessing because (among other reasons) it forms a complex strong enough for solvent extraction to take place, but weak enough that the complex can be destroyed by nitric acid to recover the uranyl cation as nitrato complexes, such as [UO2(NO3)4]2− back in the aqueous phase.
Supramolecular complexes
A typical application in molecular recognition involved the determination of formation constants for complexes formed between a tripodal substituted
An example of the use of supramolecular complexes in the development of chemosensors is provided by the use of transition-metal ensembles to sense for ATP.[33]
Anion complexation can be achieved by encapsulating the anion in a suitable cage. Selectivity can be engineered by designing the shape of the cage. For example, dicarboxylate anions could be encapsulated in the ellipsoidal cavity in a large macrocyclic structure containing two metal ions.[34]
Experimental methods
The method developed by Bjerrum is still the main method in use today, though the precision of the measurements has greatly increased. Most commonly, a solution containing the metal ion and the ligand in a medium of high
Other ion-selective electrodes (ISE) may be used. For example, a fluoride electrode may be used with the determination of stability complexes of fluoro-complexes of a metal ion.
It is not always possible to use an ISE. If that is the case, the titration can be monitored by other types of measurement.
The chemical model will include values of the protonation constants of the ligand, which will have been determined in separate experiments, a value for log Kw and estimates of the unknown stability constants of the complexes formed. These estimates are necessary because the calculation uses a non-linear least-squares algorithm. The estimates are usually obtained by reference to a chemically similar system. The stability constant databases[8][9] can be very useful in finding published stability constant values for related complexes.
In some simple cases the calculations can be done in a spreadsheet.[35] Otherwise, the calculations are performed with the aid of a general-purpose computer programs. The most frequently used programs are:
- Potentiometric and/or spectrophotometric data: PSEQUAD[36]
- Potentiometric data: HYPERQUAD,[37] BEST,[38] ReactLab pH PRO
- Spectrophotometric data: HypSpec, SQUAD,[39] SPECFIT,[40][41] ReactLab EQUILIBRIA.[42]
- NMR data HypNMR,[43] WINEQNMR2 Archived 2019-07-14 at the Wayback Machine[44]
In biochemistry, formation constants of adducts may be obtained from Isothermal titration calorimetry (ITC) measurements. This technique yields both the stability constant and the standard enthalpy change for the equilibrium.[45] It is mostly limited, by availability of software, to complexes of 1:1 stoichiometry.
Critically evaluated data
The following references are for critical reviews of published stability constants for various classes of ligands. All these reviews are published by
- ethylenediamine (en) [46]
- Nitrilotriacetic acid (NTA)[47]
- aminopolycarboxylic acids (complexones)[48]
- amino acids with polar side-chains[55]
- nucleotides[56]
- general[58]
- Chemical speciation of environmentally significant heavy metals with inorganic ligands. Part 1: The Hg2+–Cl−, OH−, CO2−
3, SO2−
4, and PO3−
4 systems.[59] - Chemical speciation of environmentally significant metals with inorganic ligands Part 2: The Cu2+–OH−, Cl−, CO2−
3, SO2−
4, and PO3−
4 aqueous systems[60] - Chemical speciation of environmentally significant metals with inorganic ligands Part 3: The Pb2+–OH−, Cl−, CO2−
3, SO2−
4, and PO3−
4 systems[61] - Chemical speciation of environmentally significant metals with inorganic ligands. Part 4: The Cd2+–OH−, Cl−, CO2−
3, SO2−
4, and PO3−
4 systems[62]
Databases
- The Ki Database is a public domain database of published binding affinities (Ki) of drugs and chemical compounds for receptors, neurotransmitter transporters, ion channels, and enzymes.
- BindingDB is a public domain database of measured binding affinities, focusing chiefly on the interactions of protein considered to be drug-targets with small, drug-like molecules
References
- ^ Bjerrum, J. (1941). Metal-ammine formation in aqueous solution. Copenhagen: Haase.
- ISBN 0-85312-143-5.
- ^ Rossotti, F. J. C.; Rossotti, H. (1961). The Determination of Stability Constants. McGraw–Hill.
- .
- ^ Ingri, N.; Sillen, L. G. (1964). "High-speed computers as a supplement to graphical methods, IV. An ALGOL version of LETAGROP-VRID". Arkiv för Kemi. 23: 97–121.
- PMID 18960446.
- PMID 18961420.
- ^ a b IUPAC SC-Database A comprehensive database of published data on equilibrium constants of metal complexes and ligands
- ^ a b NIST Standard Reference Database 46 NIST Critically Selected Stability Constants of Metal Complexes: Version 8.0 (This database has been discontinued.)
- ISBN 3-527-29482-1.
- .
- ISBN 0-306-31064-3.
- ^ Rossotti, F. J. C. (1960). "The thermodynamics of metal ion complex formation in solution". In Lewis, J.; R. G., Wilkins (eds.). Modern coordination chemistry. New York: Interscience.
- ISBN 0-85312-143-5. sections 3.5.1.2, 6.6.1 and 6.6.2
- ^ a b Rossotti, F. J. C.; Rossotti, H. (1961). "Chapter 2: Activity and Concentration Quotients". The Determination of Stability Constants. McGraw–Hill.
- ^ Gergely, A.; Nagypál, I.; E., Farkas (1974). "A réz(II)-aminosav törzskomplexek vizes oldatában lejátszodó protoncsere-reakciók kinetikájának NMR-vizsgálata" [NMR study of the proton exchange process in aqueous solutions of copper(II)-aminoacid parent complexes]. Magyar Kémiai Folyóirat. 80: 545–549.
- ^
"Project: Ionic Strength Corrections for Stability Constants". IUPAC. Archived from the originalon 2008-10-29. Retrieved 2008-11-23.
- ^
Atkins, P. W.; De Paula, J. (2006). "Section 7.4: The Response of Equilibria to Temperature". Physical Chemistry. Oxford University Press. ISBN 0-19-870072-5.
- ^ ISBN 978-0-08-037941-8. p. 910
- .
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- ISBN 0-521-40985-3.
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- ISBN 978-0-08-037941-8. p. 1100, Figure 25.7
- .
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- doi:10.1039/b107025h.
- ISBN 0-8131-1944-8.
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- S2CID 96018200.
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- ISBN 0-471-18896-4.
- ISBN 0-306-41957-2.
- PMID 18966661.
- ^ Martell, A. E.; Motekaitis, R. J. (1992). The determination and use of stability constants. Wiley-VCH.
- ISBN 0-306-41957-2.
- PMID 18963802.
- PMID 18963840.
- ^ Jplus Consulting Pty Ltd
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Further reading
Sigel, Roland K. O.; Skilandat, Miriam; Sigel, Astrid; Operschall, Bert P.; Sigel, Helmut (2013). "Chapter 8. Complex formation of cadmium with
Sóvágó, Imre; Várnagy, Katalin (2013). "Chapter 9. Cadmium(II) complexes of amino acids and peptides". In Sigel, Astrid; Sigel, Helmut; Sigel, Roland K. O. (eds.). Cadmium: From Toxicology to Essentiality. Metal Ions in Life Sciences. Vol. 11. Springer. pp. 275–302.
Yatsimirsky, Konstantin Borisovich; Vasilyev, Vladimir Pavlovich (1960). Instability Constants of Complex Compounds. Translated by Patterson, D. A. OUP.
External links
- Stability constants website: Contains information on computer programs, applications, databases and hardware for experimental titrations.