The purpose of this screencast is to take the words of a problem and interpret them
so you can draw a flow chart and eventually be able to solve for what you're being asked.
So here we have a 60:40 liquid mixture of benzene and toluene that's fed to a distillation column.
On the right you have a classic picture of a distillation column, and so here's our feed,
and it's 0.6 benzene, and 0.4 toluene. So it's fed to the distillation column, which
produces both a liquid and a vapor stream. So we have the vapor here, it leaves the top
of the column where it is completely condensed, so here's our condenser, and split into two
equal fractions. A couple of things I want to say about that particular statement. First
of all the fact that it is completely condensed means that you have two liquid streams coming
out of the condenser, but it also means that the compositions of all three of the streams
are the same. The second thing to take a look at is the fact that it states two equal fractions.
You cannot assume that the two streams coming out of a condenser are equal unless you're
told so. One of the fractions is taken off as a product stream, which is right here,
and the other is fed back to the column. Now the liquid leaving the bottom of the column
is fed to a partial reboiler, so here's our reboiler in which 40% of it is vaporized.
So that piece of information is something that we're going to use later in our analysis.
The vapor from the reboiler is recycled back to the column, and here the liquid is taken
off as the bottom products stream. So this partial reboiler is at 500mmHg, and 90 degrees
C. 90% of the benzene fed to the column leaves the condenser in the products stream, and
that's another piece of information that we're going to use later to solve for this problem,
and we're going to use a basis of 100 moles fed to the distillation column. So the first
thing we're going to do is label our knowns and unknowns. So let's call this first one
stream, the vapor coming out of the condenser, n1. Since we know that it's split into two
equal parts, we can call this stream 0.5n1, and this stream 0.5n1. We don't know any of
the compositions, all that we know is that they're the same, so we'll call this, we'll
write everything in terms of benzene, so this is z(B)n1-z(B). Next we'll look at the stream,
the liquid stream leaving the bottom of the column, and we'll call this n2, and again
we know nothing about it's composition, so we'll call it w(B), and 1-w(B). Let's look at
the stream coming out of the reboiler as a products stream. This we're going to call
n3, and it has a benzene mol fraction of x(B), and toluene is 1-x(B). Finally here we have
n4. It has a mole fraction of y(B) for the benzene, n1-y(B) for the toluene. The first
thing we're going to do is do a degree of freedom analysis to see how we can solve this.
So first we'll start by looking overall. So overall means that 100 moles that's coming
in, and then those two streams, one leaving the condenser and one leaving the reboiler.
So if we look at those we find that we have n1 as an unknown, z(B), n3, and x(B). So we
need to find four equations in order to solve for these four unknowns. So the first thing
that we can do is we can write two species balances. One for benzene, and one for toluene.
In addition, we're given the information at the end of the problem statement here that
90% of the benzene fed to column, so we'll write that as 90% of the benzene, so the benzene
is 60% of the feed, leaves the condenser in the products stream. So that's going to be
equal, z(B)*0.5n1. However, we have no other piece of information that relates those four
unknowns, so we have four unknowns, two species balances, one piece of extra information,
so that means we have one degree of freedom, and we can't use the overall balance to start
solving. One thing that I want to make sure that you understand, we have a second piece
of information right here, which says that 40% of the liquid leaving the bottom of the
column is vaporized. The way we would write that is 40% of the liquid leaving the column,
which is n2, is vaporized, which is equal to n4. The reason we can't use that piece
of information is that it does not relate to any of the variables that we're trying
to solve for. So in the next screencast we'll show you where we have to start in order to
solve this problem.