In this screencast I am going to show you how to take a word problem and turn it into
a flow chart or a diagram. We are going to look at this three component system. We will
call the components A, B, and C. We have 2 streams that are fed to a column, and let's
draw a rather large column. We have two streams that are fed to it. One stream contains a
mole fraction, because at the end it says all fractions are mole fractions, of 0.35 A.
There is more than one way to write mole fractions and some people understand
it a little bit better if we write it as that 0.35 A is the same thing as writing 0.35 moles
of A per mole of feed. If we have 0.35 A and the rest is B, then in order for it to be
100% this needs to be 0.65 B. The second stream is only B and C. We are going to call this
y_B and one of the things I do is I put the number of the stream after the component because
we will have mole fractions in many of the streams and this prevents us from mixing up
one of the mole fractions in one stream with a fraction in another. The rest of it is y_C.
However we can use the fact that the summation of mole fractions has to equal 1 so our y_C
is actually equal to 1 minus y_B2. Exiting the column are three streams. The top stream
contains only B. One way to write this is that the mole fraction of B, which is 100%
is 1. I write it as 1.0 B. The middle stream is 0.60 A and the rest B and C. But again,
we can use the fact that the summation of all the mole fractions has to equal 1 to write
y_C4 in terms of y_B4. This is going to equal 1 minus 0.6 which is our mole fraction of
A minus y_B4. This just equals 0.4 minus y_B4. The bottom stream is equimolar in A and C.
That just means this is 0.5 A and 0.5 C. Finally it says that if the first stream entering
the column is 100 moles per hour, which we will write here, find the amount of B exiting
the column in the middle stream. I am going to name this n_2, n_3, n_4 and finally this
one n_5. Note that I put dots over the n. That is because they are flow rates. Now we
want to find the amount of B exiting the column in the middle stream. Let's take a look at
what it is what we are actually looking for here. The amount of B, which is the mole fraction
times the flow rate is equal to the flow rate of B in stream 4. Instead of writing overall
flow rates we can write specific component flow rates like I did right here. For example
we could write n_A4 or n_C4 realizing that the summation of those 3 component streams
are going to equal the overall flow rate.