A small still is separating propane and butane at 135 °C, and initially contains 10 kg moles of a mixture whose composition is x = 0.3 (x = mole fraction butane). Additional mixture (x = 0.3) is fed at the rate of 5 kg mole/hr. The total volume of the liquid in the still is constant, and the concentration of the vapor from the still (xp) is related to x, as follows: Xp = How long will it take for X, to change from 0.3 to 0.35.

Hello the needed relation is missing below is the required relation

  composition : propane = 0.70, butane = 0.3

Answer : ≈ 5.75 hrs

Explanation:

Applying the data given in regards to the material balance

Butane balance input into the still = 5 mole feed/hr | 0.30 mol butane/molfeed

since the total volume of the liquid in the still is constant

The output from the still is = 5mol condensed/hr | x mol butane/mol condensed

unsteady state equation = = 0.15 -

note : to reduce the equation a single dependent variable we have to substitute for

In order to find the time it will take for X to change from 0.3 to 0.35

integrate the above equation using the limits : t = 0, x = 0.3 and t = Ф,

x

=

hence t = Ф ≈ 5.75 hrs

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