Thermodynamics & Properties LAB

Model for Mixed-Electrolyte, Aqueous Mixed-Solvent Systems

(Ind. Eng. Chem. Res. 1996)

2001. 07. 07

Lee Yunmi

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Introduction

Debye- Hückel for dilute electrolyte solution

Pitzer (1973) Single salt aqueous system

Bromley (1973) 2 ionic constants for each ion 1salt parameter, extend to mixed- electrolyte

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Introduction

Meissner (1972) 1 salt parameter, extended to mixed-electrolyte extrapolated to high concentration

Chen, Evans (1986) NRTL term + D-H term ; nonidealities 2 parameters

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Introduction

Gibbs function D-H term + short range interaction term NRTL : Cruz and Renon (1978)

Chen et al (1982), Mock et al (1986) UNIFAC : Kikic et al (1991)

Achard et al (1994) UNIQUAC : Polka et al (1994), Li et al(1994)

Macedo et al (1990), Sandler (1986)

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Introduction

Different models for solute and solvent

In this work, unified model for mixed solute and mixed

solvent system : short range : electrostatic interaction ,

non-electrostatic interaction

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Excess Gibbs Function Model

D-H term

by De M.Cardoso and O’Connell (1987)

+−+−=

2)()1ln(

4

2

3* aKaKaK

NaRTVG

a

EDH π

+

−−+=)1(22

)1ln(4

ln 3, aKaKaKaK

NaV

a

jjDH π

γ For Solvent

)1()(

16ln

3

3*

, aKaK

INazz

a

iiiDH +

−= −+± π

γ For Solute

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Excess Gibbs Function Model

Short-range interaction term segment number , surface area parameter,

nonelectrostatic interaction energy parameter from Helmholtz function

new lattice-hole theroy (Yoo et al 1995) A ≅ GE (Wong and Sandler, 1992)

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Excess Gibbs Function Model

atermal contribution in symmetric convention

residual contribution of UNIQUAC

ER

EA

E GGG +=

−+=

iM

iMii

i

ii

E

qrrqqNz

xNG ln

21ln θβ

−= )ln(2 jiji

qE zNG τθθβ

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Excess Gibbs Function Model

Solvent Activity coefficients

jM

jMj

j

jjA qr

rqzrx

ln2

1lnln ,

−+=

θγ

( )

−−=

kl

lkl

jkkkjk

jjR

zqτθ

τθτθγ ln1

2ln ,

jRjAjDHj ,,, lnlnlnln γγγγ ++=

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Excess Gibbs Function Model

osmotic coefficient :

solute activity coefficient

±−=salt

kkkiisol nxn νγφ /ln

MM

MM

i

ii

ii

iiiiA rq

rqvrz

xx

∞

∞

±∞

∞

±±

−+= ln

21lnln *

,ν

θθ

ννγ

−+=

∞

∞

∞±

±

lkjk

ijj

lkjk

ijj

jij

jij

i

iiiR

qzτθ

τθτθ

τθτθτθ

ννγ ln

2ln *

,

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Excess Gibbs Function Model

Interaction between ions interaction with uncharged species

• nonelectrostatic interaction

Parameters : molecular ( ), ions ( ), by Robinson and Stokes 1955 data

)()( nij

eijij εεε +=

)(nijij εε =

)1()( 2/1)()()(ij

njj

nii

nij k−= εεε

iiir ε,isisiii rrr −+ ,, ,,,ε

ijk

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parameters

Thermodynamics & Properties LAB

Single Electrolyte Aqueous Systems

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Mixed Elecrolyte Aqueous System

Thermodynamics & Properties LAB

Mixed Electrolyte Aqueous System

Thermodynamics & Properties LAB

Mixed Electrolyte Aqueous System

Thermodynamics & Properties LAB

Conclusion

A unified excess Gibbs function moldel for mixed-electrolyte mixed-solvent system

Short range interaction term : new lattice-hole Helmholtz free energy

2 parameters for solvent, 3 parameters for each ionic species