Consider a distillation column operating at a continuous steady state. The distillation column is seperating methanol & water at a pressure of 1 atm. This operation uses an open system instead of a heat exchanger in the reboiler.

The stream used to heat up the steam is composed of ONLY saturated vapor & is fed into the bottom of column.

The McCabe-Thiele diagram is provided below. Please use it to solve this problem graphically.

The feed is composed of 60% methanol & 40% water by mol. The feed is operating at a rate of 100 kmol/h & a temperature of 40C.

The distillate is 99% methanol by mol. & the bottoms product is 2% methanol by mol (This insights that both the total condenser & the last equilibrium stage at the bottom of column as saturated liquids). Assume CMO (Constant Molal Overflow) rules apply here. If L/D = 2.3 & q = 1.0668 answer the following using the plot provided.

1. Find the slope of the feed line (q-line) equation.
2. Find the slope of the top-operating line (L/D) equation.
3. Find the intercept of the top-operating line equation.
4. Find the optimum feed stage location (find which stage assuming you are stepping from top to bottom)
5. Find the total number of stages (Step from top to bottom)

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 X (Mole Fraction Methanol)