Excess Properties 2001. 2. 16 Kwon Jung Hun
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