CENG 3210 Separation Processes
Assignment 1
Solutions
1. Boiling-Point-Diagram Calculation. The vapor-pressure data are given below for
the system hexane-octane.

Vapor Pressure (kPa)
Temperature (oC)
n-Hexane
n-Octane

68.7
101.3
16.1
79.4
136.7
23.1
93.3
107.2
125.7
197.3
284.0
456.0
37.1
57.9
101.3

(a) Using Raoult's law, calculate and plot the xy data at a total pressure of 101.32 kPa.
(b) Plot the boiling-point diagram.
(a) The total pressure is PT = 101.32 kPa. From Raoult’s law, we have
𝑥𝐴 =
Temperature
(oC)
𝑃𝑇 −𝑃𝐵∗
𝑃𝐴∗ −𝑃𝐵∗
𝑃∗
𝑦𝐴 = [ 𝐴 ] 𝑥𝐴
𝑃𝑇
Vapor Pressure (kPa)
n-Hexane, 𝑃𝐴∗
n-Octane, 𝑃𝐵∗
Mole fraction of n-Hexane
xA
yA
1
1
68.7
101.3
16.1
79.4
136.7
23.1
0.69
0.93
93.3
197.3
37.1
0.4
0.78
107.2
284.0
57.9
0.19
0.53
125.7
456.0
101.3
0
0
1
(b)
2
2. A plant must distill a mixture containing 65 mole percent methanol and 35 mole percent
water. The overhead product is to contain 90 mole percent methanol and the bottom product
10 mole percent. The feed is cold, and for each mole of feed 0.15 mol of vapor is condensed
at the feed plate. The equilibrium data are given below for the system of methanol-water.
x
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
y
0.417
0.579
0.669
0.729
0.780
0.825
0.871
0.915
0.959
1.0
Calculate the following.
(a) the minimum number of theoretical plates.
(b) the minimum reflux ratio Rm.
(10%)
(10%)
(c) the theoretical number of trays at reflux ratio of 1.4.
(20%)
(d) Assuming an average Murphree plate efficiency of 0.72, determine the number of
trays required at reflux ratio of 1.4 and the overall efficiency.
(20%)
(a) At total reflux, the operating line is the diagonal line, the minimum number of plates
is determined as 3.3, or 2.3 plus 1 reboiler.
Minimum number of plates at total reflux ratio
1.0
0.9
0.8
0.7
0.6
ym 0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
xm
3
0.6
0.7
0.8
0.9
1.0
(b) Because the feed is cold, and for each mole of feed 0.15 mol of vapor is condensed at
the feed plate, q = 1 + 0.15 = 1.15. The q line intersects the equilibrium line at (x’, y’)
= (0.68, 0.86). Hence, the minimum reflux ratio is
xD − y′ 0.90 − 0.86
Rm = ′
=
= 0.222
y − x′ 0.86 − 0.68
Minimum reflux ratio
1.0
0.9
0.8
0.7
0.6
ym 0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
xm
4
0.6
0.7
0.8
0.9
1.0
(c) The rectifying operating line has a slope of R/(R+1) = 1.4/(1.4+1) = 0.583, which
intersects the q line at (0.67, 0.768). The stripping operating line is constructed by
drawing a straight line between (0.1, 0.1) and (0.67, 0.768). By using the McCabeThiele method, the theoretical number of trays at reflux ratio of 1.4 is 4, or 3 steps
plus 1 reboiler.
Number of plates at reflux ratio of 1.4
1.0
0.9
0.8
0.7
0.6
ym 0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
xm
5
0.6
0.7
0.8
0.9
1.0
(d) Using a Murphree efficiency of 0.72, the effective equilibrium line is established as
the dashed line. The number of actual trays at reflux ratio of 1.4 is determined as 5.7.
This gives an overall efficiency of 4/5.7 = 0.70. Hence, 6 plates, or 5 plates plus 1
reboiler, are required.
Number of actual plates at reflux ratio of 1.4 and a Murphree efficiency of 0.72
1.0
0.9
0.8
0.7
0.6
ym 0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
xm
6
0.6
0.7
0.8
0.9
1.0