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8/13/2019 Excess Function
1/21
TERMODINAMIKAMATERIAL
Helena Septian (1206239182)
David Jendra (1206238803)
TEKNIK
METALURGI &MATERIAL FTUI
SAP 9
Campuran Termodinamik:
Larutan Ideal dan Non Ideal
Excess FunctionLarutan Reguler
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Lautan Ideal
Pada pencampuran, asumsi larutan campuran
yang ideal mencakup
Antara terlarut dan pelarut tidak terpisahkan
Pembentukan komposisi
mengikuti hukum Raoult
Efek temperatur dan volume
ketika pencampuran dapatdiabaikan
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Lautan Ideal
Karakter General dari Larutan campuran (Ideal)
0mix
V(1) 0mix H(2)
0mix
S(3) 0mix
G(4)
BB
*
BB xkxpp
x xkp
*
B
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Lautan Ideal
Chemical Potential pada Larutan campuran
B
*
BBln),( xRTpT
B B B B( ) ln d
p
pT RT x V p $
$
atau
(1)
(2)
B B B( ) lnT RT x $
Hal ini merupalan ekpresi untuk
chemical potential dari pencampuran
larutran (Mixing Solution)
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Lautan Non Ideal
Pada Larutan nonideal , hukum Raoult
harus terlebih dahulu dimofidikasi
Konsep Aktivitas pada larutan non ideal
BB
*
BB xpp
,B ,B Bx xa x BB,B
,B11
B
lim( ) 1lim xxxx
ax
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Merupakan aktivitas relatif dengan
dimensi 1
Merupakan faktor aktivitas, berfungsi
untuk menentukan kedekatan lautan terhadaplaurtan ideal, dengan dimensi 1
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Menetukan chemical potential
larutan noniedal
(1) gunakan fraksi mol xBuntuk
menyatakan konsentrasi
B B B ,BB ln( / ) ( ) ln ( / ) lnx xRT p p T RT k p RT a $ $ $ $
*
B ,B= ( , ) ln xT p RT a
Dimana 1,1,1 B,B,B
xx
ax
Dengan kondisi T,
P
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(2) gunakan fraksi mol untuk menyatakan
konsentrasi
B ,BB
**
B ,B
( ) ln ln
( , ) ln
mm
mT
k mT RT
p R
R a
T a
Tp
$
$$
Bm,B m,B
m
ma
$
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adalah chemical potentialdari hipotesus yang masihmengikuti hukum Raoult ketika
**
B ( , )T p
B m,B m,B, 1, 1m m a $
Dalam kondisi TP
11mol kgm $
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(3) Gunakan konsentrasi mol untuk
menyatakan konsentrasi
B ,BB
***
B ,B
( ) ln ln
= ( , ) ln c
c
c
k c
T R
T p RT
T Tp
a
R a
$
$
$
B,B ,Bc c ca
c $
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Excess Function
Pada penggambungan laruran dengan
mol n1 dan n2 , Jika larutran adalah
larutan ideal maka :
mix mix
mix mix
0, 0
0, 0
V H
G S
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Excess Function
Namun jika larutan bukanlah larutan ideal,maka smua nilai tidak bernilai 0 , tapihukum termodinamika tetap berlaku
(1) Energi Gibbs berlebvih
Energi gibbs berelebih menyatakan
perbedaanmixGr pada pencampuransebenarnya danmixGid pencampuranideal
E
mix re mix id
defG G G
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Excess Function
(2)Entalpi berlebihEH
remixidmixremix
E HHHH
)0( idmixHkarena
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14
Excess Functionsi k Tlnai kTln i Xi kTln i k Tln XiRemember that:
For an ideal solution: i 1
i
ideal kT lnXi
i
x i
i
ideal kT lni
Gix Nix RTln
i
G
' Mx
G
' MG
' Mideal
GM
x RT XA
lnA
XB
lnB
Mi
x Mi M
i
ideal
Mx M Mideal
We define the excess functionas the
difference between the actual value
of the mixture and the value for anideal mixture:
HMideal 0 HM
x HM
VMideal 0 VM
x VM
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15
Excess FunctionsGM HM TSM
G
M
ideal
G
M
x
H
M
ideal
H
M
x
T
S
M
ideal
S
M
x
GM
ideal GMx HM
x TSMideal SM
x
GMideal TSM
ideal
GMx HMx TSMx
The entropy of mixing is usually assumed
to be ideal so that the excess Gibbs free energy
of mixing is the excess enthalpy of mixing
GMx HM
x
GMideal GM
x HMx TSM
idealThe Gibbs free energy of mixing is then
The excess enthalpy of mixing minus T
times the ideal entropy of mixing.
Lets take a closer look at the
Gibbs free energy of mixing using
the concept of excess mixing functions:
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Larutan Regular
Pada larutan regular S E=0
Sehingga
0
pB
E
n
S
p
EE
T
G
Skarena
2 E
B
( ) 0pG
n T
B
E
B
pB
E
RTInrn
G
E
B ( adalah excess chemical potential )
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Larutan Regular
Pada larutan regular,, T dan logaritma dari tiap koefisienaktivitas komponen dinyatakan dalam rasio invers
T
tconRT
T
RT
B
B
pB
1ln
tanln
0]ln(
[
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18
Regular SolutionsThe Regular Solution Modelis a simple example of a non-ideal solution.
Recall that for a mixture:
GM
XiG i
i
GM RT Xi ln aii
GiRTln ai
The partial molar Gibbs free energy
of mixing (the difference between
component is contribution to G in
the mixture versus pure i) is related
to the activity.
The Gibbs free energy of mixing
is the weighted sum of thecontributions from each
component.
The Gibbs free energy of mixing
is then related to the activities as
shown.
In the ideal casethe activities were just the mole fractions:
GM RT Xi lnXii
The excess Gibbs free energy of mixing is the difference between the non-ideal and ideal G of mixing:
GM
x RT Xiln a
i
i
RT Xi lnXii
RT Xi lnii
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Lecture 18Multicomponent Phase
19
Regular Solutions
And substituting the Regular Solution excess G of mixing:
Notice that the first two terms are the negative ideal entropy of mixingmultiplied by T:
GM GMideal
GMx
RT Xi lnXii RT Xi lnii
The Gibbs free energy of mixing is the sum of the excess and ideal Gibbs free energies of mixing :
GM
RTXA
lnXA
RTXB
lnXB
XA
XB
SM
ideal RXA
lnXA
RXB
lnXB
Thus, the last term is the enthalpy of mixing(and also the excess enthalpy of mixing since the ideal
enthalpy of mixing is just zero):
HM
HM
x XA
XB
The enthlapy of mixing
of the Regular Binary Solution
with = 10 J/mol.
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SEKIAN DAN
TERIMAKASIH
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Referensi
Gaskell,
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