# McCabe Thiele - number of stages

For rectification I am given the following information

$x_e$ = 0.95

$x_f$ = 0.50

$x_b$ = 0.15

$v$ = 8

$q$ = 1.17

**VLE Data**
x       y
0.00    0.00
0.10    0.17
0.20    0.31
0.30    0.44
0.40    0.55
0.50    0.645
0.60    0.73
0.70    0.81
0.80    0.88
0.90    0.94
0.95    0.97
1.00    1.00


The VLE data is derived from a given diagram. There may be some inaccuracies there. However drawing with pen and paper in the diagramm gives me the same error I'll explain later on.

With all this data I developed the McCabe Thiele Diagramm for this problem.

Putting everything together in Excel

The grey dotted line indicates my $x_b$ and in orange I drew the theoretical stages. My Problem is: Usually you would come up with a whole number of stages, in this case I would get $9\frac{5}{7}$.

There is also an $E_k = 0.7$ given.

$$n=\frac{n_{th}}{E_k} = 13.87$$

My question is: Why do I not get whole numbers? I am under the impression that there always have to be whole numbers. However in Absorption we where supposed to give answers like $n = 1.2$.

I thought maybe the given mole fractions took $E_k$ into account and therefore I would get a whole number after dividing $n_{th}$ by 0.7.

Is this just an error in my VLE Data and actually I would end up with n = 14? 13+1 to be accurate. It's hard to use the given diagramm since it's very small and I couldn't draw accurate enough in it. Also on what stage is the feed? I wouldn't get a whole number the either.

• Can you explain what the different x are? Some textbooks/teachers use different names for the same.
– mart
Sep 20, 2015 at 20:14
• also what's the blue line in your diagram?
– mart
Sep 20, 2015 at 20:16
• Please use this diagram for reference. The blue line is the stripping section. x_b is the bottom composition, x_f the feed and x_e the distillate composition. v is the reflux ratio. Sep 20, 2015 at 21:16
• It's been ages since I learened this and I don't work with columns but I don't recall ever arriving at an even number of stages.
– mart
Sep 21, 2015 at 8:13
• Then I'll take it we only got whole numbers for convenience during the course. Appreciated! Sep 21, 2015 at 8:15