extraction (equilibrium) constant

https://doi.org/10.1351/goldbook.E02304
The @E02301@ constant at zero @I03180@, \(K_{\textrm{ex}}^{\textrm{0}}\), is the @E02177@ of the distribution reaction expressed in terms of the reacting species. Thus, for the gross reaction: \[\textrm{M}_{aq}^{n+} + n\textrm{HL}_{org} \rightleftharpoons \textrm{ML}_{n,org} + n\textrm{H}_{aq}^{+}\] in which the @R05190@ HL initially dissolved in an organic phase reacts with a metal ion Mn in aqueous solution to form a product MLn which is more soluble in the organic phase than in water, \[K_{\textrm{ex}}^{\textrm{0}} = \frac{a_{\textrm{ML } n,org}\hspace{2pt}a_{\textrm{H}^{+},aq}^{n}}{a_{\textrm{M}^{n+},aq}\hspace{2pt}a_{\textrm{HL },aq}^{n}}\]
Notes:
  1. When concentrations are used instead of activities or mixed terms are employed as when H+ and/or Mn are measured with an electrode, the appropriate name is @E02301@ constant, symbol \(K_{\textrm{ex}}\), accompanied by a careful definition. \(K_{\textrm{ex}}^{\textrm{0}}\) may be termed the thermodynamic @E02301@ constant.
  2. The @E02301@ constant is related to other terms relevant to such systems by: \[K_{\textrm{ex}}^{0} = \frac{D_{\textrm{ML},n}\beta_{n}K_{a}^{n}}{D_{\textrm{HL}}^{n}}\] where \(\beta_{n}\) is the overall @F02485@ of MLn and \(K_{a}\) is the @D01801@ constant of HL. Where the @R05190@HL is more soluble in water than the other immiscible phase it may be more convenient to define a special @E02177@ in terms of HLaq: \[K_{\textrm{ex}}^{0} = D_{\textrm{ML},n}\beta_{n}K_{a}^{n}\]
  3. In distribution equilibria involving non-aqueous systems, e.g. liquid SO2, molten salts and metals, the mass action @E02177@ for the relevant @E02301@ process can be identified with \(K_{\textrm{ex}}\) which should be explicitly defined in this context.
  4. In actual practice, it may be necessary to include other terms to take into account other complexes formed by auxiliary reagents and the @S05747@ and/or @P04740@ of the various species. In such cases, \(K_{\textrm{ex}}\) must be defined with reference to the relevant explicit chemical equation. An example is complex formation between the metal ion and an uncharged @C01421@ ether or @C01426@ molecule followed by ion-pair @E02301@: \[\textrm{M}_{aq}^{n+} + \textrm{L}_{org} + n\textrm{A}_{aq}^{-} \rightleftharpoons \left ( \textrm{ML}^{n+}.\textrm{A}_{n}^{n-} \right )_{org}\] \[K_{ex} = \frac{\left [ \textrm{ML}^{n+}.\textrm{A}_{n}^{n-} \right ]_{org}}{\left [ \textrm{M}^{n+} \right ]_{aq}\left [ L \right ]_{org}\left [ A^{-} \right ]_{aq}^{n}}\]
  5. Use of Ringbom's 'conditional @E02301@ constant', \[K_{\textrm{ex}}^{\textrm{eff}} = \frac{ a_{\textrm{H}^{+}}^{n^{n}} \left [ \textrm{ML}^{n+}.\textrm{A}_{n}^{n-} \right ]_{org}}{\left [ \textrm{M}^{'} \right ]_{aq}\left [ \textrm{HL}^{'} \right ]_{org}^{n}}\] in conjunction with alpha coefficients is useful.
  6. The phases can also be specified by the formula of the solvent or by other symbols (preferably Roman numerals) or by overlining formulae referring to one phase, usually the less polar one. The subscript aq (or w) is often omitted; aq is preferable to w as the latter is appropriate only in English and German.
  7. The qualification 'equilibrium' is often omitted.
  8. The terms @P04438@ and @D01813@ must not be used in this sense.
Sources:
Orange Book, 2nd ed., p. 89 [Terms]
PAC, 1993, 65, 2373. (Nomenclature for liquid-liquid distribution (solvent extraction) (IUPAC Recommendations 1993)) on page 2383 [Terms] [Paper]