VLE berdasarkan Excess Gibbs Free Energy

(1)

Referensi:

1) Smith Van Ness. 2001. Introduction to Chemical Engineering Thermodynamic, 6th ed.

2) Sandler. 2006. Chemical, Biochemical adn Engineering Thermodynamics, 4th ed.

(2)

(3)

VLE BERBASIS Excess Gibbs Free Energy

(

γ

-

φ

method

)

L

i

V

i

f



0

L

V





(

i = 1, 2, . . ., N

)

(1)

(2)

0

i

L

i

V

i

φ

P

x

f

y





?

φ

V

i





?

L

i







(4)

Fungsi Excess dan Energi Bebas Gibbs Excess

id E

M



M



M

(2)

M





G

E

(2)

(5)

id E

V





id E

H





id E

S





id E

A





id E

U





V

E

S

E

H

E

U

E

G

E

(1)

H





A



A



A

(7)

(5)

(6)

(8)

•

(7)

i

M

j n P, T, i

i

n

nM

M

















(

)

(9)

j

n P, T, i

E E

i

n

nM

M

















(

)

(8)

i i

M

n

nM





i

E i i E

M

n

M

n





(11)

(12)

i E

E E

dn

RT

G

dT

RT

nH

dP

RT

nV

RT

nG

d



















2 E

i i E

M

n

M

n





i

(12)

(9)

Aktivitas dan Koefisien Aktivitas

)

(

i

T,

p,

x

f



i i i

x

a



γ

)

(

)

(

)

(

0 0 0

i i i

x

,

P

T,

f

x

p,

T,

f

x

P,

T,

a



(14)

(10)

]

n

l

n

[l

_(real) _(ideal)

(ideal)

(real) i i i

i

G

RT

f

G







(ideal) (real) i

i E

i

G





(16)

(17)

(ideal) (real) i

i

G





(ideal) (real)

n

l

i i E

i

f

RT

G



0

i

γ

x

f

(real)



0

i

x

f

(ideal)



n

l





RT

G

E

(17)

(18)

(19)

(20)

(11)

i i 2 E E E

dn

γ

dT

RT

nH

dP

RT

nV

RT

nG

d





















n

l

E





(12)

γ

_i

G

E

/

RT





i

n

l

_i

i E

γ

x

RT

G

(64)

(13)

Model Eergi Bebas Gibbs Excess

•

1 x

:



₁ ₂ _N



E

x

,

x

,

x

g

RT

G





RT

x

/x

G

E ₁ ₂







2

1 1

E

cx

bx

a

G

(28)

(14)

•



 













₁ ₂ ₁ ₂ 2

2 1

E

x

-x

C

x

-x

B

A

RT

x

G

,

(30)

•

γ

A

RT

x

G

2 1

E



2 1 E

x

A

RT

G



(15)



















































2 1 2 1 1 2 1 2 2 1 1 2 1 1 n P, T, 1 E 1

n

A

n

A

n

RT

/

nG

n

l





2

n













(32)

(33)













22

2 1 2 2 2 1 2 1 2 1

2

A

x

(16)



x

-

x



A

B



2x

-

1



B

A

RT

x

G

1 2 1 2 1 E











1 2



2 1 2 1 E

x

-x

x

Bx

x

Ax

G





(35)

(36)



1 2



2 1 2

1

x

Bx

x

-

x

Ax

RT





(17)



























































































































2 2

B

A

B

A

n

l

2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 n P, T, 1 E 1

n

-n

n

/RT

nG

γ







A

B

x



x



A

B



x





x

B



-

x



x













1

(39)

(40)







₁ ₂



₁ ₂





₁ ₂





₁ ₂



₁ ₂



2

A

B

x

A

B

x

B

-

x













1

3 2 2 2 3 2 2 2 2

2

Bx

2Bx

Ax

























A

B

4x

3



(18)





₁





₂ 2 1 E

x

B

x

B

A

RT

x

G







A

21

A

B

A





A



B



A

₁₂



1 2



2 1 E

x

-x

B

A

RT

x

G









1





₁ 1

x

(43)

(44)

2 12 1 21 2 1 E

x

A

x

A

RT

x

G



















₂₁ ₂ ₁₂ ₂₁



(19)



x

-

x





x

-

x



....

C

B

RT

x

G

2 1 2 1 2 1 E















2

D

Van Laar



₁2 ₂



1 E

x

C

B

x

RT

G











(48)



x

₁

x

₂



C

B

RT











₁2 ₂



1 E

n

C

B

x

RT

nG



































2

2 2 2 2 2 1 2 1 n P, T, 1 E 1

2x

C

B

n

x

C

B

n

C

B

n

C

B

n

/RT

nG

γ

ln

2



1















































2

x

C

B







(50)

(20)

(21)

Wilson :

(22)

Untuk sistem biner:

NRTL :

(23)

Untuk sistem biner:

UNIQUAC :