Question

One thousand kilograms/hr of a 50/50 - mass basis - benzene (B) / toluene (T) mix is separated in two streams via a distillation column. The mass flow of the benzene in the top stream is 287 kg B/hr and that of toluene in the bottom stream is 242 kg T/hr.

Calculate the mathematical difference between the toluene in the top stream and the benzene in the bottom stream

Answer 1

The mathematical difference between the toluene in the top stream and the benzene in the bottom stream from a distillation process is 45 kg/hr.

Step-by-step explanation:

The student has presented a question related to a distillation process involving a benzene/toluene solution.

Given that 1000 kg/hr of a 50/50 mass basis mix is being separated, with 287 kg B/hr of benzene in the top stream and 242 kg T/hr of toluene in the bottom stream, the task is to calculate the mathematical difference between the toluene in the top stream and the benzene in the bottom stream.

Initially, we know that each of benzene and toluene enters the distillation column at 500 kg/hr (since it's a 50/50 mix).

The top stream consists of 287 kg B/hr of benzene, hence the top stream must contains 500 - 287 = 213 kg T/hr of toluene.

Similarly, the bottom stream contains 242 kg T/hr of toluene, so it must contain 500 - 242 = 258 kg/hr of benzene.

Therefore, the mathematical difference between the toluene in the top stream and the benzene in the bottom stream is 258 kg B/hr (bottom) - 213 kg T/hr (top) = 45 kg/hr.