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I would not say that the molar flow of those two streams need to be the same but rather their sum should equal the input into the distillation column.

Moles of A in = Moles of A Distillate + Moles of A Bottom

If you think about it, it makes very little sense that both streams should be equal because that would indicate you are doing a very poor separation! You ideally want to concentrate one product in either stream as best you can, while the other products get separated somewhere else in the column.

If A is very volatile relative to other inputs, one would expect that Moles of A Distillate >> Moles of A Bottoms

Normally you should avoid molar balances as moles are not usually conserved in many processes; however, distillation is simply a separation, so therefore a molar balance is safe to use but verify your assumptions!

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Related Questions

In distillation the water inlet is down why?

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