"Regla de las Fases" que relaciona la varianza (nmero de grados de libertad) para un sistema qumicamente no reactivo que se encuentra en equilibrio heterogneo, con el nmero de fases que coexisten y el nmero de componentes presentes.Equilibrio vapor - lquido de solucionesEl estudio del equilibrio vapor - lquido de soluciones hace referencia a las condiciones de equilibrio entre un vapor y el lquido en contacto con ste. F = C - P + 2
C = nmero de componentes del sistemaP = nmero de fases presentes en el equilibrioF = nmero de grados de libertadEl nmero de grados de libertad se define como el nmero de variables independientes que tienen que fijarse para definir por completo el sistema. Para estos sistemas se considerarn sus propiedades intensivas (temperatura, presin y concentracin).F = C - P + 2
Nmero de fases P = 2 (1 fase lquida y 1 fase vapor).Si los dos componentes lquidos son completamente miscibles, se tendr una sola fase lquida. Mezclas Binarias:
Constituida por n componentes, y bajo la suposicin de que los lquidos son completamente miscibles: Nmero de componentes: C = n Nmero de fases: P = 2Entonces el nmero de grados de libertad ser:
F = 2 - 2 + 2 = 2 grados de libertad. Mezclas Multicomponentes:Luego el nmero de grados de libertad ser:
F = n - 2 + 2 = n grados de libertad.
Diagramas de FasesMezclas binarias: Es posible representar grficamente el equilibrio entre las fases vapor - lquido, relacionando las variables temperatura, presin y concentracin; lo que requiere de un diagrama tridimensional.
Fijando una de las variables, la relacin entre las dos restantes se puede representar en un diagrama plano.TemperaturaPresin vs composicinPresinTemperatura vs composicin
Representacin de la temperatura de equilibrio (T) vs composicin, expresada en fraccin molar, en las fases lquido (x) y vapor (y), a presin constante,Diagrama Temperatura Composicin
Sistema metanol agua760 mm Hg
T Cxy100.00.000.00096.40.020.13493.50.040.23091.20.060.30489.30.080.36587.70.100.41884.40.150.51781.70.200.57978.00.300.66575.30.400.72973.10.500.77971.20.600.82569.30.700.87067.60.800.91566.00.900.95865.00.950.97964.51.001.000
Grfico1
10010096.487.77873.167.6
96.496.496.487.77873.167.6
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
00
11
Pgina &P
Ejemplo
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Calor de mezcla Metanol - Agua 42.37 C
Resultado
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Metanol - agua PT = 1 atm
Diagrama
00
00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
0000000
0000000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
0
0
0
0
0
0
0
0
0
0
0
Grfico2
100100607070
96.496.47070
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Lquido subenfriado
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
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Pgina &P
Ejemplo
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Calor de mezcla Metanol - Agua 42.37 C
Resultado
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Metanol - agua PT = 1 atm
Diagrama
00
00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
600.4
700.4
700
700.4
00000
0000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Lquido subenfriado
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11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
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0
0
0
0
0
0
0
0
0
0
Grfico3
1001006075.375.3
96.496.475.375.3
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Lquido saturado o en su punto de burbuja
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
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Pgina &P
Ejemplo
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Calor de mezcla Metanol - Agua 42.37 C
Resultado
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00
00
Metanol - agua PT = 1 atm
Diagrama
00
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0
0
0
0
0
0
0
0
0
0
0
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0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
600.4
75.30.4
75.30
75.30.4
00000
0000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Lquido saturado o en su punto de burbuja
00
11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
0
0
0
0
0
0
0
0
0
0
0
Grfico5
1001006088.288.2
96.496.488.288.2
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Vapor saturado o en su punto de roco
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
00
11
Pgina &P
Ejemplo
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Calor de mezcla Metanol - Agua 42.37 C
Resultado
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Metanol - agua PT = 1 atm
Diagrama
00
00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
600.4
88.20.4
88.20
88.20.4
00000
0000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Vapor saturado o en su punto de roco
00
11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
0
0
0
0
0
0
0
0
0
0
0
Grfico4
100100609595
96.496.49595
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Vapor sobrecalentado
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
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Pgina &P
Ejemplo
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Calor de mezcla Metanol - Agua 42.37 C
Resultado
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00
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00
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Metanol - agua PT = 1 atm
Diagrama
00
00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
600.4
950.4
950
950.4
00000
0000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Vapor sobrecalentado
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F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
0
0
0
0
0
0
0
0
0
0
0
Grfico6
1001006084.484.4
96.496.484.484.4
93.593.5
91.291.2
89.389.3
87.787.7
84.484.4
81.781.7
7878
75.375.3
73.173.1
71.271.2
69.369.3
67.667.6
6666
6565
64.564.5
Mezcla lquido + vapor
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
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Pgina &P
Ejemplo
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Calor de mezcla Metanol - Agua 42.37 C
Resultado
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00
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00
00
Metanol - agua PT = 1 atm
Diagrama
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0
0
0
0
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0
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0
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0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
96.40.02T Cxy
96.40.134100.00.000.000
96.40.020.134
87.70.1093.50.040.230
87.70.41891.20.060.304
89.30.080.365
78.00.3087.70.100.418
78.00.66584.40.150.517
81.70.200.579
73.10.5078.00.300.665
73.10.77975.30.400.729
73.10.500.779
67.60.8071.20.600.825
67.60.91569.30.700.870
67.60.800.915
66.00.900.958
65.00.950.979
64.51.001.000
600.4
84.40.4
84.40
84.40.4
00000
0000
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Mezcla lquido + vapor
00
11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207
809.035420744116572.4838195734
797.345885478816423.2761497221
803.01855249116276.8300791381
820.303895988216138.1395656877
819.73989228616069.2382538783
833.30566380316004.123458899
Diagrama H-x-y metanol- agua BTU/lb mol
0
0
0
0
0
0
0
0
0
0
0
xzFy y zF= ------ zF - x
T < TburbujaLquido sub-enfriado o por debajo del punto de burbujaT = TburbujaLquido saturado, en su punto de burbuja o en su punto de ebullicinT = TrocoVapor saturado o en su punto de rocioT > TrocoVapor sobrecalentadoTroco > T > TburbujaMezcla lquido + vapor
Diagrama de distribucin diagrama x-yRepresentacin de la composicin del vapor (y) frente a la composicin del lquido (x).
Grfico8
00
0.1341
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
x
y
Ecuaciones
Clculo de Entalpas Molares
Lquido saturado o subenfriado
HL = CL . Mwprom (tL - tO) + DHs
HL =Entalpa molar de un lquido
CL =Capacidad calorfica de la solucin
CL debe evaluarse a la temperatura promedio entre tL y to.
Mwprom = Peso molecular promedio de la solucin
Mwprom = MwA . xA + MwB . xB
MwA = Peso molecular de A
MwB = Peso molecular de B
Cuando no se tiene informacin sobre CL, como una aproximacin se puede calcular CL . Mwprom
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tL y to
tL =Temperatura de la solucin
Lquido saturadotL = Temperatura de burbuja
Lquido subenfriadotL < Temperatura de burbuja
to =Temperatura de referencia
DHs =Calor integral de solucin o calor de mezcla
La temperatura a la cual estn disponibles los datos de calor de mezcla debe utilizarse como temperatura de referencia
Vapor saturado o sobrecalentado
HV = yA [ CLA . MwA (tV - tO) + lA . MwA ] + yB [ CLB . MwB (tV - tO) + lB . MwB ]
HV =Entalpa molar de un vapor
CLA = Capacidad calorfica del componente A como lquido puro
CLB = Capacidad calorfica del componente B como lquido puro
CLA y CLB deben evaluarse a la temperatura promedio entre tG y to
MwA = Peso molecular de A
MwB = Peso molecular de B
lA = Calor latente de vaporizacin de A
lB = Calor latente de vaporizacin de B
Los calores latentes de vaporizacin deben evaluarse a tG
tV =Temperatura de la mezcla en fase vapor
Vapor saturadotG = Temperatura de roco
Vapor sobrecalentadotG > Temperatura de roco
to =Temperatura de referencia
Pgina &P
Ejemplo
Construccin de datos entalpa - concentracin para el sistema metanol ( A )- agua ( B ) a 1 atm.
1.- Obtener datos de equilibrio del sistema a 1 atmsfera de presin
Datos de equilibrio metanol - agua
xyT
0.000.000100.0
0.020.13496.4
0.040.23093.5
0.060.30491.2
0.080.36589.3
0.100.41887.7
0.150.51784.4MwA =32.042lb / lb mol
0.200.57981.7
0.300.66578.0MwB =18.015lb / lb mol
0.400.72975.3
0.500.77973.1
0.600.82571.2
0.700.87069.3
0.800.91567.6
0.900.95866.0
0.950.97965.0
1.001.00064.5
2.- Obtener informacin de capacidades calorficas de solucin, calor latente de vaporizacin y calores de mezcla.
a) Capacidad calorfica de solucin
Como no se dispone de informacin para capacidad calorfica de soluciones de metanol y agua se utilizar la siguiente relacin:
CL . Mwprom = CLA . MwA . xA + CLB . MwB . xB
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KT = K
C1C2C3C4C5
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06
b) Calores latentes molares de vaporizacin
C2 + C3 . Tr + C4 . Tr2
li . Mwi =C1 (1 - Tr )J / Kmol
C1C2C3C4Tc
Metanol5.2390E+070.368200512.64 K
Agua5.2053E+070.3199-0.2120.25795647.13 K
c) Calores de mezcla a 42.37 C
xBxAQ KJ/gmol ADHs KJ/Kmol mezcla
0.001.000.00000.000
0.050.95-0.0710-67.450
0.100.90-0.1510-135.900
0.150.85-0.2510-213.350
0.200.80-0.3560-284.800
0.250.75-0.4730-354.750
0.300.70-0.5940-415.800
0.350.65-0.7240-470.600
0.400.60-0.8660-519.600
0.450.55-1.0130-557.150
0.500.50-1.1930-596.500
0.550.45-1.4020-630.900
0.600.40-1.6320-652.800
0.650.35-1.9080-667.800
0.700.30-2.2640-679.200
0.750.25-2.6910-672.750
0.800.20-3.1850-637.000
0.850.15-3.7250-558.750
0.900.10-4.3520-435.200
0.950.05-4.9970-249.850
1.000.000.00000.000
DHs =-6348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229
KJ/Kmol mezcla
Lquido saturado
HL = CL . Mwprom (tL - tO) + DHs
x =0.95
tL =65 C = 338.15 K
to =42.37 C = 315.52 K
DHs =-67.45KJ / Kmol
CL debe evaluarse a tprom y en funcin de la concentracin. Como no se tiene datos de CL, se calcular como una aproximacin CL . Mwprom
CL . Mwprom = CLA . MwA xA + CLB . MwB . xB
CLA y CLB se calcularn a la tprom
tprom = ( tL+tO ) / 2 =326.835K
CLA . MwA =8.75987E+04J / Kmol - K =87.59868KJ / Kmol - K
CLB . MwB =7.52634E+04J / Kmol - K =75.26341KJ / Kmol - K
CL . Mwprom =86.98192KJ / Kmol - K
HL =86.98192 * ( 65 - 42.37) - 67.45 =1900.9508KJ / Kmol
HL =817.8091952498BTU/lb mol
Vapor saturado
HV = y [ CLA . MwA (tv - tO) + lA . MwA ] + (1 - y) [ CLB . MwB (tv - tO) + lB . MwB ]
y =0.95000
tV =66.4 C = 339.55 K
to =42.37 C = 315.22 K
CLA y CLB se calcularn a la tprom
tprom =( tL + tO ) / 2 =327.535 K
CLA . MwA =8.77747E+04J / Kmol - K =87.77474KJ / Kmol - K
CLB . MwB =7.52677E+04J / Kmol - K =75.26765KJ / Kmol - K
lA y lB se calcularn a tvTrA =0.6624TrB=0.5247
lA . MwA =3.51259E+07J / Kmol =3.51259E+04KJ / Kmol
lB . MwB =4.22766E+07J / Kmol =4.22766E+04KJ / Kmol
Hv =0.95 { [ 87.77474*(66.4-42.37)]+[3.51259E+04] } + (1 - 0.95 { 75.26765*[66.4-42.37)]+[ 4.22766E+04] }
Hv =37577.6120KJ / KmolHv =16166.2870160926BTU/lb mol
00
11
Pgina &P
Ejemplo
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Calor de mezcla Metanol - Agua 42.37 C
Resultado
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
00
Metanol - agua PT = 1 atm
Diagrama
00
00
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
T CT KxCL . MwpromDHsHLyCLA MWACLB MWBlA MWAlB MWBHVT CxHL BTU/lbmolyHV BTU/lbmol
100.0373.150.0075.445510.004347.92500.00092.2758075.4455132442.640940799.213545147.1385100.00.001870.32950841070.00019420.7639668166
96.4369.550.0275.74709-110.313982.30470.13491.7682275.4201332748.452140966.652044058.723396.40.021713.05207627480.13418952.5647510421
93.5366.650.0476.03921-209.703678.18340.23091.3637675.4006932991.283241099.845643277.837793.50.041582.22946190790.23018616.6543449571
91.2364.350.0676.32553-296.563430.41630.30491.0457875.3859433181.715041204.430742679.080291.20.061475.6484778220.30418359.0892056138
89.3362.450.0876.60706-371.863223.30560.36590.7849875.3742033337.625441290.135942188.758889.30.081386.5564909940.36518148.1696352338
87.7360.850.1076.88484-436.563048.62600.41890.5666675.3646433467.954641361.829441766.515887.70.101311.41526766520.41817966.5350249393
84.4357.550.1577.56201-557.822702.11090.51790.1201875.3458633734.042941508.332740976.850284.40.151162.35624949350.51717626.8477506137
81.7354.850.2078.21692-631.612444.66590.57989.7586875.3314833949.102941626.853340472.760081.70.201051.61216970040.57917410.0052989911
78.0351.150.3079.49991-681.092151.48950.66589.2688475.3132334240.071441787.342539782.481178.00.30925.49762299480.66517113.0707537242
75.3348.450.4080.74678-655.322003.67400.72988.9154475.3010134449.751741903.075639276.092375.30.40861.9124191350.72916895.2395178918
73.1346.250.5081.96089-595.291923.36840.77988.6300175.2917634618.997141996.530638882.447873.10.50827.36771189180.77916725.9070591207
71.2344.350.6083.14492-516.321880.75170.82588.3853375.2843034764.029542076.639038525.787371.20.60809.03542074410.82516572.4838195734
69.3342.450.7084.28284-416.161853.57720.87088.1423575.2773234908.031042156.195738178.926669.30.70797.34588547880.87016423.2761497221
67.6340.750.8085.39540-287.761866.76430.91587.9263775.2715135036.015942226.915637838.485867.60.80803.0185524910.91516276.8300791381
66.0339.150.9086.47855-136.541906.94730.95887.7243475.2664135155.743842293.080937516.074266.00.90820.30389598820.95816138.1395656877
65.0338.150.9586.98192-62.761905.63620.97987.5986875.2634135230.219942334.241637355.900465.00.95819.7398922860.97916069.2382538783
64.5337.651.0087.536030.001937.17231.00087.5360375.2619635267.356842354.766837204.529164.51.00833.3056638031.00016004.123458899
CLi . Mwi =C1 + C2 . T + C3 . T2 + C4 . T3 + C5 . T4J/Kmol - KC2 + C3 . Tr + C4 . Tr2
T = Kli . Mwi=C1 (1 - Tr )J / Kmol
C1C2C3C4C5C1C2C3C4Tc
Metanol1.0580E+05-3.6223E+029.3791E-010.0000E+000.0000E+00Metanol5.2390E+070.368200512.64 K
Agua2.7637E+05-2.0901E+038.1250E+00-1.4116E-029.3701E-06Agua5.2053E+070.3199-0.2120.25795647.13 K
DHs =-6.348.6164 x6 + 10345.5832 x5 + 5571.5608 x4 - 21789.6758 x3 + 18218.6411 x2 - 6002.3764 x + 2.6229KJ/Kmol mezcla
to =42.37C
MwA =32.042kg / k molHL =KJ / Kmol
MwB =18.016kg / k molHV =KJ / Kmol
00
11
F0.4-842.5178F0.4-362.4225
Metanol - aguaPT = 1 atm
T Cxy
100.00.000.000
96.40.020.1348.7719298246
93.50.040.2305.2631578947
91.20.060.3044.0983606557
89.30.080.3653.5087719298
87.70.100.4183.1446540881
84.40.150.5172.7247956403
81.70.200.5792.6385224274
78.00.300.6652.7397260274
75.30.400.7293.0395136778
73.10.500.7793.5842293907
71.20.600.8254.4444444444
69.30.700.8705.8823529412
67.60.800.9158.6956521739
66.00.900.95817.2413793103
65.00.950.97934.4827586207
64.51.001.000
4347.925006650345147.13846937360
3982.304683017244058.7232627452
3678.183449895843277.8377299859
3430.41634583442679.0801821013
3223.305633160242188.7588401542
3048.62603661241766.5157751643
2702.110928091740976.8502173897
2444.665942218540472.7600484257
2151.489478468339782.4810741068
2003.673975011939276.0922943509
1923.36844820838882.4478436712
1880.751665041138525.7872997248
1853.577189919138178.9266230295
1866.764347928437838.4857918527
1906.947308685937516.0741799391
1905.636178326637355.9004056069
1937.172309766437204.5290862108
x , y
H
Diagrama Entalpa - Concentracin CH3OH - H2Oto = 42.37 C ( H KJ/Kmol)
00
0.1340
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
1870.329508410719420.76396681660
1713.052076274818952.5647510421
1582.229461907918616.6543449571
1475.64847782218359.0892056138
1386.55649099418148.1696352338
1311.415267665217966.5350249393
1162.356249493517626.8477506137
1051.612169700417410.0052989911
925.497622994817113.0707537242
861.91241913516895.2395178918
827.367711891816725.9070591207