GRUPO 4- TERMO 2

Evaluar los coeficientes de actividad para el sistema binario acetato de metilo(1)/metanol(2), empleando el modelo de UNIFAC a una T° DE 60°C

X1

PARAMETROS DE ANTOINE A T°C, P(KPa) 0.25T(ºC) P(Kpa)

60 101.3Suatancia Fornula A B C

Acetato de MetilCH3COOCH3 14.4015 2739.17 223.12 Psat1Metanol CH3OH 16.5938 3644.3 239.76 Psat2

PARAMETRO DE LA SUSTANCIA PURAFrecuencia de grupos funcionales

Sustancia Rk Qk1 CH3 0.9011 0.8482 CH3COO 1.9031 1.7283 CH3OH 1.4311 1.432

PARAMETRO DE LA SUSTANCIA EN LA MEZCLAFrcuencia de grupos secundarios

Sustancia Vk1 Vk2NG i=1 i=2

1 CH3 1 02 CH3COO 1 03 CH3OH 0 1

CALCULO DE PARAMETROS DE LA MEZCLA AREA RELATIVA DEL GRUPO FUNCIONAL AREA MOLECULAR RELATIVA

K i=1 i=2 q11 CH3 0.848 0 q22 CH3COO 1.728 03 CH3OH 0 1.432

PARAMETRO DE INTERACCION ENERGETICASustancia CH3 (1) CH3COO(11) CH3OH(6)

NGCH3 (1) 0 232.1 697.2

CH3COO(11) 114.8 0 249.6CH3OH(6) 16.51 -10.72 0

ENERGIA DE INTERACCION FUNCIONAL DE LA MEZCLA

𝑮_(𝒌,𝒊)=𝑽_(𝒌,𝒊)∗𝑸_𝒌

𝜶_(𝒊,𝒋)

𝒓_(𝒌,𝒊)= 〖𝒆𝒙𝒑〗 ^((−𝒂_(𝒌,𝒊))/𝑻)

"AM: CH3−COO−CH3"" "" Metanol CH3OH"

K i CH3 CH3COO CH3OHCH3 1 0.4982351245 0.12334734CH3COO 0.7085111204 1 0.47273889CH3OH 0.9516506684 1.0327009976 1

VOLUMENES MOLECULARES RELATIVOSϒ1 2.8042ϒ2 1.4311

VOLUMEN FRACCIONAL DE VOLUMEN MOLECULAR RELATIVOj1 1.5803874604j2 0.8065375132

AREA FRACCIONAL DEL AREA MOLECULAR RELATIVAL1 1.4994179278L2 0.8335273574

ENERGIA PARCIAL POR GRUPO FUNCIONAL EN CADA ESPECIE

K i i=1 i=21 CH3 2.0723072161 1.3627637571

2 CH3COO 2.1505033856 1.47882782863 CH3OH 0.9214913498 1.432

ENERGIA DE MEZCLA POR ESPECIEn1 1.5401496219n2 1.6467467179n3 1.3043728374

Reemplazando en la siguiente ecuación

-0.1045877484-0.0177057682

lnγR1 0.6372517996lnγR2 0.0718097703

γ1 1.7034643855γ2 1.0555943804

P 114.95815781

lnγϲ1lnγϲ2

𝒓_(𝒌,𝒊)= 〖𝒆𝒙𝒑〗 ^((−𝒂_(𝒌,𝒊))/𝑻)

𝜸=∑▒〖𝑽 _( , )𝒌 𝒊∗𝑹_𝒌 〗

𝑺_(𝒌,𝒊)= _( , )𝒓 𝒌 𝒊 ∑8_𝒊▒ _( , )𝑮 𝒌 𝒊∗ _( , )𝒓 𝒌 𝒊

𝒏_𝒌=∑8_𝒊▒ 〖𝑺 _(, )𝒌 𝒊 ∗𝒙_𝒊 〗

〖〖〗𝐥𝐧𝜸 _^𝒄 〗 _𝒊=𝟏−𝑱_𝒊+𝒍𝒏𝑱_𝒊−𝟓𝒒_𝒊 (𝟏− _𝑱 𝒊/𝑳_𝒊 +𝒍𝒏 _ / _ 𝑱 𝒊 𝑳 𝒊 )

〖𝒍𝒏𝜸 " " 〗 _ =𝒊 〖〖𝒍𝒏𝜸〗 ^𝑹 〗 _𝒊+〖〖𝒍𝒏𝜸〗^𝑪 〗 _𝒊

〖〖𝒍𝒏𝜸〗 ^𝑹 〗 _𝒊= _𝒒 𝒊 (𝟏−𝒍𝒏𝑳_𝒊 )−∑8_𝑲▒( _𝜽 𝒌∗ _( , )𝑺 𝒌 𝒊 /𝒏_𝒌 − _( , )𝑮 𝒌 𝒊∗ 𝒍𝒏 _( , )/ _ 𝑺 𝒌 𝒊 𝒏 𝒌 )

1 1 1 2 2 2* *P * *Psat satburbujaP X x

Y1 0.4746582498 Y2 0.66017055



X2

0.75

112.906101584.47092728

AREA MOLECULAR RELATIVA AREA EN MEZCLA DE GRUPO FUNCIONAL2.576 Θk1.432 Θ1 0.212

Θ2 0.432Θ3 1.074

𝒓_(𝒌,𝒊)= 〖𝒆𝒙𝒑〗 ^((−𝒂_(𝒌,𝒊))/𝑻)

"AM: CH3−COO−CH3"" "" Metanol CH3OH"

𝒓_(𝒌,𝒊)= 〖𝒆𝒙𝒑〗 ^((−𝒂_(𝒌,𝒊))/𝑻)

𝑺_(𝒌,𝒊)= _( , )𝒓 𝒌 𝒊 ∑8_𝒊▒ _( , )𝑮 𝒌 𝒊∗ _( , )𝒓 𝒌 𝒊


γ1 1.7034644γ2 1.0555944

Psat1(Kpa) 112.9061Psat2(Kpa) 84.470927

P(Kpa) 101.3

X1 Y1 P0 0 89.1670358

0.05 0.10195123 94.32526010.1 0.1933301 99.4834843

0.15 0.27570009 104.6417090.2 0.35033085 109.799933

0.25 0.41826419 114.9581570.3 0.48036292 120.116381

0.35 0.53734779 125.2746060.4 0.58982549 130.43283

0.45 0.63831043 135.5910540.5 0.68324159 140.749278

0.55 0.72499587 145.9075030.6 0.7638987 151.065727

0.65 0.80023254 156.2239510.7 0.83424371 161.382175

0.75 0.86614804 166.54040.8 0.89613541 171.698624

0.85 0.92437355 176.8568480.9 0.95101118 182.015072

0.95 0.97618062 187.1732971 1 192.331521

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.10.20.30.40.50.60.70.80.9

1

X VS Y

X - Y

𝑳𝒏 𝑷𝒔𝒂𝒕=𝑨−𝑩𝒊/(𝒕+𝑪𝒊)

𝒀=(𝐗𝐢∗𝛄𝒊∗𝐏𝐬𝐚𝐭𝒊)/𝑷

𝑷=𝑷_𝟏^𝒔𝒂𝒕∗𝑿𝒊∗𝜸𝟏+(𝟏−𝑿𝒊) 𝑷_𝟐^𝒔𝒂𝒕∗𝜸𝟐

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.10.20.30.40.50.60.70.80.9

1

X VS Y

X - Y

𝑳𝒏 𝑷𝒔𝒂𝒕=𝑨−𝑩𝒊/(𝒕+𝑪𝒊)

𝒀=(𝐗𝐢∗𝛄𝒊∗𝐏𝐬𝐚𝐭𝒊)/𝑷

𝑷=𝑷_𝟏^𝒔𝒂𝒕∗𝑿𝒊∗𝜸𝟏+(𝟏−𝑿𝒊) 𝑷_𝟐^𝒔𝒂𝒕∗𝜸𝟐

0 0.2 0.4 0.6 0.8 1 1.20

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Evaluar los coeficientes de actividad para el sistema binario acetato de metilo(1)/metanol(2), empleando el modelo de NRTL a una T° DE 60°C

Parámetros de Antoine

A B Cacetato de metilo (1) 14.4015 2739.17 223.12

metanol (2) 16.5938 3644.3 239.76

(°C) (°K)temperatura 60 333.15 R 1.987

De la ecuacion de Antoine

i Pi sat (Kpa)1 112.9061022 84.4709273

Parámetros deNRTL

b12 b21 α12 acetato de metilo (1) 381.46 346.54 0.2965

metanol (2) -253.88 845.21 0.3

G12 G210.57625051 0.52349879 0.84294103 0.85622902

y1 y2 Po0.25 0.75 90.1467464

Calculando el xi

x1 x2 γ1 lnγ2 γ20.25000 0.75000 0.56724 1.76340 0.06482 1.06696

τ12 τ21

Considerando γ=1

lnγ1

0

( )(º )

SAT BLnP KPa A

T C C

1 01

1

2 02

2

*

*

sat

sat

y Px

P

y Px

P

Coeficientes de ACTIVIDAD:

Hallando la presion de burbuja

x1 x2

0.25 0.75 1.76339578 1.0669632

P1 sat (Kpa) 112.906102P2 sat (Kpa) 84.4709273

Y1 0.44084895Y2 0.57591796

Aplicando la fórmula anterior obtenemos la Presión de Burbuja

Pburbuja 117.370064

γ1 γ2

1 01

1

2 02

2

*

*

sat

sat

y Px

P

y Px

P


1 1 11

2 1

* *

y =1- y

satx Py

P


cal/mol°K

0

( )(º )

SAT BLnP KPa A

T C C

12 2112 21 ; ij

b b

RT RT

12 12 21 121exp( ) ; G exp( ) ijG G

01 2

1 2

1

sat sat

Py y

P P

2 221 12 121 2 21 2

1 2 21 2 1 12

2 212 21 212 1 12 2

2 1 12 1 2 21

*ln ( )

* (x x * G )

*ln ( )

* (x x * G )

G Gx

x x G

G Gx

x x G

ɣ1 ɣ21.7634 1.067

2 221 12 121 2 21 2

1 2 21 2 1 12

2 212 21 212 1 12 2

2 1 12 1 2 21

*ln ( )

* (x x * G )

*ln ( )

* (x x * G )

G Gx

x x G

G Gx

x x G

1 1 11

2 1

* *

y =1- y

satx Py

P


2 221 12 121 2 21 2

1 2 21 2 1 12

2 212 21 212 1 12 2

2 1 12 1 2 21

*ln ( )

* (x x * G )

*ln ( )

* (x x * G )

G Gx

x x G

G Gx

x x G

2 221 12 121 2 21 2

1 2 21 2 1 12

2 212 21 212 1 12 2

2 1 12 1 2 21

*ln ( )

* (x x * G )

*ln ( )

* (x x * G )

G Gx

x x G

G Gx

x x G

cuadro N°1 usando la ecuacion de NRTL, para el sistema acetato de metilo (1)/metanol(2) a T=60°C

x1 ɣ1 ɣ2 P Y10 2.74353 1.00000 84.47093 0.00000

0.05 2.48426 1.00265 94.48482 0.148430.1 2.26201 1.01059 102.36879 0.24949

0.15 2.07086 1.02386 108.58504 0.322990.2 1.90597 1.04257 113.49256 0.37922

0.25 1.76340 1.06696 117.37006 0.424080.3 1.63990 1.09736 120.43312 0.46122

0.35 1.53281 1.13421 122.84707 0.493070.4 1.43991 1.17805 124.73659 0.52134

0.45 1.35938 1.22959 126.19271 0.547310.5 1.28969 1.28969 127.27771 0.57203

0.55 1.22959 1.35938 128.02839 0.596400.6 1.17805 1.43991 128.45778 0.62126

0.65 1.13421 1.53281 128.55543 0.647490.7 1.09736 1.63990 128.28644 0.67606

0.75 1.06696 1.76340 127.58891 0.708130.8 1.04257 1.90597 126.36981 0.74519

0.85 1.02386 2.07086 124.49878 0.789240.9 1.01059 2.26201 121.79952 0.84312

0.95 1.00265 2.48426 118.03792 0.911111 1.00000 2.74353 112.90610 1.00000

grafico N°1 representando con la ecuacion de NRTL para el sistema acetato de metilo(1)/metanol (2) a T=60°C

0 0.2 0.4 0.6 0.8 1 1.275.00000

85.00000

95.00000

105.00000

115.00000

125.00000

135.00000

p-x1p-y1

x-y

P (K

Pa)

0 0.2 0.4 0.6 0.8 1 1.275.00000

85.00000

95.00000

105.00000

115.00000

125.00000

135.00000

p-x1p-y1

x-yP

(KPa

)

grafico N°1 representando con la ecuacion de NRTL para el sistema acetato de metilo(1)/metanol (2) a T=60°C

0 0.2 0.4 0.6 0.8 1 1.275.00000

85.00000

95.00000

105.00000

115.00000

125.00000

135.00000

p-x1p-y1

x-y

P (K

Pa)

0 0.2 0.4 0.6 0.8 1 1.275.00000

85.00000

95.00000

105.00000

115.00000

125.00000

135.00000

p-x1p-y1

x-y

P (K

Pa)


x1 ɣ1 ɣ2 P Y10 2.74353 1.00000 84.47093 0.00000

0.05 2.48426 1.00265 94.48482 0.148430.1 2.26201 1.01059 102.36879 0.24949

0.15 2.07086 1.02386 108.58504 0.322990.2 1.90597 1.04257 113.49256 0.37922

0.25 1.76340 1.06696 117.37006 0.424080.3 1.63990 1.09736 120.43312 0.46122

0.35 1.53281 1.13421 122.84707 0.493070.4 1.43991 1.17805 124.73659 0.52134

0.45 1.35938 1.22959 126.19271 0.547310.5 1.28969 1.28969 127.27771 0.57203

0.55 1.22959 1.35938 128.02839 0.596400.6 1.17805 1.43991 128.45778 0.62126

0.65 1.13421 1.53281 128.55543 0.647490.7 1.09736 1.63990 128.28644 0.67606

0.75 1.06696 1.76340 127.58891 0.708130.8 1.04257 1.90597 126.36981 0.74519

0.85 1.02386 2.07086 124.49878 0.789240.9 1.01059 2.26201 121.79952 0.84312

0.95 1.00265 2.48426 118.03792 0.911111 1.00000 2.74353 112.90610 1.00000

0 0.2 0.4 0.6 0.8 1 1.20.00000

20.00000

40.00000

60.00000

80.00000

100.00000

120.00000

140.00000


0 0.2 0.4 0.6 0.8 1 1.20.00000

20.00000

40.00000

60.00000

80.00000

100.00000

120.00000

140.00000

X1 Y1 P x10 0 89.1670358 0

0.05 0.10195123 94.3252601 0.050.1 0.1933301 99.4834843 0.1

0.15 0.27570009 104.641709 0.150.2 0.35033085 109.799933 0.2

0.25 0.41826419 114.958157 0.250.3 0.48036292 120.116381 0.3

0.35 0.53734779 125.274606 0.350.4 0.58982549 130.43283 0.4

0.45 0.63831043 135.591054 0.450.5 0.68324159 140.749278 0.5

0.55 0.72499587 145.907503 0.550.6 0.7638987 151.065727 0.6

0.65 0.80023254 156.223951 0.650.7 0.83424371 161.382175 0.7

0.75 0.86614804 166.5404 0.750.8 0.89613541 171.698624 0.8

0.85 0.92437355 176.856848 0.850.9 0.95101118 182.015072 0.9

0.95 0.97618062 187.173297 0.951 1 192.331521 1

0 0.2 0.4 0.6 0.8 1 1.20

50

100

150

200

250

ɣ1 ɣ2 P Y12.7435261 1 84.4709273 0

2.48426184 1.00265458 94.4848203 0.148430362.26201234 1.01059482 102.368793 0.249485212.07085537 1.0238567 108.585037 0.322989541.90596591 1.04257061 113.492561 0.379223411.76339578 1.0669632 117.370064 0.424082041.63990171 1.09736234 120.433123 0.461222561.53281044 1.13420535 122.847074 0.493070581.43991252 1.17805089 124.736594 0.52133831.35937828 1.22959487 126.192706 0.54731331.28969119 1.28969119 127.277708 0.572032631.22959487 1.35937828 128.028394 0.596397541.17805089 1.43991252 128.457778 0.621258451.13420535 1.53281044 128.55543 0.647488471.09736234 1.63990171 128.286438 0.67605925

1.0669632 1.76339578 127.588911 0.708133581.04257061 1.90596591 126.369808 0.74519435

1.0238567 2.07085537 124.498779 0.789242421.01059482 2.26201234 121.799517 0.843123941.00265458 2.48426184 118.037924 0.91110997

1 2.7435261 112.906102 1

0 0.2 0.4 0.6 0.8 1 1.20

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Documents

GRUPO 4- TERMO 2