termodinamica para ingenieria quimica ejercicio

Curso:

Termodinámica de Ingeniería Química

Profesor:

Dr. Jorge Flores Franco

Alumnos:

Diego Pérez, Amilcar

Vásquez Aguilar, Jessica Karen

Vásquez Cerquera, Israel Roman

Ciclo:

Nivelación-2013

Fecha:

01 de Febrero del 2013

TRUJILLO – PERÙ

2013

FACULTAD DE INGENIERIA QUÍMICA

E S C U E L A DE I N G E N I E R Í A QUÍMICA

Ejercicio 10.7

1

Solución con Iteraciones:

ln P1sat=13.8594− 2773.78

t+220.07

ln P2sat=14.0045− 3279.47

t+213.20

ln (α )= 3279.47t+213.20

− 2773.78t+220.07

−0.1451 ; α=P1sat

P2sat

P=P2sat+ (P1sat−P2sat ) x1

P1sat=P ( y1+ y2α )

Termodinámica de Ingeniería Química: Equilibrio Vapor Líquido

Una sola etapa de separación líquido/vapor para un sistema de benceno (1)/etilbenceno (2) debe producir fases para las siguientes composiciones de equilibrio. Para uno de estos conjuntos, determine la T y P en el separador. ¿Qué información adicional se necesita calcular para las cantidades relativas de líquido y vapor que salen del separador? Suponga que se aplica la ley de Raoult.

a) x1= 0.35, y1=0.70b) x1= 0.35, y1=0.725c) x1= 0.35, y1=0.75d) x1= 0.35, y1=0.775

EJERCICIO 10.7

Parámetros para la ecuación de AntoineSustancia A B CBenceno 13.8594 2773.78 220.07

Etilenceno 14.0045 3279.47 213.20

2

a) x1= 0.35, y1=0.70

Asumimos T=135°C

Tsupuesta

ln(α) α lnP1

P1 lnP2 P2 P P1calculado

Tcalculado

135.00 1.46 4.31 6.05 423.04 4.59 98.12 211.84 422.30 134.92134.92 1.46 4.31 6.05 422.30 4.58 97.91 211.45 421.63 134.85134.85 1.46 4.31 6.04 421.63 4.58 97.71 211.08 421.00 134.78134.78 1.46 4.32 6.04 421.00 4.58 97.53 210.75 420.43 134.72134.72 1.46 4.32 6.04 420.43 4.58 97.37 210.44 419.90 134.66134.66 1.46 4.32 6.04 419.90 4.58 97.22 210.16 419.42 134.61134.61 1.46 4.32 6.04 419.42 4.58 97.08 209.90 418.97 134.56134.56 1.46 4.32 6.04 418.97 4.57 96.96 209.66 418.57 134.52134.52 1.46 4.32 6.04 418.57 4.57 96.84 209.44 418.19 134.48134.48 1.46 4.32 6.04 418.19 4.57 96.73 209.24 417.85 134.44134.44 1.46 4.32 6.04 417.85 4.57 96.64 209.06 417.53 134.40134.40 1.46 4.32 6.03 417.53 4.57 96.55 208.89 417.24 134.37134.37 1.46 4.33 6.03 417.24 4.57 96.46 208.73 416.97 134.34134.34 1.46 4.33 6.03 416.97 4.57 96.39 208.59 416.72 134.32134.32 1.46 4.33 6.03 416.72 4.57 96.32 208.46 416.50 134.29134.29 1.46 4.33 6.03 416.50 4.57 96.25 208.34 416.29 134.27134.27 1.47 4.33 6.03 416.29 4.57 96.19 208.23 416.10 134.25134.25 1.47 4.33 6.03 416.10 4.57 96.14 208.12 415.92 134.23134.23 1.47 4.33 6.03 415.92 4.57 96.09 208.03 415.76 134.21134.21 1.47 4.33 6.03 415.76 4.56 96.04 207.94 415.61 134.20134.20 1.47 4.33 6.03 415.61 4.56 96.00 207.86 415.47 134.18134.18 1.47 4.33 6.03 415.47 4.56 95.96 207.79 415.35 134.17134.17 1.47 4.33 6.03 415.35 4.56 95.93 207.72 415.23 134.15134.15 1.47 4.33 6.03 415.23 4.56 95.89 207.66 415.12 134.14134.14 1.47 4.33 6.03 415.12 4.56 95.86 207.60 415.03 134.13134.13 1.47 4.33 6.03 415.03 4.56 95.83 207.55 414.94 134.12134.12 1.47 4.33 6.03 414.94 4.56 95.81 207.50 414.85 134.11134.11 1.47 4.33 6.03 414.85 4.56 95.79 207.46 414.78 134.11134.11 1.47 4.33 6.03 414.78 4.56 95.76 207.42 414.71 134.10134.10 1.47 4.33 6.03 414.71 4.56 95.74 207.38 414.64 134.09134.09 1.47 4.33 6.03 414.64 4.56 95.73 207.35 414.58 134.08134.08 1.47 4.33 6.03 414.58 4.56 95.71 207.32 414.53 134.08134.08 1.47 4.33 6.03 414.53 4.56 95.69 207.29 414.48 134.07134.07 1.47 4.33 6.03 414.48 4.56 95.68 207.26 414.43 134.07134.07 1.47 4.33 6.03 414.43 4.56 95.67 207.24 414.39 134.06134.06 1.47 4.33 6.03 414.39 4.56 95.65 207.21 414.35 134.06134.06 1.47 4.33 6.03 414.35 4.56 95.64 207.19 414.32 134.06134.06 1.47 4.33 6.03 414.32 4.56 95.63 207.17 414.28 134.05


3

134.05 1.47 4.33 6.03 414.28 4.56 95.62 207.16 414.25 134.05134.05 1.47 4.33 6.03 414.25 4.56 95.62 207.14 414.23 134.05134.05 1.47 4.33 6.03 414.23 4.56 95.61 207.12 414.20 134.04134.04 1.47 4.33 6.03 414.20 4.56 95.60 207.11 414.18 134.04134.04 1.47 4.33 6.03 414.18 4.56 95.59 207.10 414.16 134.04134.04 1.47 4.33 6.03 414.16 4.56 95.59 207.09 414.14 134.04134.04 1.47 4.33 6.03 414.14 4.56 95.58 207.08 414.12 134.03134.03 1.47 4.33 6.03 414.12 4.56 95.58 207.07 414.10 134.03134.03 1.47 4.33 6.03 414.10 4.56 95.57 207.06 414.09 134.03134.03 1.47 4.33 6.03 414.09 4.56 95.57 207.05 414.07 134.03134.03 1.47 4.33 6.03 414.07 4.56 95.56 207.04 414.06 134.03134.03 1.47 4.33 6.03 414.06 4.56 95.56 207.03 414.05 134.03134.03 1.47 4.33 6.03 414.05 4.56 95.56 207.03 414.04 134.02134.02 1.47 4.33 6.03 414.04 4.56 95.55 207.02 414.02 134.02134.02 1.47 4.33 6.03 414.02 4.56 95.55 207.02 414.02 134.02134.02 1.47 4.33 6.03 414.02 4.56 95.55 207.02 414.02 134.02

T=134.02°C y P=207.02 kPa

b) x1= 0.35, y1=0.725

Asumimos T=115°C

tsupuesta

ln(α) α lnP1 P1 lnP2

P2 P P1calculado t calculado

115.00 1.57 4.80 5.58 265.39 4.01 55.27 128.81 263.48 114.71114.71 1.57 4.81 5.57 263.48 4.00 54.78 127.82 261.75 114.44114.44 1.57 4.82 5.57 261.75 4.00 54.34 126.93 260.17 114.20114.20 1.57 4.82 5.56 260.17 3.99 53.93 126.12 258.74 113.98113.98 1.57 4.83 5.56 258.74 3.98 53.57 125.38 257.44 113.77113.77 1.58 4.84 5.55 257.44 3.97 53.24 124.71 256.25 113.59113.59 1.58 4.84 5.55 256.25 3.97 52.93 124.09 255.17 113.42113.42 1.58 4.85 5.54 255.17 3.96 52.66 123.54 254.19 113.26113.26 1.58 4.85 5.54 254.19 3.96 52.41 123.03 253.30 113.12113.12 1.58 4.85 5.53 253.30 3.95 52.18 122.57 252.48 112.99112.99 1.58 4.86 5.53 252.48 3.95 51.98 122.15 251.74 112.88112.88 1.58 4.86 5.53 251.74 3.95 51.79 121.77 251.07 112.77112.77 1.58 4.86 5.53 251.07 3.94 51.62 121.43 250.45 112.67112.67 1.58 4.87 5.52 250.45 3.94 51.46 121.11 249.89 112.58112.58 1.58 4.87 5.52 249.89 3.94 51.32 120.82 249.38 112.50112.50 1.58 4.87 5.52 249.38 3.94 51.19 120.56 248.92 112.43112.43 1.58 4.87 5.52 248.92 3.93 51.07 120.32 248.49 112.36112.36 1.58 4.88 5.52 248.49 3.93 50.96 120.10 248.11 112.30112.30 1.58 4.88 5.51 248.11 3.93 50.87 119.90 247.75 112.24


4

112.24 1.58 4.88 5.51 247.75 3.93 50.78 119.72 247.43 112.19112.19 1.59 4.88 5.51 247.43 3.93 50.70 119.55 247.14 112.14112.14 1.59 4.88 5.51 247.14 3.92 50.62 119.40 246.87 112.10112.10 1.59 4.88 5.51 246.87 3.92 50.56 119.27 246.63 112.06112.06 1.59 4.88 5.51 246.63 3.92 50.49 119.14 246.40 112.02112.02 1.59 4.89 5.51 246.40 3.92 50.44 119.03 246.20 111.99111.99 1.59 4.89 5.51 246.20 3.92 50.39 118.92 246.02 111.96111.96 1.59 4.89 5.51 246.02 3.92 50.34 118.83 245.85 111.93111.93 1.59 4.89 5.50 245.85 3.92 50.30 118.74 245.69 111.91111.91 1.59 4.89 5.50 245.69 3.92 50.26 118.66 245.55 111.89111.89 1.59 4.89 5.50 245.55 3.92 50.22 118.59 245.42 111.86111.86 1.59 4.89 5.50 245.42 3.92 50.19 118.52 245.31 111.85111.85 1.59 4.89 5.50 245.31 3.92 50.16 118.46 245.20 111.83111.83 1.59 4.89 5.50 245.20 3.91 50.13 118.41 245.10 111.81111.81 1.59 4.89 5.50 245.10 3.91 50.11 118.36 245.01 111.80111.80 1.59 4.89 5.50 245.01 3.91 50.09 118.31 244.93 111.78111.78 1.59 4.89 5.50 244.93 3.91 50.07 118.27 244.86 111.77111.77 1.59 4.89 5.50 244.86 3.91 50.05 118.23 244.79 111.76111.76 1.59 4.89 5.50 244.79 3.91 50.03 118.20 244.73 111.75111.75 1.59 4.89 5.50 244.73 3.91 50.02 118.17 244.67 111.74111.74 1.59 4.89 5.50 244.67 3.91 50.00 118.14 244.62 111.73111.73 1.59 4.89 5.50 244.62 3.91 49.99 118.11 244.58 111.73111.73 1.59 4.89 5.50 244.58 3.91 49.98 118.09 244.53 111.72111.72 1.59 4.89 5.50 244.53 3.91 49.97 118.06 244.49 111.71111.71 1.59 4.89 5.50 244.49 3.91 49.96 118.04 244.46 111.71111.71 1.59 4.89 5.50 244.46 3.91 49.95 118.03 244.43 111.70111.70 1.59 4.89 5.50 244.43 3.91 49.94 118.01 244.40 111.70111.70 1.59 4.89 5.50 244.40 3.91 49.93 117.99 244.37 111.69111.69 1.59 4.89 5.50 244.37 3.91 49.92 117.98 244.35 111.69111.69 1.59 4.89 5.50 244.35 3.91 49.92 117.97 244.32 111.69111.69 1.59 4.90 5.50 244.32 3.91 49.91 117.96 244.30 111.68111.68 1.59 4.90 5.50 244.30 3.91 49.91 117.95 244.28 111.68111.68 1.59 4.90 5.50 244.28 3.91 49.90 117.94 244.27 111.68111.68 1.59 4.90 5.50 244.27 3.91 49.90 117.93 244.25 111.67111.67 1.59 4.90 5.50 244.25 3.91 49.89 117.92 244.24 111.67111.67 1.59 4.90 5.50 244.24 3.91 49.89 117.91 244.22 111.67111.67 1.59 4.90 5.50 244.22 3.91 49.89 117.91 244.21 111.67111.67 1.59 4.90 5.50 244.21 3.91 49.88 117.90 244.20 111.67111.67 1.59 4.90 5.50 244.20 3.91 49.88 117.89 244.19 111.66111.66 1.59 4.90 5.50 244.19 3.91 49.88 117.89 244.18 111.66111.66 1.59 4.90 5.50 244.18 3.91 49.88 117.88 244.17 111.66

T=111.66°C y P=117.89 kPa


5

c) x1= 0.35, y1=0.75

Asumimos T=90°C

tsupuesta ln(α) α lnP1 P1 lnP2 P2 P P1calculado t calculado90.00 1.73 5.61 4.91 136.15 3.19 24.25 63.41 136.57 90.1190.11 1.72 5.61 4.92 136.57 3.19 24.34 63.62 136.96 90.2190.21 1.72 5.61 4.92 136.96 3.20 24.43 63.81 137.31 90.3090.30 1.72 5.60 4.92 137.31 3.20 24.50 63.99 137.63 90.3890.38 1.72 5.60 4.92 137.63 3.20 24.57 64.14 137.92 90.4590.45 1.72 5.60 4.93 137.92 3.20 24.64 64.29 138.18 90.5190.51 1.72 5.60 4.93 138.18 3.21 24.70 64.42 138.42 90.5790.57 1.72 5.59 4.93 138.42 3.21 24.75 64.53 138.63 90.6390.63 1.72 5.59 4.93 138.63 3.21 24.80 64.64 138.83 90.6890.68 1.72 5.59 4.93 138.83 3.21 24.84 64.74 139.01 90.7290.72 1.72 5.59 4.93 139.01 3.21 24.88 64.82 139.17 90.7690.76 1.72 5.59 4.94 139.17 3.22 24.91 64.90 139.31 90.8090.80 1.72 5.58 4.94 139.31 3.22 24.95 64.97 139.44 90.8390.83 1.72 5.58 4.94 139.44 3.22 24.97 65.04 139.56 90.8690.86 1.72 5.58 4.94 139.56 3.22 25.00 65.10 139.67 90.8990.89 1.72 5.58 4.94 139.67 3.22 25.03 65.15 139.77 90.9190.91 1.72 5.58 4.94 139.77 3.22 25.05 65.20 139.86 90.9390.93 1.72 5.58 4.94 139.86 3.22 25.07 65.24 139.94 90.9590.95 1.72 5.58 4.94 139.94 3.22 25.08 65.28 140.01 90.9790.97 1.72 5.58 4.94 140.01 3.22 25.10 65.32 140.07 90.9990.99 1.72 5.58 4.94 140.07 3.22 25.11 65.35 140.13 91.0091.00 1.72 5.58 4.94 140.13 3.22 25.13 65.38 140.19 91.0291.02 1.72 5.58 4.94 140.19 3.22 25.14 65.41 140.24 91.0391.03 1.72 5.58 4.94 140.24 3.22 25.15 65.43 140.28 91.0491.04 1.72 5.58 4.94 140.28 3.23 25.16 65.45 140.32 91.0591.05 1.72 5.58 4.94 140.32 3.23 25.17 65.47 140.36 91.0691.06 1.72 5.57 4.94 140.36 3.23 25.18 65.49 140.39 91.0791.07 1.72 5.57 4.94 140.39 3.23 25.18 65.51 140.42 91.0791.07 1.72 5.57 4.94 140.42 3.23 25.19 65.52 140.45 91.0891.08 1.72 5.57 4.94 140.45 3.23 25.20 65.54 140.47 91.0991.09 1.72 5.57 4.95 140.47 3.23 25.20 65.55 140.49 91.0991.09 1.72 5.57 4.95 140.49 3.23 25.21 65.56 140.51 91.1091.10 1.72 5.57 4.95 140.51 3.23 25.21 65.57 140.53 91.1091.10 1.72 5.57 4.95 140.53 3.23 25.22 65.58 140.55 91.1191.11 1.72 5.57 4.95 140.55 3.23 25.22 65.59 140.56 91.1191.11 1.72 5.57 4.95 140.56 3.23 25.22 65.59 140.58 91.1191.11 1.72 5.57 4.95 140.58 3.23 25.23 65.60 140.59 91.1291.12 1.72 5.57 4.95 140.59 3.23 25.23 65.61 140.60 91.1291.12 1.72 5.57 4.95 140.60 3.23 25.23 65.61 140.61 91.1291.12 1.72 5.57 4.95 140.61 3.23 25.23 65.62 140.62 91.1291.12 1.72 5.57 4.95 140.62 3.23 25.24 65.62 140.63 91.1391.13 1.72 5.57 4.95 140.63 3.23 25.24 65.62 140.64 91.13


6

91.13 1.72 5.57 4.95 140.64 3.23 25.24 65.63 140.64 91.1391.13 1.72 5.57 4.95 140.64 3.23 25.24 65.63 140.65 91.1391.13 1.72 5.57 4.95 140.65 3.23 25.24 65.63 140.65 91.1391.13 1.72 5.57 4.95 140.65 3.23 25.24 65.64 140.66 91.1391.13 1.72 5.57 4.95 140.66 3.23 25.24 65.64 140.66 91.1391.13 1.72 5.57 4.95 140.66 3.23 25.25 65.64 140.67 91.1491.14 1.72 5.5

74.95 140.67 3.23 25.2

565.65 140.67 91.14

91.14 1.72 5.57

4.95 140.67 3.23 25.25

65.65 140.67 91.14

91.14 1.72 5.57

4.95 140.67 3.23 25.25

65.65 140.67 91.14

T=91.14°C y P=65.65 kPa

d) x1= 0.35, y1=0.775

Asumimos T=71°C

tsupuesta ln(α) α lnP1

P1 lnP2 P2 P P1calculado t calculado

71.00 1.86 6.45 4.33 75.93 2.47 11.77 34.22 76.22 71.1171.11 1.86 6.45 4.33 76.22 2.47 11.82 34.36 76.47 71.2271.22 1.86 6.44 4.34 76.47 2.47 11.87 34.48 76.70 71.3171.31 1.86 6.44 4.34 76.70 2.48 11.91 34.59 76.91 71.3971.39 1.86 6.43 4.34 76.91 2.48 11.96 34.69 77.10 71.4771.47 1.86 6.43 4.35 77.10 2.48 11.99 34.78 77.27 71.5471.54 1.86 6.43 4.35 77.27 2.49 12.02 34.86 77.42 71.6071.60 1.86 6.42 4.35 77.42 2.49 12.05 34.93 77.56 71.6571.65 1.86 6.42 4.35 77.56 2.49 12.08 35.00 77.68 71.7071.70 1.86 6.42 4.35 77.68 2.49 12.10 35.05 77.79 71.7471.74 1.86 6.42 4.35 77.79 2.50 12.12 35.11 77.89 71.7871.78 1.86 6.41 4.36 77.89 2.50 12.14 35.15 77.98 71.8271.82 1.86 6.41 4.36 77.98 2.50 12.16 35.20 78.06 71.8571.85 1.86 6.41 4.36 78.06 2.50 12.18 35.23 78.13 71.8871.88 1.86 6.41 4.36 78.13 2.50 12.19 35.27 78.19 71.9071.90 1.86 6.41 4.36 78.19 2.50 12.20 35.30 78.25 71.9271.92 1.86 6.41 4.36 78.25 2.50 12.21 35.33 78.30 71.9471.94 1.86 6.41 4.36 78.30 2.50 12.22 35.35 78.35 71.9671.96 1.86 6.40 4.36 78.35 2.50 12.23 35.37 78.39 71.9871.98 1.86 6.40 4.36 78.39 2.50 12.24 35.39 78.43 71.9971.99 1.86 6.40 4.36 78.43 2.51 12.25 35.41 78.47 72.0172.01 1.86 6.40 4.36 78.47 2.51 12.26 35.43 78.50 72.0272.02 1.86 6.40 4.36 78.50 2.51 12.26 35.44 78.52 72.0372.03 1.86 6.40 4.36 78.52 2.51 12.27 35.46 78.55 72.0472.04 1.86 6.40 4.36 78.55 2.51 12.27 35.47 78.57 72.0572.05 1.86 6.40 4.36 78.57 2.51 12.28 35.48 78.59 72.06


7

72.06 1.86 6.40 4.36 78.59 2.51 12.28 35.49 78.61 72.0672.06 1.86 6.40 4.36 78.61 2.51 12.28 35.50 78.62 72.0772.07 1.86 6.40 4.36 78.62 2.51 12.29 35.50 78.64 72.0772.07 1.86 6.40 4.36 78.64 2.51 12.29 35.51 78.65 72.0872.08 1.86 6.40 4.37 78.65 2.51 12.29 35.52 78.66 72.0872.08 1.86 6.40 4.37 78.66 2.51 12.29 35.52 78.67 72.0972.09 1.86 6.40 4.37 78.67 2.51 12.30 35.53 78.68 72.0972.09 1.86 6.40 4.37 78.68 2.51 12.30 35.53 78.69 72.1072.10 1.86 6.40 4.37 78.69 2.51 12.30 35.54 78.70 72.1072.10 1.86 6.40 4.37 78.70 2.51 12.30 35.54 78.71 72.1072.10 1.86 6.40 4.37 78.71 2.51 12.30 35.54 78.71 72.1072.10 1.86 6.40 4.37 78.71 2.51 12.30 35.55 78.72 72.1172.11 1.86 6.40 4.37 78.72 2.51 12.30 35.55 78.72 72.1172.11 1.86 6.40 4.37 78.72 2.51 12.30 35.55 78.73 72.1172.11 1.86 6.40 4.37 78.73 2.51 12.31 35.55 78.73 72.11

T=72.11°C y P=35.55 kPa


8

Solución Matemática:

ln P1sat=13.8594− 2773.78

t+220.07

ln P2sat=14.0045− 3279.47

t+213.20

P1sat=

y1x1P

P2sat=

y2x2P

ln (α )= 3279.47t+213.20

− 2773.78t+220.07

−0.1451 ; α=P1sat

P2sat=

y1x1y2x2


a. x1= 0.35, x2= 0.65, y1=0.70 y y2= 0.30

ln (0.700.350.300.65

)= 3279.47t+213.20

−2773.78t+220.07

−0.1451

1.47= 3279.47t+213.20

− 2773.78t+220.07

−0.1451

t=134.02 °C

ln P1sat=13.8594− 2773.78

134.02+220.07P1sat=413.98kPa

ln P2sat=14.0045− 3279.47

134.02+213.20P2sat=95.54kPa


Parámetros para la ecuación de AntoineSustancia A B CBenceno 13.8594 2773.78 220.07

Etilenceno 14.0045 3279.47 213.20

9


P=95.54+(413.98−95.54 )0.35P=206.99 kPa

b. x1= 0.35, x2= 0.65, y1=0.725 y y2= 0.275

ln (0.7250.350.2750.65

)= 3279.47t+213.20

−2773.78t+220.07

−0.1451

1.59= 3279.47t+213.20

− 2773.78t+220.07

−0.1451

t=111.65 °C

ln P1sat=13.8594− 2773.78

111.65+220.07

P1sat=244.13kPa

ln P2sat=14.0045− 3279.47

111.65+213.20

P2sat=49.87kPa


P=49.87+(244.13−49.87 )0.35

P=117.86 kPa

c. x1= 0.35, x2= 0.65, y1=0.75 y y2= 0.25

ln (0.750.350.250.65

)= 3279.47t+213.20

−2773.78t+220.07

−0.1451


10

1.72= 3279.47t+213.20

− 2773.78t+220.07

−0.1451

t=91.15 ° C

ln P1sat=13.8594− 2773.78

91.15+220.07

P1sat=140.74kPa

ln P2sat=14.0045− 3279.47

91.15+213.20

P2sat=25.26kPa


P=25.26+(140.74−25.26 )0.35

P=65.68kPa

d. x1= 0.35, x2= 0.65, y1=0.775 y y2= 0.225

ln (0.7750.350.2250.65

)= 3279.47t+213.20

−2773.78t+220.07

−0.1451

1.86= 3279.47t+213.20

− 2773.78t+220.07

−0.1451

t=72.18 °C

ln P1sat=13.8594− 2773.78

72.18+220.07

P1sat=78.90kPa

ln P2sat=14.0045− 3279.47

72.18+213.20

P2sat=12.34kPa



11

P=12.34+(78.90−12.34 )0.35

P=35.64 kPa


termodinamica para ingenieria quimica ejercicio

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