Journal of ISSN: 2473-0831 JAPLR

Analytical & Pharmaceutical Research
Opinion
Volume 3 Issue 7 - 2016
On Two Kinds of Equilibrium Constants in an Extraction System: Does an Interfacial Equilibrium Potential Control the Equilibrium Constant?
Yoshihiro Kudo*
Chiba University, Japan
Received: December 20, 2016| Published: December 22, 2016
*Corresponding author: Yoshihiro Kudo, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan, Fax: +81-43-290-2874; Tel: +81 43-290-2786; E-mail:
Citation: Kudo Y (2016) On Two Kinds of Equilibrium Constants in an Extraction System: Does an Interfacial Equilibrium Potential Control the Equilibrium Constant? J Anal Pharm Res 3(7): 00078. DOI: 10.15406/japlr.2016.03.00078

Abstract

Two kinds of equilibrium constants were discussed based on a thermodynamic cycle of overall extraction equilibrium. Consequently, it was clarified that the individual distribution constants of cation and anion into an organic (o) phase is controlled by an equilibrium potential at the water/o solution interface.

Keywords: Individual distribution constant; Interfacial equilibrium potential; Two kinds of equilibrium constants; Extraction constant; Dissociation of extracted ion pair

Abbreviations

O: Organic; Org: organic

Introduction

An extraction constant with the dissociation of the M L + A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbGaamitaSWdamaaCaaabeqaaKqzadWdbiabgUcaRaaa jugibiaadgeajuaGpaWaaWbaaSqabeaajugWa8qacqGHsislaaaaaa@3EE3@  ion pair has been defined as

K ex± = [ M L + ] o [ A ] o /( [ M + ] [ L ] o [ A ] ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGLbGaamiEaiab gglaXcWcpaqabaqcLbsapeGaeyypa0tcfa4damaadmaakeaajugib8 qacaWGnbGaamitaSWdamaaCaaabeqaaKqzadWdbiabgUcaRaaaaOWd aiaawUfacaGLDbaalmaaBaaabaqcLbmapeGaam4BaaWcpaqabaqcfa 4aamWaaOqaaKqzGeWdbiaadgeajuaGpaWaaWbaaSqabeaajugWa8qa cqGHsislaaaak8aacaGLBbGaayzxaaqcfa4aaSbaaKqaGfaajugWa8 qacaWGVbaal8aabeaajugib8qacaGGVaqcfa4damaabmaakeaajuaG daWadaGcbaqcLbsapeGaamytaSWdamaaCaaabeqaaKqzadWdbiabgU caRaaaaOWdaiaawUfacaGLDbaajuaGdaWadaGcbaqcLbsapeGaamit aaGcpaGaay5waiaaw2faaSWaaSbaaeaajugWa8qacaWGVbaal8aabe aajuaGdaWadaGcbaqcLbsapeGaamyqaKqba+aadaahaaWcbeqaaKqz adWdbiabgkHiTaaaaOWdaiaawUfacaGLDbaaaiaawIcacaGLPaaaaa a@6AA9@ (1)

in a molar concentration unit [1,2], where M + MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbWcpaWaaWbaaeqabaqcLbmapeGaey4kaScaaaaa@39C8@ , L, and A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGbbGcpaWaaWbaaSqabeaajugWa8qacqGHsislaaaaaa@39D1@  refer to a univalent metal ion, a ligand such as crown ethers, and a pairing anion as picrate and permanganate ions, respectively. This equation corresponds to the overall extraction equilibrium, M + +  L o +  A M L + o +  A o MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbWcpaWaaWbaaeqabaqcLbmapeGaey4kaScaaKqzGeGa ey4kaSIaaeiiaiaadYeajuaGpaWaaSbaaSqaaKqzadWdbiaad+gaaS WdaeqaaKqzGeWdbiabgUcaRiaabccacaWGbbWcpaWaaWbaaeqabaqc LbmapeGaeyOeI0caaKqzGeGaamytaiaadYeal8aadaahaaqabeaaju gWa8qacqGHRaWkaaWcpaWaaSbaaeaajugWa8qacaWGVbaal8aabeaa jugib8qacqGHRaWkcaqGGaGaamyqaSWdamaaCaaabeqaaKqzadWdbi abgkHiTaaal8aadaWgaaqaaKqzadWdbiaad+gaaSWdaeqaaaaa@5400@ [1,2], and is expressed by the product of K M/ML ( =  [ M L + ] o /[ M + ] [ L ] o ) with  K D,A (=  [ A ] o /[ A ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaajuaGdaqadaGcbaqcLbsapeGaeyypa0JaaeiiaK qba+aadaWadaGcbaqcLbsapeGaamytaiaadYeal8aadaahaaqabeaa jugWa8qacqGHRaWkaaaak8aacaGLBbGaayzxaaWcdaWgaaqaaKqzad Wdbiaad+gaaSWdaeqaaKqzGeWdbiaac+cajuaGpaWaamWaaOqaaKqz GeWdbiaad2eajuaGpaWaaWbaaSqabeaajugWa8qacqGHRaWkaaaak8 aacaGLBbGaayzxaaqcfa4aamWaaOqaaKqzGeWdbiaadYeaaOWdaiaa wUfacaGLDbaalmaaBaaabaqcLbmapeGaam4BaaWcpaqabaaakiaawI cacaGLPaaajugib8qacaqGGaGaam4DaiaadMgacaWG0bGaamiAaOGa aiiOaKqzGeGaam4saSWdamaaBaaabaqcLbmapeGaamiraiaacYcaca WGbbaal8aabeaajugibiaacIcapeGaeyypa0JaaeiiaKqba+aadaWa daGcbaqcLbsapeGaamyqaSWdamaaCaaabeqaaKqzadWdbiabgkHiTa aaaOWdaiaawUfacaGLDbaalmaaBaaabaqcLbmapeGaam4BaaWcpaqa baqcLbsapeGaai4laKqba+aadaWadaGcbaqcLbsapeGaamyqaKqba+ aadaahaaWcbeqaaKqzadWdbiabgkHiTaaaaOWdaiaawUfacaGLDbaa aaa@7903@  [1]:

K ex± = K M/ML × K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGLbGaamiEaiabggla XcWcpaqabaqcLbsapeGaeyypa0Jaam4saSWdamaaBaaabaqcLbmape Gaamytaiaac+cacaWGnbGaamitaaWcpaqabaqcLbsapeGaey41aqRa am4saSWdamaaBaaabaqcLbmapeGaamiraiaacYcacaWGbbaal8aabe aaaaa@4B5A@ (2)

at given values of ionic strength. The constants, K M/ML (= K D,M × K ML,org ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaajugibiaacIcapeGaeyypa0Jaam4saKqba+aada WgaaWcbaqcLbmapeGaamiraiaacYcacaWGnbaal8aabeaajugib8qa cqGHxdaTcaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaamitaiaacY cacaWGVbGaamOCaiaadEgaaSWdaeqaaKqzGeGaaiykaaaa@4F31@ and K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGebGaaiilaiaadgea aSWdaeqaaaaa@3B3C@ , are the functions of an interfacial equilibrium-potential difference ( Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@ ) [3,4] as follows:

log  K M/ML = ( F/2.303RT )(Δ ϕ eq Δ ϕ M 0 ' ) + log  K ML,org MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGSbGaam4BaiaadEgacaGGGcGaam4saSWdamaaBaaabaqc LbmapeGaamytaiaac+cacaWGnbGaamitaaWcpaqabaqcLbsapeGaey ypa0JaaeiiaKqba+aadaqadaGcbaqcLbsapeGaamOraiaac+cacaaI YaGaaiOlaiaaiodacaaIWaGaaG4maiaadkfacaWGubaak8aacaGLOa GaayzkaaqcLbsacaGGOaWdbiabgs5aejabew9aMTWdamaaBaaabaqc LbmapeGaamyzaiaadghaaSWdaeqaaKqzGeWdbiabgkHiTiabgs5aej abew9aMLqba+aadaWgaaWcbaqcLbmapeGaamytaaWcpaqabaWaaWba aeqabaqcLbmapeGaaGimaaaal8aadaahaaqabeaajugWaiaacEcaaa qcLbsacaGGPaWdbiaabccacqGHRaWkcaqGGaGaamiBaiaad+gacaWG NbGaaiiOaiaadUeajuaGpaWaaSbaaSqaaKqzadWdbiaad2eacaWGmb Gaaiilaiaad+gacaWGYbGaam4zaaWcpaqabaaaaa@6F68@      (3)

with

( F/2.303RT )(Δ ϕ eq Δ ϕ M 0 ' ) = log  K D,M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbaoaabmaake aajugibabaaaaaaaaapeGaamOraiaac+cacaaIYaGaaiOlaiaaioda caaIWaGaaG4maiaadkfacaWGubaak8aacaGLOaGaayzkaaqcLbsaca GGOaWdbiabgs5aejabew9aMTWdamaaBaaabaqcLbmapeGaamyzaiaa dghaaSWdaeqaaKqzGeWdbiabgkHiTiabgs5aejabew9aMTWdamaaBa aabaqcLbmapeGaamytaaWcpaqabaWaaWbaaeqabaqcLbmapeGaaGim aaaal8aadaahaaqabeaajugWaiaacEcaaaqcLbsacaGGPaWdbiaabc cacqGH9aqpcaqGGaGaamiBaiaad+gacaWGNbGccaGGGcqcLbsacaWG lbqcfa4damaaBaaaleaajugWa8qacaWGebGaaiilaiaad2eaaSWdae qaaaaa@6042@ (3a)

log  K D,A = ( F/2.303RT )(Δ ϕ eq Δ ϕ A 0 ' ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGSbGaam4BaiaadEgacaGGGcGaam4saKqba+aadaWgaaWc baqcLbmapeGaamiraiaacYcacaWGbbaal8aabeaajugib8qacqGH9a qpcaqGGaGaeyOeI0scfa4damaabmaakeaajugib8qacaWGgbGaai4l aiaaikdacaGGUaGaaG4maiaaicdacaaIZaGaamOuaiaadsfaaOWdai aawIcacaGLPaaajugibiaacIcapeGaeyiLdqKaeqy1dy2cpaWaaSba aeaajugWa8qacaWGLbGaamyCaaWcpaqabaqcLbsapeGaeyOeI0Iaey iLdqKaeqy1dy2cpaWaaSbaaeaajugWa8qacaWGbbaal8aabeaadaah aaqabeaajugWa8qacaaIWaaaaSWdamaaCaaabeqaaKqzadGaai4jaa aajugibiaacMcaaaa@6118@  [5]         (4)

  The symbols, K D,M , K D,A , K ML,org ,Δ ϕ M 0 ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGebGaaiilaiaa d2eaaSWdaeqaaKqzGeWdbiaacYcacaWGlbWcpaWaaSbaaeaajugWa8 qacaWGebGaaiilaiaadgeaaSWdaeqaaKqzGeWdbiaacYcacaWGlbqc fa4damaaBaaaleaajugWa8qacaWGnbGaamitaiaacYcacaWGVbGaam OCaiaadEgaaSWdaeqaaKqzGeWdbiaacYcacqGHuoarcqaHvpGzjuaG paWaaSbaaSqaaKqzadWdbiaad2eaaSWdaeqaamaaCaaabeqaaKqzad WdbiaaicdaaaWcpaWaaWbaaeqabaqcLbmacaGGNaaaaaaa@56D1@ , and Δ ϕ A 0 ' MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadgea aSWdaeqaamaaCaaabeqaaKqzadWdbiaaicdaaaWcpaWaaWbaaeqaba qcLbmacaGGNaaaaaaa@40DF@ , in Eqs. (3)-(4) denote the individual distribution constant, [ M + ] o /[ M + ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbaoaadmaake aajugibabaaaaaaaaapeGaamytaKqba+aadaahaaWcbeqaaKqzadWd biabgUcaRaaaaOWdaiaawUfacaGLDbaajuaGdaWgaaWcbaqcLbmape Gaam4BaaWcpaqabaqcLbsapeGaai4laKqba+aadaWadaGcbaqcLbsa peGaamytaKqba+aadaahaaWcbeqaaKqzadWdbiabgUcaRaaaaOWdai aawUfacaGLDbaaaaa@485E@ , of M + MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbWcpaWaaWbaaeqabaqcLbmapeGaey4kaScaaaaa@39C8@  into an o phase, that of A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGbbGcpaWaaWbaaSqabeaajugWa8qacqGHsislaaaaaa@39D1@  into the o phase, the complex formation constant, [ M L + ] o / [ M + ] o [ L ] o MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqbaoaadmaake aajugibabaaaaaaaaapeGaamytaiaadYeal8aadaahaaqabeaajugW a8qacqGHRaWkaaaak8aacaGLBbGaayzxaaWcdaWgaaqaaKqzadWdbi aad+gaaSWdaeqaaKqzGeWdbiaac+cajuaGpaWaamWaaOqaaKqzGeWd biaad2eajuaGpaWaaWbaaSqabeaajugWa8qacqGHRaWkaaaak8aaca GLBbGaayzxaaWcdaWgaaqaaKqzadWdbiaad+gaaSWdaeqaaKqbaoaa dmaakeaajugib8qacaWGmbaak8aacaGLBbGaayzxaaqcfa4aaSbaaS qaaKqzadWdbiaad+gaaSWdaeqaaaaa@51A4@ , for M L + MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbGaamitaKqba+aadaahaaqcbawabeaajugWa8qacqGH RaWkaaaaaa@3B86@  in the o phase ( Δ ϕ eq = 0 V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaajugib8qacqGH9aqpcaqGGaGaaGimaiaabccaca WGwbaaaa@424A@ because of the reaction in the homogeneous phase), a standard formal potential for the M + MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGnbWcpaWaaWbaaeqabaqcLbmapeGaey4kaScaaaaa@39C8@ transfer across the water/o solution interface, and that for A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGbbGcpaWaaWbaaSqabeaajugWa8qacqGHsislaaaaaa@39D1@  across the interface, respectively [3,4,6].

Combinations of the experimental K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaaaaa@3C25@  and K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGebGaaiilaiaadgea aSWdaeqaaaaa@3B3C@  values are infinite in the variation of Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@ . On the other hand, the combination of the K M/ML s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaadaahaaadbeqaaKqzadGaam4Caaaaaaa@3E79@ and K D,A s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKaaGbbaaaaaaa aapeGaam4saOWdamaaBaaajeaybaWdbiaadseacaGGSaGaamyqaaWd aeqaaSWaaWbaaWqabeaajugWaiaadohaaaaaaa@3CA5@  values which are defined as the K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaaaaa@3C25@  and K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGebGaaiilaiaadgea aSWdaeqaaaaa@3B3C@  ones at Δ ϕ eq = 0 V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaajugib8qacqGH9aqpcaqGGaGaaGimaiaabccaca WGwbaaaa@424A@  is only one. However, their products, Eq. (2), have to equal with each other by a compensation of the two Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@  terms between Eqs. (3) and (4) [4,6].

Also, Eq. (3) is showing us an interesting fact in an equilibrium condition of the extraction system. For example, the log K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaaaaa@3C25@ value is not generally equal to the log K M/ML s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaadaahaaadbeqaaKqzadGaam4Caaaaaaa@3E79@  one. This reason is because the K M/ML s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaadaahaaadbeqaaKqzadGaam4Caaaaaaa@3E79@  value is of the condition of Δ ϕ eq = 0 V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaajugib8qacqGH9aqpcaqGGaGaaGimaiaabccaca WGwbaaaa@424A@ , while the K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaaaaa@3C25@  ones are of that of certain Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@  values. The latter value (or also K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGebGaaiilaiaadgea aSWdaeqaaaaa@3B3C@ ) becomes a constant only under the condition that all the P,T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeGaamiuai aacYcacaWGubaaaa@38D8@  and Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@ values are fixed. That is, there are two kinds of equilibrium constants, K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaaaaa@3C25@  ( P,T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeGaamiuai aacYcacaWGubaaaa@38D8@ , Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@  = constant) and K M/ML s MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaai4laiaad2ea caWGmbaal8aabeaadaahaaadbeqaaKqzadGaam4Caaaaaaa@3E79@  ( P,T MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeGaamiuai aacYcacaWGubaaaa@38D8@ = constant) or K ML,org MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbWcpaWaaSbaaeaajugWa8qacaWGnbGaamitaiaacYca caWGVbGaamOCaiaadEgaaSWdaeqaaaaa@3E27@ , in the extraction system.

Moreover, this means that zero of the E ex± MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGfbWcpaWaaSbaaeaajugWa8qacaWGLbGaamiEaiabggla XcWcpaqabaaaaa@3CCC@ or Δ G ex± MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcaWGhbWcpaWaaSbaaeaajugWa8qacaWGLbGaamiE aiabgglaXcWcpaqabaaaaa@3E35@  value, which corresponds to the overall extraction system of Eq. (1) and is related with zF E ex ± 0 =RTln  K ex ± (=Δ G ex± 0 ) at  E ex ± = 0 V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHsislcaWG6bGaamOraiaadweal8aadaWgaaqaaKqzadWd biaadwgacaWG4baal8aabeaadaWgaaqaaKqzadWdbiabgglaXcWcpa qabaWaaWbaaeqabaqcLbmapeGaaGimaaaajugibiabg2da9iabgkHi TiaadkfacaWGubGaamiBaiaad6gajaaycaGGGcqcLbsacaWGlbWcpa WaaSbaaeaajugWa8qacaWGLbGaamiEaaWcpaqabaWaaSbaaeaajugW a8qacqGHXcqSaSWdaeqaaKqzGeGaaiika8qacqGH9aqpcqGHuoarca WGhbWcpaWaaSbaaeaajugWa8qacaWGLbGaamiEaiabgglaXcWcpaqa baWaaWbaaeqabaqcLbmapeGaaGimaaaajugib8aacaGGPaWdbiaabc cacaWGHbGaamiDaKaaGjaacckajugibiaadweal8aadaWgaaqaaKqz adWdbiaadwgacaWG4baal8aabeaadaWgaaqaaKqzadWdbiabgglaXc WcpaqabaqcLbsapeGaeyypa0JaaeiiaiaaicdacaqGGaGaamOvaaaa @7123@ , is not necessarily agreeable to zero of the Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbaal8aabeaaaaa@3DCA@  value at the water/o solution interface. In other words, the condition of

E ex± =Δ ϕ eq,M + (Δ ϕ eq,A ) = 0 V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGfbWcpaWaaSbaaeaajugWa8qacaWGLbGaamiEaiabggla XcWcpaqabaqcLbsapeGaeyypa0JaeyiLdqKaeqy1dywcfa4damaaBa aaleaajugWa8qacaWGLbGaamyCaiaacYcacaWGnbaal8aabeaajugi b8qacqGHRaWkcaqGGaWdaiaacIcapeGaeyOeI0IaeyiLdqKaeqy1dy wcfa4damaaBaaaleaajugWa8qacaWGLbGaamyCaiaacYcacaWGbbaa l8aabeaajugibiaacMcapeGaaeiiaiabg2da9iaabccacaaIWaGaae iiaiaadAfaaaa@5975@  (5)

Should be satisfied at the extraction equilibrium [3,4,6]. That is, the relation, Δ ϕ eq,M =Δ ϕ eq,A =Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbGaaiilaiaad2eaaSWdaeqaaKqzGeWdbiabg2da9iabgs5aej abew9aMLqba+aadaWgaaWcbaqcLbmapeGaamyzaiaadghacaGGSaGa amyqaaWcpaqabaqcLbsapeGaeyypa0JaeyiLdqKaeqy1dy2cpaWaaS baaeaajugWa8qacaWGLbGaamyCaaWcpaqabaaaaa@51DE@ , holds in the extraction system [3,4,6]. Here, the symbols, Δ ϕ eq,M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbGaaiilaiaad2eaaSWdaeqaaaaa@3F4C@  and Δ ϕ eq,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbGaaiilaiaadgeaaSWdaeqaaaaa@3F40@ , denote the Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzl8aadaWgaaqaaKqzadWdbiaadwgacaWG Xbaal8aabeaaaaa@3D3C@  value evaluated from the K D,M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGebGaaiilaiaa d2eaaSWdaeqaaaaa@3BD6@  and K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGebGaaiilaiaa dgeaaSWdaeqaaaaa@3BCA@  ones, respectively; the front sign of Δ ϕ eq,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzjuaGpaWaaSbaaSqaaKqzadWdbiaadwga caWGXbGaaiilaiaadgeaaSWdaeqaaaaa@3F40@ in Eq. (5) shows the formal charge of A− with the sign [5].

Conclusion

Consequently, we can see that the two kinds of equilibrium constants, K ML,org ( P,T ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGnbGaamitaiaa cYcacaWGVbGaamOCaiaadEgaaSWdaeqaaKqbaoaabmaakeaajugib8 qacaWGqbGaaiilaiaadsfaaOWdaiaawIcacaGLPaaaaaa@43EC@   K M/ML ( P,T,Δ ϕ eq ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGnbGaai4laiaa c2eacaGGmbaal8aabeaajuaGdaqadaGcbaqcLbsapeGaamiuaiaacY cacaWGubGaaiilaiabgs5aejabew9aMLqba+aadaWgaaWcbaqcLbma peGaamyzaiaadghaaSWdaeqaaaGccaGLOaGaayzkaaaaaa@49B9@ , are present in an extraction system at the same time. With respect to this fact, Δ ϕ eq MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacqGHuoarcqaHvpGzl8aadaWgaaqaaKqzadWdbiaadwgacaWG Xbaal8aabeaaaaa@3D3C@  controls magnitudes of K M/ML MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGnbGaai4laiaa c2eacaGGmbaal8aabeaaaaa@3CB1@  and K D,A MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaKqzGeaeaaaaaa aaa8qacaWGlbqcfa4damaaBaaaleaajugWa8qacaWGebGaaiilaiaa dgeaaSWdaeqaaaaa@3BCA@  at least.

References

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