Welcome to a brief introduction to the principles behind fractional distillation. We're going to begin our discussion with a question based upon one of our earlier discussions, which you may want to view if you haven't yet, and that would be the simple distillation lecture. The question we'll be asking in this particular presentation is, can distillation be used to obtain liquids of greater purity than those predicted by Raoult's, Dalton's, and ideal gas laws? In other words, can we somehow, instead of achieving our 80 mole percent benzene purification as we did in our previous example, achieve a higher purity of benzene in a distillate?
Now you'll recall from our previous discussion that if we have a 50-50 mixture by mole of toluene and benzene, and we boil that mixture on a hot plate, we expect the vapor above that boiling mixture to have a composition of 80 mole percent. This is based upon our calculations using Raoult's, Dalton's, and ideal gas laws. But of course, the question always comes up, is it possible to get a distillate that's 99% benzene or 100% benzene?
And the answer to this question is yes, but we have to think carefully about how we build our distillation apparatus in order to achieve this. Shown here is a schematic of a simple distillation apparatus, like the one that we discussed in our previous lecture. Call it each part is and the purpose for it in this apparatus.
Now if we build a simple still, charging the boiling flask with 50 mol percent benzene and toluene, we then channel the vapor into another region of the glassware, condensing it with a jacket of cold water. We expect the accumulating distillate to be of a composition that is predicted by Routh's, Dalton's, and ideal gas laws to be 80 mol percent benzene. At this point I often challenge my students, is it possible to create a distillate of higher purity from such a sample?
The most common answer that I get to this question is yes, if you redistill the distillate. And that is in fact true. What I've got here is a schematic of a simple distillation apparatus in which I have attached the collection flask from apparatus one to yet another stillhead and condenser, thereby making it also a boiling flask for a second round of distillation.
And let's start this up and see what happens. As I boil my 50 mole percent benzene solution in the first boiling flask, then recondense the vapor in another region of the glassware, the accumulating distillate is expected to be 80 mole percent benzene by our calculations. If, however, I heated the second flask, Thereby vaporizing this 80 mole percent benzene, I would have to apply a new set of calculations using a new set of mole fractions and vapor pressures.
The consequence of this is that I would have an even higher purity distillate collecting in my second flask. In the case of benzene and toluene, this is a highly pure distillate of about 99 to 100 mole percent benzene. It will be very very pure.
The reason for this can be seen in the liquid vapor composition plot to the left. If I begin with a 50 mole percent liquid, I expect to collect an 80 mole percent vapor. Now if that vapor is then condensed and redistilled, I'm starting from the liquid portion of that 80 percent line, meaning I get another step along the liquid vapor composition plot, reaching a position on the phase diagram where it's approximately 97 mole percent benzene.
So I have successfully in this case achieved a higher purity distillate from my 50 mole percent starting material. However, this is a very large apparatus and would require a great deal of time to build and a great deal of energy to run. And there's actually a much easier way to accomplish the same effect.
The tool which we use to achieve the same effect as in the previous example is a fractional still, which differs from a simple still only by the addition of something called the fractionating column. The fractionating column is inserted between the boiling liquid and the still head. Sometimes it's packed with solid materials to provide additional surface area, and we'll discuss why that's so in a moment. But for now, let's just take a look at our fractional still in which we have charged the boiling flask with 50 mol percent benzene in toluene.
What will go on inside of that fractionating column as the vapor begins to ascend? Well, let's watch a small aliquota vapor move up the column and we'll see what happens. Recall again that we're beginning with a boiling 50 mole percent liquid.
Our liquid vapor composition plot predicts that the vapor, which will be ascending the column, should be of an 80 mole percent composition. However, as it ascends the column, the column temperature drops, and our small aliquot of mixture here is expected to condense along the walls of that fractionating column. And in doing so, it becomes a liquid. This 80 mole percent benzene liquid will then potentially revaporize, and in doing so become even more enriched, just as though we had run a second distillation on it.
So some of the toluene will reflux back into the boiling flask, whereas more of the benzene achieves a second round of vaporization. If we allow this vapor to condense, we see that we now have a 97 mole percent mixture. If our droplet were to vaporize once more, we would expect to have a highly pure sample, about a hundred percent pure benzene and toluene. This is the principle on which a fractional distillation apparatus functions. Now that we've considered the behavior of just a small aliquot, like a single drop of mixture within a fractionating column, let's try to get a better visualization of what it really looks like, of what's really going on inside of that fractionating column.
So here again I built a fractional still and I've charged the boiling flask with 50 mol percent benzene in toluene. Let's zoom in on that fractionating column again and see what's going on inside. What you notice is going on here is that the toluene molecules, due to their lower volatility, are more likely to condense and fall back into the boiling flask, whereas the more volatile benzene molecules have a much greater tendency to traverse the entire length of the fractionating column, reaching the top. This is accomplished based on multiple rounds of vaporization and condensation as the mixture moves through the column. So we expect that near the boiling flask, we'll find a region in which the composition of the material is about 80 mole percent benzene.
Moving higher up along the column, we find a region where we have about 97 mole percent benzene. So if we were to divert the vapor at this point into a condenser and collect it, we would have a distillate of about 97 mole percent benzene. Looking at the top of our hypothetical column, we have a situation where only benzene is reaching that position, and therefore if we were to divert vapor from the top of the column to a condenser, we should collect a sample which is essentially 100 mole percent benzene, or absolutely pure benzene. So what we're really achieving here is the same effect as multiple distillations, but we're only running a single distillation using a fractionating column. If we look back at our liquid vapor composition plot, starting from a 50 mole percent mixture of the two, we expect that a single distillation should yield an 80 percent pure distillate.
If we were to run a second distillation, we would expect that we would have a 97 percent pure distillate. And if we were to again collect that and redistill it once more, we expect to have a situation where we have essentially 100 percent pure benzene. If we were to set up a fractional still and then empirically determine that the collected distillate is 97 mol percent benzene, we would report that our still is operating at two theoretical plates, meaning that it is producing a distillate of similar purity to that which would be expected in two rounds of serial distillation. And similarly, if we have about a 100% pure sample of benzene in toluene, we would then report that our still is operating at about three theoretical plates.
This gives us a way to report on the efficiency and the effectiveness of a fractional still.