excess function

8/13/2019 Excess Function

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TERMODINAMIKAMATERIAL

Helena Septian (1206239182)

David Jendra (1206238803)

TEKNIK

METALURGI &MATERIAL FTUI

SAP 9

Campuran Termodinamik:

Larutan Ideal dan Non Ideal

Excess FunctionLarutan Reguler


2/21

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


3/21

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

$


9/21

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:


16/21

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(

[


18/21

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,

excess function

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