mass balance in distillation column

Example

Sulphuric acid is fed into a distillation column at molar flowrate of 150 mol/h with mol fraction of 0.3 sulphuric acid and the rest being water. The bottom product has a flowrate of 90 mol/h and mol fraction of 0.1 sulphuric acid and 0.9 water. Find the molar flowrate of the overhead product and it's composition.

First, we draw the flowchart

Then do the D.O.F analysis

Unknowns = 3 (nᵥ, X, Y)

Independent eq = 3 (overall material balance and specific balance of S & W, constraint of fraction)

D.O.F = 3 - 3 = 0 (solvable)

Once we've verified that this question is solvable, we can write down the mass balance equations and solve

150 = nᵥ + 90

nᵥ = 60

overall material balance

0.3(150) = Xnᵥ + 0.1(90)

60X = 45 - 9

X = 0.6

X+Y = 1

Y= 0.4

specific balance of S

constraint of fraction

Try this question and post your answer in the comments section below.

Pak Usman runs a methanol distillery. To find the theoretical output of his distillation column, he uses a simulation. Unfortunately, right when the simulation completed, someone else connected to the UTP PC, and he is no longer able to connect to it. He was only able to note down the the overhead product flowrate and the composition of the bottom product, which was 200L/h and 5% v/v methanol and 95% v/v water, respectively.

i) Given the input is 1000 L/h of 20 %v/v methanol, find the composition of the overhead product.

ii) Pak Usman has to sell 3000 metric tonnes of his overhead product in a year. Can he reach his quota? (assume his methanol is 100% pure)

iii) After letting his plant run, he finds that the flowrate of overhead product is significantly lower than the theoretical value. What are possible reasons for this discrepancy?