• Goal

(a) preparative work: to purify (or partial purify) component (drugs, fuel, metals, chemical feedstocks)

特徵 : continuous operation; large in scale, etc.

(b) analytical goals: to generate information about the mixture; to eliminate the interference component for measurement.

Ch. 2 Basic concepts of separations

Giddings, J.C.; Unified Separation Science, John Wiley & Sons, Inc, 1991.

• Complete separation

(a+b+c+d)→(a)+(b)+(c)+(d)

• Partial separation

(a+b+c+d)→(a+b)+(b+a)

• 熱力學上的限制：(a) + (b) + (c) + (d) (a+b+c+d) (mixing)

(a) (a) (diffusion)

• 分離須進行搬運的動作 (包含兩部分 )

Bulk flow displacement

無分離作用(壓力、重力、離心力、電力 )

Relative displacement

具分離作用

Driving force of relative displacement: Eq.`

(1) Molecular equilibrium in a closed system1st law：

2nd law：

Gibbs free energy：

VPdW

WqdE

PdVTdSdE

WqWTdS

qTdST

qdS

SdTTdSVdPPdVdEdG

TdSPVETSHG

VdPSdTdG

TdSPdVdE

0

(2) Molecular equilibrium in open system

iidndG

jnPTii n

G

,,

iidnVdPSdTdG

μ： chemical potential

Two open system α,β

(α,β)： a closed system

at eq. , T , P constant

ii

iii dn

dGdGdG

0

0

(K： partition coefficient)

at eq.

RT

i

i

oi

i

i

oi

oi

oi

i

ioi

oi

ioii

oi

oi

eC

CK

RTC

C

C

CRT

CRTCRT

ln

ln

lnln

,,

,,

,,

ioii

ii

CRT ln

)( oi

ii

oi

oi

oi

oi

CC

,,

,, 0

Intermolecular force

• Ionic force

• Non-ion molecular interaction(1) dipole - dipole

(2) dipole - induced dipole

(3) induced dipole - induced dipole

(4) H – bonding

2r

qqcoulombs

E

Solvent extraction

Tech. phase 1 phase 2

Chromatography stationary mobile

LLE raffinate extractant

Dialysis retentate diffusate

← extractant

← raffinate(sample was dissolvent in)

q： fraction of solute extracted

1-q： fraction of solute unextracted

11

22

1.

2.

VW

VWor

VW

VW

C

CphaseinAconc

phaseinAconcK

A

A

raffraffA

extextA

raffA

extA

D

1

2

A

A

W

W

is the ratio of total amount (weight) of A in one phase to that in the 2nd phase

partition ratio ：(capacity factor)

phase ratio：

ext

raff

W

W1

q

qk

1

2

raff

ext

V

V

V

V

kKD

(1) Partition coefficient

(2)

(3)

(4)

1

2

rafft

ext 1

solute

solute

V

V

q

qkKD

kKVCVC

VCq

D

1

1

1

1

raffraffextext

extext

111

raffext

raff

ext

ext

k

k

VKV

VK

VKV

Vq

D

D

raffD

D

D

Kkq

Kk

1

1

1

1

1

11

D

D

K

Kq

操作模式

(3) Multiple contact (countercurrent extraction)

(2) Multiple contact (crosscurrent extraction)

(1)Single contact

Multiple extraction

extracted left

0 0 0

1st extract q 1-q

2nd q(1-q) 1-q-q(1-q)=(1-q)2

.......

N q(1-q)n-1 (1-q)n

11

1raffext

raff ifK

K

VKV

VKq

n

D

D

n

D

Dn

A solute with a partition coefficient of 4.0 is extracted from 10 mL of phase 1 into phase 2. (a) What volume of phase 2 is needed to extract 99% of solution in one extraction? (b) What volume of phase 2 is needed to remove 99% of solution in three equal extractions instead?

Effect of pH value on extraction

KD ─→ D ( distribution coeff. )

H

K1K

K1

HKH

K1

H

K1

D

HA

AHK

HAHA

HAA1

HA

AHA

extractantinsoluteofformallofconc.

raffinateinsoluteofformallofconc.D

aD

D

a

D

a

a

aqo

aqaq

o

aqaq

HAo

org.

aq.

HAaq + H2O

H3O+ + A-

H

KHKD a

D

(b) at pH

D

a

2KD

KH

(a) very acid [H+] >>Ka D=KD

(c) [H+] <<Ka

D >>KD H

KKD a

D

Effect of pH value on extraction

KD ─→ D ( distribution coeff. )

Bo

org.

aq.

BH+

aq H+ + B

a

D

a

aqo

aqaq

o

aqaq

KK

1

H1

D

BH

BHK

BB

BB1

B

BB

extractantinsoluteofformallofconc.

raffinateinsoluteofformallofconc.D

DDaa KHKKK

HH

(b) at pH

2/KD

KH

D

a

(a) very acid [H+] >>Ka D >> KD

(c) [H+] <<Ka

DKD

a

a

K

K D

HKD

Suppose that the partition coefficient for an amine, B, is 0.33 and the acid dissociation constant of BH+ is Ka=1.0x10-9. If 50 mL of 0.010M aqueous amine is extracted with 100 mL of solvent. What will be the formal concentration remaining in the aqueous phase (a) at pH 10.0? (b) 8.0?

ApplicationExtraction of metal ions

H++HL

HL

+ Mn+ MLn

MLn

organic phase (ionic liquid)

aqueous phase

L-Ka

nL-Kf

加入 chelator (HL)

HL (aq) HL (o)

)(

)(

1aq

od HL

HLK (1)

HL (aq)+ H2O H3O+(aq) +L-

(aq)

aq

a HLLOH

K

3

(2)

Mn+(aq)+ nL-

(aq) MLn(aq)

)()(

)(

aqnaq

aqf LM

MLK (3)

MLn(o)MLn(aq)

)(

)(

2aqn

ond HL

HLK

(4)

→ HL, MLn在有機相中溶解度大,

1dK2dK >>1

→ [L-] is pH dependent

n(aq)

M

nML

n(aq)MLn(aq)

M

nML

aqCoCD

CL： orignal molar conc. of HL in organic phase mass balance

n(o)n(aq)(aq)(aq)(o)L MLnMLnLHLHLC

(5)

→ excess chelator CL≈[HL(o)] (6)

(3)(4)

naq

naqdfon

n

aqnaq

ondf

LMKKML

LM

HLKK

)()()(

)()(

)(

2

2

naq

n

Lexn

aq

n

Ln

d

n

adf

aq

o

OH

CK

OH

C

K

KKK

CC

D

代入

)(3)(31

1

)7()6(

代入 (5) naqdf

aq

o LKKCC

D )(2(6)

)(3)(3

)()(

11)1()2(

aq

L

d

a

aq

o

d

aaq OH

CKK

OH

HL

KK

L (7)