Stability Constant

5 Key excerpts on "Stability Constant"

• 

  eBook - ePub

  Introduction to Coordination Chemistry

  • Geoffrey A. Lawrance(Author)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  K values under non-ideal (in a thermodynamic sense) conditions, the term ‘constant’ here is not absolutely correct, as discussed above. Remember that it is defined only under the particular experimental conditions employed in reality, although it is fairly true to say that the value varies in only a limited way across the range of conditions that we are most likely to apply.

  There is also a direct relationship between the Stability Constant and the free energy (ΔG 0 , in kJ mol−1 ) of a reaction, expressed in terms of the relationship (5.6):

  (5.6)

  where R is the gas constant and T the temperature in Kelvin. This means that the higher is K , the more negative is the free energy of the reaction. We feel this usually as a release of heat on complexation, because of the relationship between free energy and reaction enthalpy (ΔH 0 ) and reaction entropy (ΔS 0 ), namely (5.7):

  (5.7)

  Examination of Equation (5.5) shows that a large value of K means a high concentration of MLn+ relative to Mn+ and L; in other words, a large K means a strong preference for complex formation. The size of K with metal complexes is usually so large that we tend to report log10 K values, for ease of use; obviously, it’s simply easier to refer to a (log) K of 7.5 rather than a K of 3.16 × 107 .

  In this discussion, we shall also meet another closely related type of Stability Constant, the overall Stability Constant (β), which represents the stability for a set of sequential complexation steps, rather than for an individual component step. It allows us to represent, for example, the Stability Constant for an overall reaction M + n L forming MLn , rather than just for a single ligand addition step such as M + L forming ML. As for K

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Modern Aspects of Rare Earths and their Complexes

  • Vinny R. Sastri, J.R. Perumareddi, V. Ramachandra Rao, G.V.S. Rayudu, J.-C. G. Bünzli(Authors)
  • 2003(Publication Date)
  • Elsevier Science

    (Publisher)

  chapter 3

  STABILITY OF COMPLEXES

  CONTENTS

  1 Methods

  2 Stability of rare earth complexes in solution

  3 Thermodynamic considerations

  4 Stability of macrocyclic complexes

  5 Double–double effect

  6 Applications

  References

  Appendix

  Stability Constants of complexes may be determined by: (i) kinetic and (ii) equilibrium methods. In the present discussion, attention will be focused on mononuclear complexes and the fact that the activity coefficients of all the species can be held effectively constant by using suitable ionic media. The kinetic approach is applicable when: (i) the rates of formation and dissociation of a complex are sufficiently slow and (ii) accessible to experimental measurement by suitable techniques. Using the law of mass equation

  the above gives the Stability Constant provided: (i) there is only one species in solution and (ii) there is only one rate-determining step involved. The ratio of forward and reverse reaction rate constants of a general nature may be written as [1 ]

  and similarly we may write

  The kinetic approach is of restricted utility because it is applicable to: (i) slow reactions, (ii) some transition metal ions, (iii) the role played by the electronic structure of the central metal ion. The equilibrium approach is more convenient than the kinetic approach and hence discussed here in a detailed manner. In general when a metal M complexes with a ligand A and forms complexes of the type MA, MA1 … MAN we may write for the total concentrations of M and A as

  (3.1)

  (3.2)

  provided mononuclear complexes are formed and the terms ‘m ’ and ‘a ’ represent the free concentrations of metal ion and ligand, respectively.

  When the system is inert or made inert, the equilibrium concentrations of some or all the species in solution can be determined analytically and hence the Stability Constants evaluated. In labile systems, free concentrations of metal ions may be determined by potentiometry or polarography and hydrogen ions and many anions by potentiometry. When there is a distinct difference in colors of the solutions, such as complexes with chromophores, UV-vis spectroscopy may be used in the determination of the equilibrium concentration of one of the species. Competitive reaction technique may also be used to determine free concentrations of metal (m ) and ligand (a ). Knowledge of the values of ‘m ’ and ‘a

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Supramolecular Chemistry

  From Concepts to Applications

  • Stefan Kubik(Author)
  • 2020(Publication Date)
  • De Gruyter

    (Publisher)

  This efficiency is described in quantitative terms by + R S C + Figure 2.1: Schematic representation of the complexation of a substrate S by a structurally complementary receptor R and the respective reaction scheme. https://doi.org/10.1515/9783110595611-002 using K a , the stability or association constant, which results from the law of mass action according to the following equation. K a = c C c R c S (2 : 1) Note that equation (2.1) specifies the amounts of receptor, substrate, and complex in concentrations ( c R , c S , c C ) instead of dimensionless activities. This is more practi-cal since activity constants are usually not available for the species involved in binding equilibria. The approximation of using concentrations is even justified to some extent because binding equilibria are often investigated in dilute solutions, but it causes the resulting Stability Constants to have dimensions. Stability con-stants associated with 1:1 equilibria, for example, have units of M − 1 (L/mol) because the denominator in equation (2.1) contains a product of two concentrations. Supramolecular chemists prefer the use of Stability Constants to characterize binding equilibria, maybe because there is a direct correlation between magnitude and stability: the larger the K a the more stable the respective complex. In biochemis-try, binding efficiency is usually denoted in terms of dissociation constants K d , which are the reciprocal values of Stability Constants ( K d = K -1 a ). Thus, K d is expressed in units of M (mol/L) and becomes smaller with increasing complex stability. No matter which value one prefers, K a and K d belong to the key thermodynamic parameters to describe the stability of supramolecular complexes. They are charac-teristic for every receptor – substrate combination, but depend strongly on external influences such as temperature or solvent.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  An Introduction to Co-Ordination Chemistry

  International Series of Monographs in Inorganic Chemistry

  • D. P. Graddon, H. Taube, A. G. Maddock(Authors)
  • 2017(Publication Date)
  • Pergamon

    (Publisher)

  85 86 AN INTRODUCTION TO CO-ORDINATION CHEMISTRY The constants /:,, &,,... , k n are the successive Stability Constants of the system. For statistical reasons and because of the repulsion of a co-ordinated ligand for an incoming ligand of similar type the values of these constants nearly always decrease in the order k A > k 2 > k :i > . . . k n as in the examples in Table 1. TABLE 1. SUCCESSIVE AND OVERALL FORMATION CONSTANTS! System Hg 2 +/Br-Cd 2+ /I~ Ni 2+ /NH :{ Zn 2+ /en Co 2+ /glycinate Th 4+ /oxinate log£, 8-9 2-4 2-8 6 0 4-6 10-5 log L· 7-9 1-0 2-0 4-8 3-8 100 log k :i 2-3 1-6 1-7 2-2 2-4 9-5 log k 4 1-7 1-1 1-3 8-9 log* 5 0-7 log k H 0-4 Overall log/3 4 =20-8 logjS 4 = 6-1 log j8 e = 8-9 log ft = 13-0 log ft = 10-8 l o g f t -3 8 -9 tData throughout this chapter are taken from Stability Constants, published by the Chemical Society, London (1964). For many systems numerous conflicting results are given, and there is no uniform basis of solvent conditions for comparison. Where possible, data have been chosen corresponding to ionic strength zero, but the choice has been made arbitrarily, and some of the doubt about the validity of the data eliminated by rounding off to one decimal point. The product of the successive Stability Constants: / v / v / / [ML„] * , χ * , χ * , . . . * „ = [MiOH2)ii]x[Lr =ß is the overall Stability Constant of the system and is commonly used as a general guide to the stability of the complex in this sense. Values of the overall Stability Constant may cover a very wide range: for extremely stable complexes, such as theferrocyanide ion, [Fe(CN) 6 ] 4 ~, values greater than 10 30 may occur and for very unstable complexes ß may even be less than unity; on account of this wide range the values of the constants are frequently quoted on a logarithmic scale. As a rough guide, a value of log ß greater than about 8 represents what we should normally think of as a stable complex.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Chemical Thermodynamics of Zirconium

  • OECD, Federico J. Mompean(Authors)
  • 2005(Publication Date)
  • Elsevier Science

    (Publisher)

  22 // Standards, Conventions, and contents of the Tables periments, the formation constants of metal ion complexes are determined by adding a ligand in its protonated form to a metal ion solution. The complex formation reactions thus involve a deprotonation reaction of the ligand. If this is the case, the equilibrium constant is supplied with an asterisk, as shown in Eqs.(II.13) and (11.14) for mononu-clear and in Eq.(II.15) for polynuclear complexes. K, = ^ 1 ^ (11.13) . [ML T H + T M + oHL ^ ML ff + oH + B = ± '-^= —=L- (II. 14) H [M][HLf (11.15) * q -[M]'[HL]' Example: UOf +HF(aq) ^ UO 2 F + +H + K t = ft (aq)] f +5H 2 O(1) ^ (UO 2 ),(OH) 5 + +5H + Note that an asterisk is only assigned to the formation constant if the proto-nated ligand that is added is deprotonated during the reaction. If a protonated ligand is added and coordinated as such to the metal ion, the asterisk is to be omitted, as shown in ( , ) M + qW,L — M(H r L)<7 p = ^ — ii . (II. 16) [M][H,.L]' Example: UOf +3H 2 PO ^ UO 2 (H 2 PO 4 )-Pi II.1.6.3 Solubility constants Conventionally, equilibrium constants involving a solid compound are denoted as sol-ubility constants rather than as formation constants of the solid. An index s to the equilibrium constant indicates that the constant refers to a solubility process, as shown inEqs.(II.17)to(II.19) //. 1 Symbols, terminology and nomenclature 23 M a h b (s) ^ aU + bL K sfi = [M] a [L] h . (II. 17) K s0 is the conventional solubility product, and the subscript 0 indicates that the equilibrium reaction involves only uncomplexed aqueous species. If the solubility constant includes the formation of aqueous complexes, a notation analogous to that of Eq.(II.12) is used: Example: UO 2 F 2 (cr) — UO 2 F + + F K sXl = K st = [ U O 2 F + ] [ F ] .

  Sign up to read

  Learn more about book