Unformatted text preview: hat mole fraction to be 0.45. Then the operating
line will intersect the equilibrium line at x = 0.45, creating the pinch zone of infinite stages. The
value of y at the intersection is given by Eq. (1):
2.5(0.45)
= 0.672
1 + 15(0.45)
.
Therefore the operating line passes through the two points, as {y, x}, of {0.75, 0.75} and
{0.672, 0.450}. Therefore, the slope = L/V = (0.75  0.672)/(0.75  0.45) = 0.260. Now compute
the overall material balances:
Overall total material balance,
F = 100 = D + B
(18)
Overall benzene material balance, xFF = yDD + xBB or 50 = 0.75D + 0.45B
(19)
Solving Eqs. (18) and (19), D = 16.67 moles or 16.67 mol/100 mol feed, and B = 83.33 moles y= Calculations for other values of the benzene mole fraction in the bottoms can be made in the
same manner.
(f) At total reflux, there is no distillate, but there is a boilup. The moles of distillate per 100
moles of feed = 0. Exercise 7.13
Subject:
Distillation of a mixture of benzene and toluene at 101 kPa for specified reflux
ratio and product compositions.
Given: Feed of 30 kg/h of saturated liquid feed containing 40 mass% benzene and 60 mass%
toluene. Distillate to contain 97 mass% benzene and bottoms to contain 98 mass% toluene.
Reflux ratio = 3.5 and feed is to optimal stage. Table of vaporliquid equilibrium data in mole
fractions. At 101 kPa.
Assumptions: Total condenser and partial reboiler. Saturated liquid reflux. Constant molar
overflow.
Find: (a) Flow rates of distillate and bottoms.
(b) Number of equilibrium stages needed.
Analysis: First solve the material balance in mass units. Then convert to moles and mole
fractions so that the McCabeThiele method can be used for part (b).
Overall total mass balance:
30 = D + B
(1)
(2)
Overall benzene mass balance:
0.40(30) = 12 = 0.97D + 0.02B
D = 12.1 kg/h
B = 17.9 kg/h
Solving Eqs. (1) and (2):
Converting to moles with molecular weights of 78.11 for benzene and 92.13 for toluene,
Benzene
Toluene
Product kmol/h Mass fraction Mole fraction Mass fraction Mole fraction
Distillate
0.154
0.97
0.974
0.03
0.0235
Bottoms
0.196
0.02
0.026
0.98
0.9765
1.00
1.000
1.00
1.0000
Total: 0.350
(b) Because benzene is the more volatile component of the feed, the x and y coordinates will be
those of benzene in the diagram on the next page.
. In moles, the feed consists of:
Component kmol/h Mole fraction
Benzene
0.154
0.44
Toluene
0.196
0.56
Total: 0.350
1.00
For a saturated liquid feed, the qline is vertical and passes through x = 0.44. The slope of the
rectifying operating line, L/V, is obtained from Eq. (77), using the specified reflux ratio = 3.5,
L/V = R/(1 + R) = 3.5/4.5 = 0.778
For saturated liquid reflux, the rectifying operating line passes through the point {0.974, 0.974}.
See the McCabeThiele construction on the next page, where it is seen that slightly more than 10
stages + a partial reboiler acting as an equilibrium stage are required. The top 5 stages are in the
rectifying section. Analysis: (b) (continued) Exercise 7.13 (continued)
McCabeThiele Diagram Exercise 7.14
Subject:
Distillation of a mixture of benzene and...
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 Spring '11
 Levicky
 The Land

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