Theory of Distillation Part 2 (Laboratory Manual)

 

By : James W Zubrick
Email: j.zubrick@hvcc.edu

What Does It All Mean?

Getting back to the temperature-mole fraction diagram (Figure 140), suppose you start with a mixture such that the mole fractions are as follows: isobutyl alcohol, 0.60, and isopropyl alcohol, 0.40. On the diagram, that composition is point A at a room temperature of 20 °C. Now you heat the mixture and you travel upwards from point A to point B; the liquid has the same composition, it’s just hotter.

At 95 ° C, point B, the mixture boils. Vapor, with the composition at point C comes flying out of the liquid (the horizontal line tying the composition of the vapor to the composition of the liquid is the liquid—vapor tie line.), and this vapor condenses (Point C to point D), say, part of the way up your distilling column.

Look at the composition of this new liquid (Point E). It is richer in the lower-boiling component. The step cycle B-C-D represents one distillation.

If you heat this new liquid that’s richer in isopropyl alcohol (Point D), you get vapor (composition at Point G along a horizontal tie-line) that condenses to liquid H. So step cycle D-G-H is another distillation. The two steps represent two distillations.

Temperature vs. Mole Fraction Calculations

 

Compound	Normal BP (C)
2-Propanol	82.3	1440 torr
2-Methyl-l-propanol	108.2	570 torr
Data from Moore (3rd. ed.)
	2-Propanol	9515.73 cal/mol
	2 -Methyl- 1-propanol	10039.70 cal/mol

Comparison of Data from Moore and Calculated Data (T= 100 (C))

		Moore	Calc.
Vapor pressures:	2-Propanol	1440	1440.05
(torr)	2-Methyl-l-propanol	570	570.02
Mole fraction:	2-Propanol	0.219	0.2184
(in liquid)	2-Methyl-2-propanol	0.781	0.7861
Mole fraction:	2-Propanol	0.415	0.4137
(in vapor)	2-Methyl-2-propanol	0.585	0.5863

Mole Fraction of 2-Propanol Liquid Data

	XCalc	X Lit.	Diff	% Diff
1 83.2	0.9458	0.9485	-.0027	-0.286
2 85.4	0.8213	0.8275	-.0062	-0.748
3 86.9	0.7425	0.7450	-.0025	-0.331
4 88.7	0.6540	0.6380	0.0160	2.505
5 90.9	0.5539	0.5455	0.0084	1.540
6 95.8	0.3591	0.3455	0.0136	3.949
7 99.9	0.2215	0.2185	0.0030	1.357
8 103.4	0.1191	0.1155	0.0036	3.096
9 106.2	0.0458	0.0465	-.0007	-1.507

Mole Fraction of 2-Propanol Vapor Data

	XCalc	X Lit.	Diff	% Diff
1 83.2	0.9785	0.9805	-.0020	-0.201
2 85.4	0.9228	0.9295	-.0067	-0.723
3 86.9	0.8820	0.8875	-.0055	-0.618
4 88.7	0.8300	0.8245	0.0055	0.663
5 90.9	0.7615	0.7580	0.0035	0.460
6 95.8	0.5880	0.5845	0.0035	0.600
7 99.9	0.4182	0.4270	-.0088	-2.063
8 103.4	0.2533	0.2510	0.0023	0.936
9 106.2	0.1070	0.1120	-.0050	-4.433

Fig. 140 Temperature-mole fraction diagram for the isobutyl-isoropyl alcohol systems.

Much of this work was carried out using a special distilling column called a bubble-plate column (Fig. 141). Each plate really does act like a distilling flask with a very efficient column, and one distillation is really carried out on one physical plate. To calculate the number of plates (separation steps, or distillations) for a bubble-plate column, you just count them!

Unfortunately, the fractionating column you usually get is not a bubble-plate type. You have an open tube that you fill with column packing (see “Class 3: Fractional Distillation”) and no plates. The distillations up this type of column are not discreet, and the question of where one plate begins and another ends is meaningless. Yet, if you use this type of column, you do get a better separation than if you used no column at all. It’s as if you had a column with some bubble-plates. And if your distilling column separates a mixture as well as a bubble-plate column with two real plates, you must have a column with two theoretical plates.

You can calculate the number of theoretical plates in your column if you distill a two-component liquid mixture of known composition (isobutyl and isopropyl alcohols perhaps?), and collect a few drops of the liquid condensed from the vapor at the top of the column. You need to determine the composition of that condensed vapor (usually from a calibration curve of known compositions versus their refractive indices [see Chapter 22, "Refracto-metry"]), and you must have the temperature-mole fraction diagram (Fig. 140).

Fig. 141 A bubble-plate fractionating column.

Suppose you fractionated that liquid of composition A, collected a few drops of the condensed vapor at the top of the column, analyzed it by taking its refractive index, and found that this liquid had a composition corresponding to point J on our diagram. You would follow the same path as before (B-C-D, one distillation; D-G-H, another distillation) and find that composition J falls a bit short of the full cycle for distillation #2.

Well, all you can do is estimate that it falls at, say, a little more than half of the way along this second tie-line, eh (Point K)? OK then. This column has been officially declared to have 1.6 theoretical plates. Can you have tenths of plates? Not with a bubble-plate column, but certainly with any column that does not have discrete separation stages.

Now you have a column with one-point-six theoretical plates. “Is that good?” you ask. “Relative to what,” I say. If that column is six feet high, that’s terrible. The Height Equivalent to a Theoretical Plate (HETP) is 3.7feet/ plate. Suppose another column also had 1.6 theoretical plates, but was only 6 inches (0.5 ft) high. The HETP for this column is 3.7in/plate, and if it were 6 feet high, it would have 19 plates. The smaller the HETP, the more efficient the column is. There are more plates for the same length.

One last thing. On the temperature-mole fraction diagram, there’s a point F I haven’t bothered about. F is the grade you’ll get when you extend the A-B line up to cut into the upper curve and you then try to do anything with this point. I’ve found an amazing tendency for some folk to extend that line to point F. Why? Up the temperature from A to B and the sample boils. When the sample boils, the temperature stops going up. Heat going into the distillation is being used to vaporize the liquid (heat of vaporization, eh?) and all you get is a vapor, enriched in the lower-boiling component, with the composition found at the end of a horizontal tie-line.

Reality Intrudes I: Changing Composition

To get the number of theoretical plates, we fractionally distilled a known mixture and took off a small amount for analysis, so as not to disturb things very much. You, however, have to fractionally distill a mixture and hand in a good amount of product, and do it within the time limits of the laboratory.

So when you fractionally distill a liquid, you continuously remove the lower boiling fraction from the top of the column. And where did that liquid come from? The boiling liquid at the bottom of the column. Now if the distillate is richer in the lower boiling component, what happened to the composition of the boiling liquid? I’d better hear you say that the boiling liquid gets richer in the higher-boiling component (Fig. 142).

Fig. 142 Changing composition as the distillation goes on.

So as you fractionally distill, not only does your boiling liquid get richer in the higher-boiling component, so also does your distillate, your condensed vapor. Don’t worry too much about this effect. It happens as long as you have to collect a product for evaluation. Let your thermometer be your guide, and keep the temperature spread less than 2°C.

Reality Intrudes II: Nonequilibrium Conditions

Not only were we forced to remove a small amount of liquid to accurately determine the efficiency of our column, we had to do it very slowly. This allowed the distillation to remain at equilibrium. The throughput, the rate at which we took material out of the column, was very low. Of all the molecules of vapor that condensed at the top of the column, most fell back down the column; few were removed. A very high reflux ratio. With an infinite reflux ratio (no throughput), the condensed vapor at the top of the column is as rich in the lower-boiling component as it’s ever likely to get in your setup. As you remove this condensed vapor, the equilibrium is upset, as more molecules rush in to take the place of the missing. The faster you distill, the less time there is for equilibrium to be reestablished—less time for the more volatile components to sort themselves out and move to the top of the column. So you begin to remove higher-boiling fractions as well, and you cannot get as clean a separation. In the limit, you could remove condensed vapor so quickly that you shouldn’t have even bothered using a column.

Reality Intrudes III: Azeotropes

Occasionally, you’ll run across liquid mixtures that cannot be separated by fractional distillation. That’s because the composition of the vapor coming off the liquid is the same as the liquid itself. You have an azeotrope, a liquid mixture with a constant boiling point.

Go back to the temperature-mole fraction diagram for the isopropyl alcohol-isobutyl alcohol system (Fig. 140). The composition of the vapor is always different from that of the liquid, and we can separate the two compounds. If the composition of the vapor is the same as that of the liquid, that separation is hopeless. Since we’ve used the notions of an ideal gas in deriving our equations for the liquid and vapor compositions (Clausius-Clapyron, Dalton, and Raoult), this azeotropic behavior is said to result from deviation from ideality, specifically deviations from Raoult’s Law. Although you might invoke certain interactive forces in explaining nonideal behavior, you cannot predict azeotrope formation a priori. Very similar materials form azeotropes (ethanol-water). Very different materials form azeotropes (toluene-water). And they can be either minimum-boiling azeotropes or maximum-boiling azeotropes.

Minimum-Boiling Azeotropes

The ethanol-water azeotrope (95%ethanol-5%water) is an example of a minimum boiling azeotrope. Its boiling point is lower than that of the components (Fig. 143). If you’ve ever fermented anything and distilled the results in the hopes of obtaining 200 proof (100%) white lightning, you’d have to content yourself with getting the azeotropic 190 proof mixture, instead. Fermentation usually stops when the yeast die in their own 15% ethanol solution. At room temperature, this is point A on our phase diagram. When you heat the solution, you move from point A to point B and, urges to go to point F notwithstanding, you cycle through distillation cycles B-C-D and D-E-G, and, well, guess what comes off the liquid? Yep, the azeotrope. As the azeo-trope comes over, the composition of the boiling liquid moves to the right (it gets richer in water), and finally there isn’t enough ethanol to support the azeotropic composition. At that point, you’re just distilling water. The process is mirrored if you start with a liquid that is > 95% ethanol and water. The azeotrope comes off first.

Fig. 143 Minimum-boiling ethanol-water azeotrope.