Distillation lab report calculations PDF

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Results Tables and figures show the relationship between composition of ethanol and refractive index in tabulated form and graphically, respectively. The later graphs include the T-x-y diagram of ethanol, and the mole fraction data obtained for top and bottom product.

Table 1: Relationship for composition of ethanol and refractive index (RI) Composition of ethanol

Refractive Index (RI)

0 0.03

1.3328 1.3376

0.07

1.3430

0.12

1.3471

0.17

1.3520

0.24

1.3559

0.32

1.3580

0.42 0.55

1.3602 1.3620

0.74

1.3627

1.00

1.3622

Graph of Refractive index against composition of ethanol 1.37

Refractive Index (RI)

1.36

f(x) = − 0.03 x² + 0.06 x + 1.33

1.35 1.34 1.33 1.32 1.31

0

0.1

0.2

0.3

0.4

0.5

0.6

Composition of ethanol, (x)

Figure 1: Graph of RI vs x

0.7

0.8

0.9

1

T-x-y Graph 105 100

T (oC)

95 90 85 80 75 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Composition (x)

Figure 2: T-x-y graph for ethanol in water

Table 2: Experimental data for distillate and bottoms t (min) 0

T12 67

T13 77.10

RI 1.3614

xD 0.78

T20 83.6

RI 1.3428

xB 0.191

5

69.9

76.98

1.3619

0.822

84.3

1.3418

0.172

10

63.4

76.60

1.3616

0.796

83.7

1.3416

0.168

15

63.2

77.12

1.3619

0.822

84.2

1.3415

0.166

20

61.4

77.20

1.361

0.752

84.4

1.3405

0.147

25

63

77.10

1.3616

0.796

84.1

1.3416

0.168

30

61.1

77.39

1.3616

0.796

85.6

1.3411

0.158

35

63

77.27

1.3614

0.78

85.3

1.34

0.137

40

60.6

77.29

1.3611

0.758

85.7

1.338

0.100

45

63.4

77.00

1.361

0.752

85.2

1.336

0.065

50

59.9

77.65

1.361

0.752

85.5

1.3345

0.0396

Sample Calculations



5 litres of ethanol-water mixture: 1.5L of ethanol and 3.5L of water

For the Feed: Refractive index (RI):1.3495 

Compositions: At the top: xD = 0.752 At the feed: xF = 0.30 At the bottom: xB = 0.0396



Using the feed line equation for subcooled liquid, q=1+

q=1+ 

(Eq. 1)

0.143 (78.4 −60 ) =1 39 ×10 3

Feed line equation,

Slope ¿−q/( 1−q )



C ❑ p , L (T b−T F ) λ

=∞

Rectifying Operating Line (ROL)

Using the ROL equation, y n+1 =

xD R xn + R+1 R+1

y n+1 =

0.752 2 xn + 2+1 2+1

y n+1 =0.667 xn + 0.251

Using the results from the above calculations, a graph was plotted to determine the number of theoretical trays required for an ethanol-water mixture according to the McCabe-Thiele graphical method.

McCabe Thiele Diagram for Ethanol/Water mixture 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 3: Graph for determining the number of theoretical trays required

From the graph, Number of theoretical trays required: 5.7 trays + 1 reboiler Overall Efficiency of the distillation column:

5.7 ×100=57 % 10

Table 3: x and y data for real ethanol-water mixture T 100 95.5 89 86.7 85.3 84.1 82.7

Ptot 760 760 760 760 760 760 760

Psat1 1689.062 1443.805 1141.864 1048.417 994.7 950.49 900.981

Psat2 759.983 645.737 506.195 463.294 438.701 418.501 395.924

γ1 1.983 1.778 1.403 1.258 1.176 1.115 1.059

γ2 1 1.003 1.041 1.083 1.124 1.17 1.239

x1 0 0.058 0.217 0.316 0.394 0.474 0.582

y1 0 0.197 0.457 0.548 0.607 0.661 0.729

82.3 81.5 80.7 79.8 79.7 79.3 78.7 78.4 78.2

760 760 760 760 760.004 760 760.016 760.002 756.098

887.235 860.266 833.98 805.209 802.064 789.585 771.17 762.097 756.098

389.664 377.393 365.448 352.391 350.964 345.308 336.966 332.859 330.145

1.047 1.027 1.013 1.004 1.003 1.001 1 1 1

1.261 1.307 1.353 1.402 1.407 1.426 1.449 1.458 1.46

0.614 0.684 0.758 0.846 0.856 0.897 0.96 0.992 1

0.75 0.795 0.842 0.9 0.906 0.933 0.974 0.995 1

Sample Calculations At 95.5°C, the vapor pressures of ethanol and water are calculated using the Antoine equation For ethanol, For water,

B ( A− T +C )=10( 8.04494− 95.51554.3 + 222.65) =1443.805 mmHg

Psat 1=10

B 1668.21 ( A− T +C )=10( 7.96681−95.5 + 228 ) =645.737 mmHg

Psat 2=10

The sample calculations were repeated at different temperatures to obtain vapor pressures at other temperatures. Using modified Raoult’s law: Ptot =x 1 γ 1 P sat 1+ x2 γ 2 P sat 2

(1)

Using equations for two parameter Margules Model: ln γ 1=x 2 ( A 12 +2 ( A 21− A 12) x 1 )

(2)

ln γ 2=x 12 ( A 21 +2 ( A 12− A 21) x 2 )

(3)

2

Combining (2) and (3) into (1) with data at 95.5°C gives, 2 (1−x 1 ) (0.6848−0.6134 x 1) x 0.3781 + 0.6134( 1−x ) ) ¿ 760=1 443.805 x 1 e ¿+ 645.737 ( 1−x 1) e ( 2 1

1

Solving the above equation gives, x 1=0.058, x 2=0.942, γ 1=1.778, γ 2=1.003 Same calculations were carried out at other temperatures to give x and y data in table 3.

Using the results from the above calculations, a graph was plotted to determine the actual number of trays required for a real ethanol-water mixture according to the McCabe-Thiele graphical method.

McCabe Thiele Diagram for real mixture 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Figure 4: Graph for determining the number of actual trays required for real mixture

From Figure 4, Number of actual trays required: 5.8 trays + 1 reboiler Overall Efficiency of the distillation column:

5. 8 ×100=5 8 % 10

1...