Excess Properties

2001. 2. 16Kwon Jung Hun

Thermodynamics and properties

ContentsI. Behavior of Excess Properties of Liquid Mixtures

1. Excess Gibbs energyExcess enthalpy • • • • relationsExcess entropy

2. Definitions of Regions on the vs. Diagram

II. Wohl’s Expansion for the Excess Gibbs Energyvan Laar Equation, Margules Equation …

III. Wilson, NRTL, and UNIQUAC Equations

ĝ ĥ

Thermodynamics and properties

I. Behavior of Excess Properties 1. Excess Gibbs energy, Excess enthalpy, Excess

entropy are related by

EEE Tshg −=

Rs

RTh

RTg EEE −=

XP

EE

TRTgT

RTh

,

)/(

∂

∂−=

Thermodynamics and properties

Definitions of Regions on the vs. Diagram

For convenience,

at

• 액체혼합물의 과잉물성과 상대적 크기들은 공학적목적이나 관찰된 용액의 거동을 근거로 분자현상을규명하는데 유용하게 쓰인다.

ĝ ĥ

Rcc

RssRThh

RTgg

EP

E

E

E

/ˆ

/ˆ/ˆ/ˆ

≡

≡≡

≡

5.021 == xx

Thermodynamics and properties

Definitions of Regions(I~VI) Definitions of Regions on the vs. Diagramĝ ĥ

Thermodynamics and properties

50°C 의 6성분계과잉물성(a) 클로로포름(1)/n-헵탄(2) (b) 아세톤(1)/메탄올(2)(c) 아세톤(1)/ 클로로포름(1) (d) 에탄올(1)/ n-헵탄(2) (e) 에탄올(1)/ 클로로포름(2) (f) 에탄올(1)/ 물(2)

Thermodynamics and properties

Trends for equimolar mixtures( 298K의 2성분계 )

[그림설명]

: NP/NP 혼합물: NA/NP 혼합물: AS/NP 혼합물: AS/NA 혼합물과

AS/AS 혼합물: 용매화 NA/NA

혼합물

Thermodynamics and properties

II. Wohl’s Expansion for the Excess Gibbs Energy

Wohl’s Expansion

van Laar Equation

22

211122

32112222

311112

221122

22

111221122211

6443

32)(

zzazzazzazza

zzazzaqxqxRT

g E

++++

+=+

2211

222

2211

111 , qxqx

qxzqxqx

qxz+

=+

=

2211

2121122qxqxqqxxa

RTgE

+=

Thermodynamics and properties

Wohl’s Expansion

Margules Equation

Scatchard-Hamer Equation

41

31

22

42

32

221

')'38'()'2'

23'(ln

'''ln

xCxCBxCBA

xCxBxA

++−++=

++=

γ

γ

31

1

221

1

22

32

221

)('))('23'(ln

''ln

zvvBz

vvBA

zBzA

−+=

+=

γ

γ

Thermodynamics and properties

III. Wilson, NRTL,and UNIQUAC Equations

(1) Wilson Equation* 개념 … 각 성분 분자 주위의 국부적 환경이 용액

내의 거시적인 몰용액의 특성과 다름

* 완전 혼합 용액에서 적용 가능

)ln()ln( 1212221211 xxxxxxRTg E Λ+−Λ+−=

)()ln(ln1212

21

2121

12221211 xxxx

xxxΛ+

Λ−Λ+

Λ+Λ+−=γ

)()ln(ln1212

21

2121

12112122 xxxx

xxxΛ+

Λ−Λ+

Λ−Λ+−=γ

)exp( 11121

212 RT

λλυυ −−=Λ )exp( 2221

12

121 RT

λλυυ −−=Λ

Thermodynamics and properties

(2) NRTL Equation

* 완전한 혼합 성계와 불완전한 혼합의 적용

)(1212

1212

2121

212121 Gxx

GGxx

GxxRTg E

++

+= ττ

RTgg 1121

21−=τ

RTgg 2212

12−=τ

)exp( 211221 τα−=G)exp( 121212 τα−=G

))(

)((ln 21212

12122

2121

2121

221 Gxx

GGxx

Gx+

++

= ττγ

))(

)((ln 22121

21212

1212

1212

212 Gxx

GGxx

Gx+

++

= ττγ

Thermodynamics and properties

Wilson Equation과 NRTL Equation의비교[ system : ethanol(1) / water(2) ]

Thermodynamics and properties

Wilson Equation과 NRTL Equation의비교

Thermodynamics and properties

Wilson Equation과 NRTL Equation의비교

Excess property

-800.00

-600.00

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1000.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

x1

GE

HE

TSE

Thermodynamics and properties

Wilson Equation과 NRTL Equation의비교

energy change of mixing

-1200.00

-1000.00

-800.00

-600.00

-400.00

-200.00

0.00

200.00

400.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

delta H

delta G

delta S

Thermodynamics and properties

(3) UNIQUAC Equation

* 극성 , 무극성 , partial miscible mixture에서도 적용* 단지 2개의 ajustable parameter만으로도 대부분의경우에 잘 만족시킴

residual

E

ialcombinator

EE

RTg

RTg

RTg

+

=

Φ

+Φ

+Φ+Φ=

*2

222*

1

111

2

*2

21

*1

1 lnln2lnln θθ qxqxz

xx

xx

RTg

ialcombinator

E

)ln()ln( 12'

1'2

'2221

'2

'1

'11 τθθτθθ +−+−=

qxqx

RTg

residual

E

Thermodynamics and properties

[ The definitions of parameters ]

2211

22*2 rxrx

rx+

=Φ2211

11*1 rxrx

rx+

=Φ

2211

222 qxqx

qx+

=θ221111

1 qxqxqx

+=θ

'22

'11

'11'

1 qxqxqx

+=θ '

22'11

'22'

2 qxqxqx

+=θ

)exp()exp( 121212 Ta

RTu −≡Δ−=τ )exp()exp( 212121 T

aRTu −≡Δ−=τ

Thermodynamics and properties

UNIQUAC Equation

+

−+

++−

−Φ+

Φ+Φ=

12'

1'2

12

21'2

'1

21'1

'221

'2

'1

'12

2

11

*2*

1

11

1

*1

1 )ln(ln2lnln

τθθτ

τθθτθτθθθγ qql

rrlqz

x

+

−+

++−

−Φ+

Φ+Φ=

21'2

'1

21

12'

1'2

12'2

'112

'1

'2

'21

1

22

*2*

2

22

2

*2

2 )ln(ln2lnln

τθθτ

τθθτθτθθθγ qql

rrlqz

x

)1()(2 1111

−−−= rqrzl )1()(2 2222

−−−= rqrzl

[ Merits of UNIQUAC Equation ] ... (relative) simplicity

only two ajustable parameter

wide range of applicability

Thermodynamics and properties

[참고] Activity models