10.2 thermo probset

7/26/2019 10.2 Thermo Probset

1/20

University of San Carlos

Nasipit, Talamban, Cebu City 6000

Department of Chemical Engineering

CHE !!N

Assignment on Low Pressure Vapor-Liquid Equilibria in Non-ideal Mixtures

Submitte" by#

Duterte, $an %ommel T&

Submitte" to#

Engr& 'uis (& Cabatingan

)nstructor

September !, *0!+


2/20

10.2-1

iven#

ethyl bromi"e -!. / nheptane -*. mi1ture at 202&!+ (

P1

vap= 0.7569 bar , P2

vap= 0.0773 bar

regular solution parameters

3'-cm24mol. 5 -cal4cm2.!4*

ethyl bromi"e + 7&8

nheptane !7 &

%e9uire"#

a. Composition of the vapor in e9uilibrium :ith a li9ui" containing &*2 mol ; ethyl bromi"e at

202&!+ ( an" 0&+2 bar, assuming the solution is i"eal

b. 3apor composition in part a assuming the solution is regular

c. 3apor composition in part a using the UN)


3/20

values are use" to calculate the van 'aar an" F parameters& These parameters are then use" to

calculate the activity coefficients at the ne: composition -1!@ 0&*2 an" @ 0&+2 bar., an"

the mo"ifie" %aoult>s 'a: use" to calculate the ne: vapor compositions&


4/20

vapor pressure "ata

Species Temperature -C. vap-bar.

Iater!08&+ !&077

!00&6 !&02+*


5/20

ethanol -!. / benGene -*. mi1ture at +C

e1perimental "ata

x1 y1 -bar.

0 0 0&*828

0&02 0&!86+ 0&26!20&08* 0&*78+ 0&28+2

0&*!72 0&220 0&077

0&2!! 0&26*+ 0&!*

0&!+0 0&27* 0&!*7

0&+!88 0&06+ 0&!00

0&+*7 0&!0! 0&082

0&6!++ 0&22 0&0*7

0&07 0&+! 0&278!

0&7!0* 0&++6 0&26!+

0&8!82 0&07 0&2026

0&8+8! 0&7*0! 0&*!!

!&00 !&00 0&*2*!%e9uire"#

repare an 1y an" 1 "iagram for the system assuming, separately,

a. the mi1ture is i"eal

b. the mi1ture is regular

c. the mi1ture is "escribe" by the UN)


6/20

The "iagrams can no: be constructe", as sho:n in s Chemical Engineers> Han"booK to calculate

the ethanol vapor pressure at T!@ +C an" T*@ 6C,vap @ !&7+ K$4mol& This is use"

to calculate the solubility parameter for ethanol, :hich is calculate" to be !*&66 -cal4cm 2.!4*& )n

summary,

3'-cm24mol. 5 -cal4cm2.!4*

Ethanol +7&28 !*&66

PenGene 78 8&*

The volume fractions can then be calculate" from

( =x ( V (

x1 V1+ x2 V2

The activity coefficients are calculate" from

1 = e

V1 22

( 1- 2)2

RT

2 = e

V2 12

( 1 - 2)2

RT

The e9uilibrium pressure an" vapor composition is calculate" using the mo"ifie" %aoult>s 'a:#

Pe = x11 P1vap

+ x22 P2vap

y ( =x ( ( P (vap

Pe

The follo:ing table summariGes the calculate" values&

Table *& 3alues obtaine" using the regular solution mo"el

A! A* B! B* 1! e9 y!0 ! 2&02+2 ! 0&00 0&*828 0

6


7/20

0&068 0&82*! *&6*2 !&007 0&!0 0&2*+ 0&!760

0&!08 0&7+8! *&*682 !&02* 0&*0 0&27+ 0&20*2

0&*!8+ 0&70+ !&8668 !&078 0&20 0&260* 0&2702

0&202 0&68+ !&!!6 !&!686 0&0 0&26+* 0&2+*

0&286* 0&6027 !&88! !&20* 0&+0 0&26+6 0&+7

0&860 0&+00 !&2*+7 !&+!6 0&60 0&26*8 0&+077

0&608 0&28+! !&!782 !&7+ 0&0 0&2+0 0&+!2

0&*! 0&*+8 !&077* *&*76 0&70 0&27 0&+760

0&7++* 0&!7 !&0*26 2&6 0&80 0&2!+! 0&67+

! 0 ! +&2* !&00 0&*2*! !

The "iagrams can no: be constructe", as sho:n in


8/20

2'I

= e

&

(1+& x2#x1)

2

=n" the vapor composition is then

y1 =x

1

1

'IP

1

vap

P

The follo:ing table summariGes the calculate" values&

Table & 3alues obtaine" using the van 'aar mo"el

1! 1* B! B* e9 y!

0&00 !&00 &+760 ! 0&*828 0

0&!0 0&80 &6*67 !&0*+8 0&27 0&*72+

0&*0 0&70 2&!0* !&!002 0&0* 0&2+6

0&20 0&0 *&*+0 !&**2 0&076 0&27!

0&0 0&60 !&+** !&00+ 0&086 0&28!

0&+0 0&+0 !&*7 !&6!0 0&076 0&0870&60 0&0 !&*6 !&8+80 0&00 0&200

0&0 0&20 !&!* *&226 0&28*0 0&66!

0&70 0&*0 !&0+06 *&808+ 0&266! 0&+2*8

0&80 0&!0 !&0!!7 2&+87+ 0&2!! 0&666+

!&00 0&00 ! &707 0&*2*! !

The "iagrams can no: be constructe", as sho:n in


9/20

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.000.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

Ide

al mixture model UNIFAC mixture model van aar model

!e"ular mixture model #x$erimental data

x#t%&

() *ar


10/20


11/20

$% 1=

(1+ x 1 x2 )2

$% 2=

(1+ x2

x 1 )2


12/20

b. Determine the enthalpy an" entropy changes on mi1ing :hen ! mole of benGene an" * moles of

cyclohe1ane are mi1e" at T @ 200 ( an" constant pressure

c. iven the follo:ing vapor pressure "ata at T @ 2*0 (, P1vap= 0&2*02 bar an" P2

vap=

0&2*!7 bar, "etermine the bubble point pressure of the li9ui" in part -b. at T @ 2*0 (, an" the

composition of the vapor in e9uilibrium :ith that li9ui"

Solution#

a. ex

= x11ex

+ x22ex

= x1 RT$%1 + x2 RT$%2

1

ex= RT $% 1 an" 2

ex= RT $% 2

ex

= x1 x2=(11+2 )(2

1 + 2 )= 1 2 ( 1+ 2 )-2

ex

= 1 2 ( 1+2 )-1

1ex

=;

ex

; 1= 12(1 + 2 )

-2+ 2 (1 + 2 )

-1= (21 + 2

1 2

( 1+ 2 )2 )= x22

2ex=

Nex

N2

=A N1N2(N1+N2 )2+A N1 (N1+N2 )

1=A ( N1N1+N2

N1N2

(N1+N2 )2 )=A x12

Since 1ex

= RT $% 1 ,

1 =e1

ex

RT = ex2

2

RT =e(1- x1)

2

RT

Similarly,

2 =e

2ex

RT = e

x12

RT =e

(1- x2)2

RT

b.x1=

1

3 an"x2=

2

3

%ecall,

(x = (x +T


13/20

P= x11P1vap

+ x22 P2vap

=0.3557 bar

y1 =x11 P1

vap

Pb?bb$e= 0.3662

y2 =x22 P2vap

Pb?bb$e= 0.6338

=ns:er4s#

a. The activity coefficients of the benGene an" cyclohe1ane can be "escribe" by

1 = e

( 1-x 1 )2

RT a% 2= e

( 1-x2)2

RT , respectively&

b. Ihen ! mole of benGene an" * moles of cyclohe1ane are mi1e" at T @ 200 ( an" constant

pressure,


14/20

& =(1+ x1 $% 1BC(

x2 $% 2BC( )

2

$% 2BC(

= 1.0800

Since the final li9ui" compositions are yet to be foun" an" they are nee"e" to calculate the final activity

coefficients -:hich are use" to calculate the final vapor compositions., a trialan"error solution is use"&

The follo:ing e9uations must be satisfie" in or"er to fin" the vapor an" li9ui" compositions#

x1+ x2 = 1) y1+ y2= 1

1BCD

= e

#

(1+#x 1&x2)

2

) 2BCD

= e

&

(1+ &x2#x1)

2

593.425x11 = y1P) 416.5845 x22 = y2 P

P= x11P1vap

+ x22 P2vap

= trial value of 1!an" 1*is use" to calculate 1BCD

an" 2BCD & The activity coefficients are use" to

calculate the total e9uilibrium pressure, then the vapor compositions& The calculation is repeate" until

x (= y (=1 an" x (=y ( & Using the icrosoft E1cel Solver function, the aGeotropic vapor an"li9ui" compositions are foun" to be 1!@ y!@ 0&6+22 an" 1*@ y*@ 0&26 at +0C an" 62&8 mm Hg&

=ns:er4s# The aGeotropic composition of a methyl acetate / methanol mi1ture at +0C is 1 =@ y=@

0&6+22 an" 1eH@ yeH@ 0&26 at a pressure of 62&8 mm Hg&

10.2-2$

iven#

PenGene -!. / polyisobutylene -*. mi1ture at !0C

Data on physical properties

benGene polyisobutylene

olecular :eight, g4mol 70 000

!0 -monomeric.

olar volume, cm24mol 77&*6 !2!&8 -monomeric.

3apour pressure, bar0&!*66 -at *87&!+ (.

0&*28* -at 2!*&+ (.=ssume" to be negligible

Data for the activity of benGene in )P as a function of the mass ratio of benGene to )P

E /PIE aE=xEE

0&722! 0&87!!

0&++2 0&8+8+

0&*8! 0&7277

%e9uire"#

a. Using the "ata in )llustration !0&*, compare the pre"ictions of the


15/20

an" are 0&++, 0&2+66 an" 0&**+, respectively& The benGene mole fractions -in terms of the

:eight fraction. are then calculate" as

xE =

HE

78

H E

78 +

HPIE

40000

an" are 0&88, 0&886+ an" 0&8822, respectively& The


16/20

b. The partial pressures of benGene are sho:n in table 6&

10.2-$%

iven#

Component ! an" * mi1ture in vapourli9ui" e9uilibrium

=t 80C an" !&7+0+ bar, a vapour of composition y! @ 0&26 coe1ists :ith a li9ui" ofcomposition 1!@ 0&

3apour pressures are given by

$:@10 P(vap

= (E(

T

for pressure in bar an" T in (, :here =!@ &!*+, P!@ !+00, =*@ +&000 an" P*@ !+0

%e9uire"#

a. Determine the van 'aar parameters of the system using the given "ata

b. Determine :hether the mi1ture has an aGeotrope at 80C an", if so, "etermine its composition an"

i"entify :hether it is a ma1imum or minimumpressure aGeotropec. btain 1y an" 1y "iagrams for the system at 80C

". =n e9uimolar mi1ture of species ! an" * initially at very lo: pressure is compresse" at a constant

80C& =t :hat pressure "oes the first "rop of li9ui" form, an" :hat is its compositionQ =t :hat

pressure "oes the last bubble of vapour "isappear, an" :hat :as its compositionQ

Solution#

a.


17/20

0&0 !&!+8* *&!*6 !&672 0&+2!

0&70 !&0677 *&!!! !&6668 0&+06+

0&80 !&0!0 2&+82+ !&80 0&6*2

!&00 ! &8++0 0&87 !

The highlighte" ro: is the aGeotropic pointJ the mi1ture forms an aGeotrope at appro1imately

0&2 mole fraction of species ! at 80C an" a pressure of !&7+!2 bar& The mi1ture is a ma1imum

pressure aGeotrope since the activity coefficients of both species are greater than !&0, an" there

are positive "eviations from %aoult>s 'a:&

c. Using the values summariGe" in the previous table, the 1y an" 1y "iagrams can be

constructe"&

0.00 0.20 0.40 0.60 0.80 1.000

0.2

0.4

0.6

0.8

1

x1

'1


18/20

b. The mi1ture forms an aGeotrope at appro1imately 0&2 mole fraction of species ! at 80C an" a

pressure of !&7+!2 bar& The mi1ture is a ma1imum pressure aGeotrope since the activity

coefficients of both species are greater than !&0, an" there are positive "eviations from %aoult>s

'a:&

c. See figures an" +&

". The pressure at :hich the first "rop of li9ui" forms is appro1imately !&6 bar, an" this "rop has acomposition 1!@ 0&70& The last bubble of vapor "isappears at !&7 bar, an" the bubble ha" a

composition of y!@ 0&0&

10.2-$

iven#

Iater -!. / !,"io1ane -*. mi1ture at 2*2&!+ (

3aporli9ui" e9uilibrium "ata

-mm Hg. 1! y!!*0&8 0&0000 0&0000

!0&7+ 0&0+60 0&!8*0

!+!&!6 0&080 0&*670

!+8&! 0&!00 0&2+0

!6&+ 0&*!60 0&2720

!6+&6+ 0&*870 0&020

!6&78 0&2660 0&*+0

!6& 0&00 0&20

!6&8 0&60 0&60

!6&8+ 0&70 0&+!0

!66&7 0&+280 0&++0

!6+&7 0&6*80 0&660

!60&7* 0&80 0&8+0

!++&! 0&7!!0 0&+20!*&6 0&7800 0&600

!!&6 0&860 0&8+0

8*&+! !&0000 !&0000

%e9uire"#

a. =ctivity coefficients at each of the reporte" compositions

b. =re these "ata thermo"ynamically consistentQ

c. lot of e1cess ibbs energy as a function of composition

Solution#

a. The van 'aar mo"el :ill be use" to calculate the activity coefficients&


19/20

&!1-x1

1+# x1

1'I

= e

#

( )2

&!1-x11+

2'I

= e

&

(# x1)2

The results are summariGe" in the follo:ing table&

Table 7& =ctivity coefficients of the :ater"io1ane system

1! B! B*0&0000 +&76* !

0&0+60 &60 !&00

0&080 &!662 !&0!*

0&!00 2&*+7 !&0+20&*!60 2&08 !&0+*

0&*870 *&8+ !&!+!8

0&2660 *&!08 !&*2*

0&00 !&72+ !&28+

0&60 !&7!27 !&28*6

0&70 !&6762 !&72

0&+280 !&+*72 !&6

0&6*80 !&2*6 *&00*

0&80 !&!2 *&786

0&7!!0 !&070 2&!02

0&7800 !&0*2 &++**

0&860 !&00*+ 6&*627

!&0000 ! &*680

b.


20/20

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00+2

+1.5

+1

+0.5

0

0.5

1

1.5

2

2.5

x1

ln ,2-,1

10.2 thermo probset

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