Unformatted text preview: L
(3)
Solving for yB
L
3
y B = y1 + ( x1 − x D )
= 0.750 + (0.545 − 0.750)
= 0.596
V
4 Analysis: (b) (continued) Exercise 7.12 (continued) The mole fraction of benzene in the bottoms product is in equilibrium with yB =0.596.
Therefore,
the form of Eq. (2) applies,
yB
0.596
xB =
=
= 0.371
y B + α (1 − y B ) 0.596 + 2.5(1 − 0.596)
Overall total material balance,
F = 100 = D + B
(4)
Overall benzene material balance, xFF = xDD + xBB or 50 = 0.75D + 0.371B (5)
Solving Eqs. (4) and (5), D = 34.2 moles or 34.2 mol/100 mol feed, and B = 65.8 moles.
(c) With the feed to the theoretical plate, the following results apply from part (b), y1 = 0.75
xD = 0.75
x1 = 0.545
Benzene material balance around Stage 1, which now includes the feed,
xFF + y BV + x D L = y1V + x1 L
(6)
Solving for yB,
V
L
L
F
V
L
L
100
y B = y1
+ x1
− xD
− xF
= 0.750
+ 0.545
− 0.750
− 0.50
(7)
V
V
V
V
V
V
V
V
Because the feed is a saturated liquid, , V =V and L = L + 100 From above, V = 4D and L/V = 3/4. Also, L / V = L / V + 100 / V = 3 / 4 + 100 / V
Therefore, Eq. (7) becomes,
3 100
3
100
4.5
1125
.
(8)
y B = 0.750 + 0.545 +
− 0.750
− 0.50
= 0.596 −
= 0.596 −
4V
4
V
V
D
The vapor from the reboiler is in equilibrium with the liquid bottoms (residue). From the lefthand part of Eq. (2),
yB
xB =
(9)
y B + 2.5(1 − y B )
Overall total material balance,
F = 100 = D + B
(10)
Overall benzene material balance, xFF = xDD + xBB or 50 = 0.75D + xBB
(11)
Solving Eqs. (8), (9), (10), and (11),
yB = 0.647, xB = 0.423, D = 23.5 moles or 23.5 mol/100 mol feed, B = 76.5 moles
(d) With a partial condenser, the mole fraction of the liquid reflux is that in equilibrium
with the vapor distillate. Therefore, from the above results,
yD = 0.75
xR = 0.545
y1 = 0.596
x1 = 0.371
Benzene material balance around the theoretical plate, which includes the feed,
xFF + y BV + x R L = y1V + x1 L
(12)
Solving for yB,
V
L
L
F
V
L
L
100
y B = y1
+ x1
xR
− xF
= 0.596
+ 0.371
− 0.545
− 0.50
(13)
V
V
V
V
V
V
V
V Exercise 7.12 (continued) Analysis: (d) (continued)
Because the feed is a saturated liquid,
From above, V = 4D and L/V = 3/4.
Therefore, Eq. (13) becomes,
3 100
y B = 0.596 + 0.371 +
− 0.545
4V , V =V and L = L + 100 Also, L / V = L / V + 100 / V = 3 / 4 + 100 / V
3
100
12.9
3.23
− 0.50
= 0.466 −
= 0.466 −
4
V
V
D (14) The vapor from the reboiler is in equilibrium with the liquid bottoms (residue). From the lefthand part of Eq. (2),
yB
xB =
(15)
y B + 2.5(1 − y B )
Overall total material balance,
F = 100 = D + B
Overall benzene material balance, xFF = yDD + xBB or 50 = 0.75D + xBB
Solving Eqs. (14), (15), (16), and (17),
yB = 0.405,
xB = 0.214,
D = 53.4 moles or 53.4/100 mol feed, (16)
(17) B = 46.6 moles (e) At minimum reflux, with the feed sent to the still pot (partial reboiler), an infinite number of
theoretical plates is needed between the condenser and reboiler. This part is not completely
specified. In order to compute the distillate, we must assume a bottoms benzene mole fraction
less than that in the feed. Suppose we choose t...
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 Spring '11
 Levicky
 The Land

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