A distillation column is to be designed to separate methanol and water continuously. The feed contains 40 mol/s methanol and 60 mol/s water and is a saturated liquid. The column pressure is 101.3 kPa (1 atm). The binary equilibrium data in terms of the methanol composition (in mol %) at equilibrium are as follows:

\[
\begin{array}{cc}
\text{Liquid} & \text{Vapor} \\
2.0 & 13.4 \\
6.0 & 30.4 \\
10.0 & 41.8 \\
20.0 & 57.9 \\
30.0 & 66.5 \\
40.0 & 72.9 \\
50.0 & 77.9 \\
60.0 & 82.5 \\
70.0 & 87.0 \\
80.0 & 91.5 \\
90.0 & 95.3 \\
95.0 & 97.9 \\
\end{array}
\]

The feed is to be introduced at the optimal location to yield the minimum number of stages. 95 mole percent of the methanol is to be recovered in a liquid distillate consisting of 98 mol-% methanol. The reflux is to be a saturated liquid with a flow rate 1.25 times the minimum reflux rate, which would correspond to an infinite number of stages.

Assuming constant molar overflow, find the number of equilibrium stages required in the column.

The given reflux ratio (Rp) is 3.5, and the distillate composition (Xp) is 0.96. We will use the McCabe-Thiele method to find the number of equilibrium stages.

Start by plotting the operating line and equilibrium line on Figure (1).

The slope of the operating line (L/D) is given by (1 + Rp) = (1 + 3.5) = 4.5.

Plot the point (Xp, Xp) on the equilibrium line.

Draw a line with a slope of 4.5 passing through this point until it intersects the equilibrium line. This intersection point gives the required number of stages, which is approximately 5.

b) Position of Feed Plate:

To find the position of the feed plate, we locate the intersection of the q-line (line connecting the feed composition with the intersection of the operating line and equilibrium line) with the equilibrium line.

The feed composition is 40 mol% methanol (0.4) and 60 mol% water (0.6).

The q-line connects this feed composition (0.4, 0.6) with the intersection point on the operating line and equilibrium line.

The q-line intersects the equilibrium line between stages 2 and 3, so the feed plate is positioned between these stages.

c) Liquid and Vapor Flow Rates in Stripping Section:

The lever rule can be used to determine the fractions of liquid (L) and vapor (V) leaving the feed plate and then calculate their flow rates.

For the given feed composition of 0.4 methanol and 0.6 water:

Fraction of liquid (L/F) = (Xf - Xp) / (Xb - Xp) = (0.4 - 0.96) / (0.96 - 0.96) = -0.56 / 0 = 0

Fraction of vapor (V/F) = 1 - L/F = 1 - 0 = 1

The liquid flow rate in the stripping section = L/F * Total feed rate = 0 * (40 mol/h + 60 mol/h) = 0 mol/h.

The vapor flow rate in the stripping section = V/F * Total feed rate = 1 * (40 mol/h + 60 mol/h) = 100 mol/h.

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Q4. A distillation column is to be designed to separate methanol and water continuously. The feed of 100 kmol contains 40 mol/h of methanol and 60 mol/h of water and is a mixture of two- thirds vapor and one-third liquid. The column pressure will be 101.3 kPa (1 atm), for which the equilibrium data are shown in figure (1) The distillate composition (methanol) is Xp 0.96 and the water composition in the bottoms is 96%. The reflux ratio Rp 3.5. Find: a) The number of equilibrium stages required in the column. (6 pts) b) The position of feed plate? (2 pts) c) Liquid and vapor flow rates in the stripping section. (4 pts)