4. nonideal behavior
TRANSCRIPT
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Nonideal Behavior
TKM 406
Termodinamika Teknik Kimia II
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Nonideal Behavior, Outline
Introduction: Efect o Nonideality
Partial Molar Properties Residual Properties
Fugacity Fugacity
!oe"cient E#cess Properties
$ctivity $ctivity !oe"cient
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Intorduction: Efect o Nonideality:%etrahydrouran&'()!ar*on+tetrachloride&(
t-x-y diagramP-x-y
30o
C1 atm
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Efect o Nonideality:!hloroor-&'()%etrahydrouran&(
t-x-y diagramP-x-y
30o
C1 atm
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Efect o Nonideality:Furan&'()!ar*ontetrachloride&(
t-x-y diagramP-x-y
30o
C1 atm
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Efect o Nonideality:Ethanol&'()%oluene&(
t-x-y diagramP-x-y
65o
C 1 atm
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Efect o Nonideality:# . y /iagra- at !onstant P 0 ' at-
a. Tetrahydrofuran(1)/Carbon-tetrachlorid
b Chloroform(1)/Tetrahydrofuran(
c. Furan(1)/Carbontetrachloride(2)
d. Ethanol(1)/Toluene(2)
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Partial Molar Properties
.etc,Gor,V,S,H,UM iiiiii=
= ii MxMSolutionPropertie!
"#are propertie o$ %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!
.etc,Gor,V,S,H,UM iiiiii=
NOT: =
ii MxM
*&at p&yi%al interpretation %an +e
gi,en $or' ,i# partial molar ,olume .
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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
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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
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!he-ical Potential as Partial Molar Property!riteria or 3apor + ;i
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!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&:
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Evaluation o Partial Molar PropertiesMethanol . 1ater Mi#ture E#a-ple
121
x
MxMM
+=
112
xMxMM
=
= ii MxM
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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
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Fugacity,
( )P*ndTdG ig =
( )*ndTdG
( ) *ndTdG
Ideal ga !
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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 =
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Evaluation o Pure !o-ponentFugacity, i
>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
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Evaluation o Pure !o-ponentFugacity, i
>rom t&e $ollo(ing %omprei+ility data $or io+utane'
determine t&e $uga%ity o$ +utane at ,arioutemperature and preure
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Evaluation o Pure !o-ponentFugacity, i ro- E
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!ritical !onstants $ccentric Factors:Para"ns
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!ritical !onstants $ccentric Factors:Ole@n Miscellaneous Organics
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!ritical !onstants $ccentric Factors:Miscellaneous Organic !o-pounds
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!ritical !onstants $ccentric Factors:Ele-entary ases
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!ritical !onstants $ccentric Factors:Miscellaneous Inorganic !o-pounds
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Evaluation o Pure !o-ponent Fugacity,i ro- 3irialE
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Evaluation o Pure !o-ponentFugacity, i ro- E
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Evaluation o Pure !o-ponent Fugacity,i ro- Redlich+C>ong E
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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
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Evaluationo Pure!o-ponent
Fugacity, i :
PitDers
eneraliDed!orrelation
cc
E l tir
TT =
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Evaluationo Pure!o-ponent
Fugacity, i :
PitDers
eneraliDed!orrelation
cr
TT
!
i
cr
P
PP =
E l ti
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Evaluationo Pure!o-ponent
Fugacity, i :
PitDers
eneraliDed!orrelation
cc
E l tir
TT =
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Evaluationo Pure!o-ponent
Fugacity, i :
PitDers
eneraliDed!orrelation
cr P
P
P =
cr
T1i
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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!
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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%!
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Esti-ation o;i
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E#a-ples oEvaluation o ;i
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E#a-ples oEvaluation o ;i
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E#a-ples oEvaluation o as ;i
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E#a-ples oEvaluation o as ;i
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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!
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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
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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 $or pure%omponent' +ut (e ue (i;ing -u&estoo+tain t&e parameter
iria&
:
>or +inary mixture' i 1' and G 1'
icoonent8reo iii ==
2
jiij
+=
( ) )1(TTT ijcjcicij 21
=
cij
cijcijcij
V
T0P
=
2
000
cjcicij
+=
3
cjcicij
2
VVV
31
31
+
=
TP*n ii=
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E#a-ple o !alculation orFugacity o Mi#tures sing 3irial E
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Fugacity o !o-ponents inMi#ture
P6
9
9iii
( )
n
*nn9*n
jnP,T,i
i
=
i
i 9*nT
G=
T&u!
i
i *nT
G=
i partial molarproperty o$
)9*n( i )*n( i
iria&7 inar/mi;tures:
)6(T
P9*n
)6(T
P9*n
122
1222
122
2111
+=
+=
12111212 2 =
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Fugacity o !o-ponents in BinaryMi#tures, E#a-ple using 3irialE
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More on 3irial Eor ternary mixture' i 1''3
and G 1''3icoonent8reo iii ==
2
2
iiii
iiii
ii
ii
!
!
=
==
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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
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Evaluation o Mi#ture Fugacity, ,ro- E
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Evaluation o Mi#ture Fugacity, , using
Redlich+C>ong E
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Evaluation o !o-ponent Fugacity inMi#ture Fugacity, , ro- E
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Evaluation o Mi#ture Fugacity, , using
Redlich+C>ong E
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%A '
E i** E
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E#cess i**s Energy
ig GGG =
.etc,Gor,V,S,H,UM iiiiii=
= ii MxMSolutionPropertie!
PartialPropertie!
Pure-pe%iePropertie!
.etc,Gor,V,S,H,UM iiiiii=
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E#cess i**s Energy
ig GGG =
.etc,Gor,V,S,H,UM iiiiii=
= ii MxMSolutionPropertie!
PartialPropertie!
Pure-pe%iePropertie!
.etc,Gor,V,S,H,UM iiiiii=
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$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
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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
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Models or Binary Mi#tures $ctivity !oe"cient:
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
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Models or Binary Mi#tures $ctivity !oe"cient:
1ilson
=
T
ex
V
V 21
2
121
=
T
ex
V
V 12
1
212
i2112
21
x
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Models or Binary Mi#tures $ctivity!oe"cient:
Renon: NonRando- %>o+;i
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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
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Multico-ponentMi#tures $ctivity!oe"cient:
NIversalG$si!he-ical
&NIG$!(&$*ra-s PrausnitD(
(o#e&s %or (u&ticom+onent (i;tures
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NI
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NIF$!: R? G?,cti$it/ oe
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NIF$!: R? G?E#a-ple
,cti$it/ oe
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NIF$!: a-?
,cti$it/ oe