A stream consisting of 44.6 mole% benzene and 55.4% toluene is fed at a constant rate to a process unit that produces two product streams, one a vapor and the other a liquid. The vapor flow rate is initially zero and asymptotically approaches half of the molar flow rate of the feed stream. Throughout this entire period, no material accumulates in the unit. When the vapor flow rate has become constant, the liquid is analyzed and found to be 28.0 mole% benzene.(a) Sketch a plot of liquid and vapor flow rates versus time from startup to when the flow rates become constant.
(b) Is this process batch or continuous? Is it transient or steady-state before the vapor flow rate reaches its asymptotic limit? What about after it becomes constant?
(c) For a feed rate of 100 mol/min, draw and fully label a flowchart for the process after the vapor flow rate has reached its limiting value, and then use balances to calculate the molar flow rate of the liquid and the composition of the vapor in mole fractions.

a)In the beginning, the vapor Flow rate is 0% which means that the liquid Flow rate is 100%. The figure attached shows how at time=0, liquid=100 and vapor=0. With time, the Flow rate of vapor and liquid approach to 50% of the molar flow rate of the feed stream. The figure shows the plot of Vapor/liquid Flow rates versus time.

b)The problem mentions that the feed stream is fed at a constant rate to the reactor, thus the process is continuous. As is shown in the figure, before the Flow rate reaches the asymptotic limit, the flowrate is changing and it is time-dependent, which means before the asymptotic limit, the process is in transient state. Then, after the asymptotic limit, the vapor/liquid flowrates are constants which means the process is in steady-state.

c)The Flow diagram process is shown in the figure where Benzene is represented as B and toluene as T.

Feed flow rate:

In the feed Flow rate, B and T are given, the molar fraction for B is 0.446 and the one for T is 55.4

B balance

we make a balance for B, we can calculate the molar Flow rate in vapor stream, the balance for B is:

A*Xba= CXbc + DXbd wher A, C and D are the feed, vapor and liquid streams, respectively, and Xba, Xbc and Xbd are the molar fractions of bencene in the corresponding stream.

A=100 mol/min, Xba=0.446, C=50 mol/min, Xbc=?, D=50 mol/min, Xbd= 0.28.

If you solve for Xbc, yo get the molar fraction of bencene in vapor stream is 0.388 and the toluene fraction is 0.612