4. Nonideal Behavior

7/25/2019 4. Nonideal Behavior

1/65

Nonideal Behavior

TKM 406

Termodinamika Teknik Kimia II


2/65

Nonideal Behavior, Outline

Introduction: Efect o Nonideality

Partial Molar Properties Residual Properties

Fugacity Fugacity

!oe"cient E#cess Properties

$ctivity $ctivity !oe"cient


3/65

Intorduction: Efect o Nonideality:%etrahydrouran&'()!ar*on+tetrachloride&(

t-x-y diagramP-x-y

30o

C1 atm


4/65

Efect o Nonideality:!hloroor-&'()%etrahydrouran&(

t-x-y diagramP-x-y

30o

C1 atm


5/65

Efect o Nonideality:Furan&'()!ar*ontetrachloride&(

t-x-y diagramP-x-y

30o

C1 atm


6/65

Efect o Nonideality:Ethanol&'()%oluene&(

t-x-y diagramP-x-y

65o

C 1 atm


7/65

Efect o Nonideality:# . y /iagra- at !onstant P 0 ' at-

a. Tetrahydrofuran(1)/Carbon-tetrachlorid

b Chloroform(1)/Tetrahydrofuran(

c. Furan(1)/Carbontetrachloride(2)

d. Ethanol(1)/Toluene(2)


8/65

Partial Molar Properties

.etc,Gor,V,S,H,UM iiiiii=

= ii MxMSolutionPropertie!

"#are propertie o$ %omponent i in t&e tate o$mixture' (&i%&' in general di)erent $romt&at in t&e tate o$ pure pe%ie

PartialPropertie!

Pure-pe%iePropertie!


NOT: =

ii MxM

*&at p&yi%al interpretation %an +e

gi,en $or' ,i# partial molar ,olume .


9/65

Methanol . 1ater Mi#ture, $n E#a-ple

For pure species at 2o!:

Methanol &'( : 3'0 45677 c-8)-ol1ater &( : 30 '9659 c-8)-ol

*&at i t&e ,olume o$ 10 mole o$ met&anol/(aterolution %ontaining 30 mol o$ met&anol.

Mot people (ould t&ink' logi%ally!Mol o$ met&anol ! 0#3 x 10 mole 3 mole

Mol o$ (ater ! 21-0#3 x 10 mole mole

olume o$ met&anol ! 3 mole x 40# 1#171

%m3

olume o$ (ater ! mole x 17#067 16#46%m3

T&u' t&e total ,olume! 1#171 8 16#4647#65 %m3

Wronganswer!

The correct answer is240.251 cm3

Thus there is 240.251 248.65 "8.406 cm3 #e$iation%rom ex ected$a&ue

= ii MxM

M P i l M l


10/65

More on Partial MolarProperties

( )

jn,P,Ti

in

nMM

( ) ( ) ( ) ( )

.dnn

nMdP

P

nMdT

T

nMnMd i

n,P,Tin,Tn,P j

+

+

=

.),.........n,n,n,P,T(MnM 321=

( ) ( ) ( )

( ) ( ).....dnn

nM

dnn

nM

dPP

nMdT

T

nMnMd

2,...n,n,P,T2

1,...n,n,P,T1

n,Tn,P

3132+

+

+

+

=

=ii MxMNOT =

ii MxM


11/65

!he-ical Potential as Partial Molar Property!riteria or 3apor + ;i


12/65

!he-ical Potential as Partial MolarProperty

( )

jn,P,Ti

in

nGG

ii G=

( ) ( ) ( ) ( )

.dnn

nGdP

P

nGdT

T

nGnGd i

n,P,Tin,Tn,P j

+

+

= '% we set (

):

Thus:

jn,P,Ti

i

n

)nG(

The #e*nition o% chemica&

+otentia&:


13/65

Evaluation o Partial Molar PropertiesMethanol . 1ater Mi#ture E#a-ple

121

x

MxMM

+=

112

xMxMM

=

= ii MxM


14/65

E#ercise

$ group o students ca-e across an unsuspected supply o la*oratory

alcohol, containing = -ass+percent ethanol and 4 -ass+percent >ater6$s an e#peri-ent they decided to convert ; o this -aterial into vod?a,

having a co-position o 2 -ass+percent ethanol and 44 -ass+percent>ater6 1ishing to peror- the e#peri-ent careully, they search theliterature and ound the ollo>ing partial+speci@c volu-e data or

ethanol . >ater -i#tures at 2o

! and '5'68 ?Pa6

T&e pe%i9% ,olume o$ (ater at 5oC i 1#003 :/kg# ;o(

many : o$ (ater &ould +e added to t&e : o$la+oratory al%o&ol' and &o( many : o$ ,odka reult.

1.2431.273L/g,V!."#3!.$1%L/g,V

&n 'odetno*"%+&n

H-t

H2


15/65

Fugacity,

( )P*ndTdG ig =

( )*ndTdG

( ) *ndTdG

Ideal ga !


16/65

Evaluation o Pure !o-ponentFugacity, i

dPVdG

i

i = =P

!

i

i dP

T

V

T

dG

P ii =

uga%ityCoe)i%ient!

T&e $uga%ity !

i

i *nT

G=

,t constantT:

=

P

!

i

i

P

dP)10(

T

G

=P

!

iiP

dP)10(*n

P

T)10(V i

i =


17/65


>rom t&e $ollo(ing %omprei+ility data $or&ydrogen at 0oC' determine t&e $uga%ity o$&ydrogen at ?50 atm

100 1.069 600 1.431200 1.138 700 1.50

300 1.209 800 1.57


18/65


>rom t&e $ollo(ing %omprei+ility data $or io+utane'

determine t&e $uga%ity o$ +utane at ,arioutemperature and preure


19/65

Evaluation o Pure !o-ponentFugacity, i ro- E


20/65

!ritical !onstants $ccentric Factors:Para"ns


21/65

!ritical !onstants $ccentric Factors:Ole@n Miscellaneous Organics


22/65

!ritical !onstants $ccentric Factors:Miscellaneous Organic !o-pounds


23/65

!ritical !onstants $ccentric Factors:Ele-entary ases


24/65

!ritical !onstants $ccentric Factors:Miscellaneous Inorganic !o-pounds


25/65

Evaluation o Pure !o-ponent Fugacity,i ro- 3irialE


26/65

Evaluation o Pure !o-ponentFugacity, i ro- E


27/65

Evaluation o Pure !o-ponent Fugacity,i ro- Redlich+C>ong E


28/65

Evaluation o Pure !o-ponent Fugacity, i :

PitDers eneraliDed !orrelation

( )T,P rr!

i =

( ) ( ) = 1i!ii

( )T,P rr1

i =

cr

PPP =

cr

TTT =

E l ti


29/65

Evaluationo Pure!o-ponent

Fugacity, i :

PitDers

eneraliDed!orrelation

cc

E l tir

TT =


30/65


Fugacity, i :

PitDers


cr

TT

!

i

cr

P

PP =

E l ti


31/65


Fugacity, i :

PitDers


cc

E l tir

TT =


32/65


Fugacity, i :

PitDers


cr P

P

P =

cr

T1i


33/65

Evaluation o Pure !o-ponentFugacity, i : PitDer !orrelation

@ing Piter Correlation'

%al%ulate t&e $uga%ity and $uga%ity %oe)i%ient o$!

1# Pure met&yl-et&yl-ketone

# Pure toluene

at 50oC and 5 kPa#

T&e reAuired data!


34/65

Evaluation o ;iugaity o$ aturated ,apor'

%al%ulated exa%tly a %al%ulating ga

( )T

PPV

exP

tiit

i

t

ii

=

Sin%e li a (eak $un%tion o$ P at temperature(ell +elo( T%!


35/65

Esti-ation o;i


36/65

E#a-ples oEvaluation o ;i


37/65

E#a-ples oEvaluation o ;i


38/65

E#a-ples oEvaluation o as ;i


39/65

E#a-ples oEvaluation o as ;i


40/65

Fugacity o Atea- and 1ater,sing Atea- %a*le

)SS(T

HH

1

5P

*n

5ii

5iii

=

P ! lo(et ,alue o$ P inteam ta+le

Dt P E Piat' i#e# liAuid p&ae

(ater! ( )

T

PPVexP

tiit

it

ii

=

@p to Piat' i#e# ga p&ae (ater

2team!


41/65

E#a-ple o Atea- and 1ater Fugacity!alculation sing Atea- %a*le

11.

>rom data in t&e team ta+le' determine a goodetimate $or $/$ato$ liAuid (ater at 100oC and 100

+ar' (&ere $at i t&e $uga%ity o$ aturated liAuidat 100oC#11#7

Steam at 13000 kPa and 370oC undergoe aniot&ermal %&ange o$ tate to a preure o$ 5

kPa# Fetermine t&e ratio o$ t&e $uga%ity in t&e9nal tate to t&at in t&e initial tate11#?

Steam at 1750 pia and 00o> undergoe aniot&ermal %&ange o$ tate to a preure o$ 40

pia# Fetermine t&e ratio o$ t&e $uga%ity in t&e


42/65

Fugacity o Mi#tures

66626 222

21221112

1 ++=

[ ]1

ij!

cij

cijjiij P

T

+

==

=i

ij

j

ji 66

Dre $ormulated exa%tly a %al%ulation $or pure%omponent' +ut (e ue (i;ing -u&estoo+tain t&e parameter

iria&

:

>or +inary mixture' i 1' and G 1'

icoonent8reo iii ==

2

jiij

+=

( ) )1(TTT ijcjcicij 21

=

cij

cijcijcij

V

T0P

=

2

000

cjcicij

+=

3

cjcicij

2

VVV

31

31

+

=

TP*n ii=


43/65

E#a-ple o !alculation orFugacity o Mi#tures sing 3irial E


44/65

Fugacity o !o-ponents inMi#ture

P6

9

9iii

( )

n

*nn9*n

jnP,T,i

i

=

i

i 9*nT

G=

T&u!

i

i *nT

G=

i partial molarproperty o$

)9*n( i )*n( i

iria&7 inar/mi;tures:

)6(T

P9*n

)6(T

P9*n

122

1222

122

2111

+=

+=

12111212 2 =


45/65

Fugacity o !o-ponents in BinaryMi#tures, E#a-ple using 3irialE


46/65

More on 3irial Eor ternary mixture' i 1''3

and G 1''3icoonent8reo iii ==

2

2

iiii

iiii

ii

ii

!

!

=

==


47/65

More on 3irial: Fugacity o%ernary Multico-ponent Mi#turesE#a-ple

11.19

Htimate t&e $uga%ity and $uga%ity %oe)i%ient o$ ea%&

%omponent in a ternary mixture o$ met&ane 21 /et&ane 2 / propane 23 at 40oC and 0 +ar (it&t&e %ompoition o$ 1 met&ane and 35 et&ane

Set all kiG 0


48/65

Evaluation o Mi#ture Fugacity, ,ro- E


49/65

Evaluation o Mi#ture Fugacity, , using

Redlich+C>ong E


50/65

Evaluation o !o-ponent Fugacity inMi#ture Fugacity, , ro- E


51/65

Evaluation o Mi#ture Fugacity, , using

Redlich+C>ong E


52/65

%A '

E i** E


53/65

E#cess i**s Energy

ig GGG =



PartialPropertie!




54/65

E#cess i**s Energy

ig GGG =



PartialPropertie!




55/65

$ctivity !oe"cient

=

i

iii

9*nTGG

( )*ndTdG

)x*n(TGG iiid

i =

Fe9nition o$$uga%ity!

Integration

=

ii

iidii

x

9*nTGG

=

iii

-i

x

9*n

T

G

T&e de9nition o$ a%ti,ity%oe)i%ient i

2Idealolution

( )( )i

n,P,T

i

-

*nn

T/Gn

j

=

ii

-

*nxT

G=

d l i i i i " i


56/65

Models or Binary Mi#tures $ctivity !oe"cient:

Margules&'92 . '=5(

21212121

-

x:x:Txx

G+=

( ) ( )jn,P,T

i

-

in

T/Gn*n

=

[ ]

[ ]22112212

12

11221122

21

x)::(2:x*n

x)::(2:x*n

+=

+=

d l i i i i " i


57/65


van ;aar

2;

211;

12

;21;12

21

-

x:x:

::Txx

G

+=

( ) ( )

jn,P,Ti

-

i

n

T/Gn*n

=

2

1;12

2;21;

212

2

2;21

1;12;

121

x:

x:1:*n

x:

x:1:*n

+=

+=

M d l Bi Mi t $ ti it ! " i t


58/65


1ilson

=

T

ex

V

V 21

2

121

=

T

ex

V

V 12

1

212

i2112

21

x


59/65

Models or Binary Mi#tures $ctivity!oe"cient:

Renon: NonRando- %>o+;i


60/65

Models or Multico-ponent Mi#tures

$ctivity !oe"cient:

1ilson

=i j

ijji-

x*nxT

G

=j

j

jjiijji

x

xx*n1*n

j)(i1

j)(iT

ex

V

V

ij

ij

i

j

ij

==

=

ncooitio


61/65

Multico-ponentMi#tures $ctivity!oe"cient:

NIversalG$si!he-ical

&NIG$!(&$*ra-s PrausnitD(

(o#e&s %or (u&ticom+onent (i;tures


62/65

NI


63/65

NIF$!: R? G?,cti$it/ oe


64/65

NIF$!: R? G?E#a-ple

,cti$it/ oe


65/65

NIF$!: a-?

,cti$it/ oe

Documents

4. Nonideal Behavior