Ethanol is often used as a fuel additive, but to function in most engines, the ethanol must be very pure and contain little water. It is difficult to distill ethanol and water above $90$ mole percent ethanol because at this concentration, the vapor and the liquid phases of this mixture have the same composition. To get around this effect, benzene is often added to the mixture. The distillation column then separates the mixture into a very nearly pure ethanol stream and a mixture of benzene and water. The benzene may be separated from the water and then recycled to use again in the ethanol$-$water distillation.

A company wishes to distill a $0\mathrm{.}880$ mole fraction ethanol mole fraction water$)$ solution. To aid in the distillation process, a $0\mathrm{.}980$ mole fraction benzene $(0\mathrm{.}020$ mole fraction water$)$ mixture containing fresh benzene and a recovered benzene solution is added. The plant wishes to produce $52\mathrm{.}0mo\frac{l}{h}r$ of a $0\mathrm{.}999$ mole fraction ethanol $(0\mathrm{.}001$ mole fraction benzene$)$ mixture from a distillation column. The other product from the distillation is a water and benzene mixture. This mixture is sent to a separator which produces a $4\mathrm{.}85mo\frac{l}{h}r$ stream of water, and a $0\mathrm{.}9000$ mole fraction benzene mole fraction water

Answer Bank

What flow rate of the ethanol and water feed stream is needed to provide $52\mathrm{.}0mo\frac{l}{h}r$ of the $0\mathrm{.}999$mole fraction ethanol stream?

flow rate:

$mo\frac{l}{h}r$

What flow rate of fresh benzene is required?

flow rate:

mol benzene$/$hr

What is the flow rate of the recycle line?

flow rate:

mol$/$hr