Data Required

If, for mixtures of any two substances, the curve representing the relations between boiling point and molecular composition has been constructed, and if the relation between the composition of the liquid mixture and of its vapour is known, the boiling point of the distillate may be read from the curve. We have seen that if the two substances are closely related we may safely assume that the boiling points of mixtures may be calculated from the vapour pressures of the components, and that Brown's formula, taking the mean ratio of the vapour pressures for the value of the constant, c, gives the relation between the composition of liquid and vapour with fair accuracy.

Benzene And Toluene

In the case of benzene and toluene, the boiling points of mixtures have been found to agree very closely with those read from the theoretical curve, but the relation between the composition of liquid and vapour has only been indirectly determined. The mean ratio of the vapour pressures at temperatures between 80° and 110° is roughly 2.5, and for our present purpose we may assume that the relation is expressed with sufficient accuracy by the formula m'B/mA = 2.5mB/mA.

In Table 45 are given1. The molecular percentages of benzene in mixtures which boil at the temperatures in the first column.

2. The corresponding molecular percentages of benzene in the distillate, calculated by means of Brown's formula.

3. The boiling points of these distillates read from the curve.

4. The differences (At) between the boiling points of liquid and distillate.

Isopentane And Normal Pentane

The corresponding data for mixtures of isopentane and normal pentane are given in Table 46, but in this case neither the boiling points of mixtures nor the relation between the composition of liquid and of vapour have been directly determined. The theoretical boiling point curve differs very slightly from a straight line, the maximum deviation being 0.28° when the molecular percentage of normal pentane is 51.5 (p. 46). The ratio of the vapour pressures at 30° is 1.33, and this has been taken as the constant in Brown's formula.

Table 45. Benzene and Toluene

Table 46. Isopentane and n-Pentane

Application To Distillation Of Benzene And Toluene

Let us consider first the case of benzene and toluene. In the first four fractionations, details of which are given on p. 100, the range of temperature for most of the fractions was 3°. For fraction 6, collected from 92.2° to 954°, the middle temperature is 93.8°, and from Table 45 we see that the distillate from a mixture boiling at 93.8° would have a boiling point about 6.2° lower, or 87.6°. That is to say, if this fraction were distilled in such a manner that no condensation could take place in the still-head, it would begin to boil at 87.6°, but, as a matter of fact, there was some condensation which would lower the temperature to some extent at first. On the other hand, in the actual fractionation, the fractions, with the exception of the first, were not distilled separately but were added to the residues left in the still. Thus the fraction that came over from 92.2° to 954° was added to the residue from No. 5, which was boiling at 92.2°, and was therefore richer in toluene, and the boiling point would therefore be somewhat higher than if the fraction were distilled alone. We may perhaps suppose that the two disturbing factors would about counterbalance each other, and that the mixture would actually begin to boil at about 87.5°. The temperature ranges below 92.2° to 954° were as follows : No. 5, 89.2° to 92.2° ; No. 4, 86.2° to 89.2°, and it is clear that a considerable amount of distillate would be collected below 89.2° in receiver No. 4.

In the sixth fractionation (p. 106) the corresponding temperature ranges were - No. 4, 84.0° to 87.0° ; No. 5, 87.0° to 90.5° ; No. 6, 90.5° to 95.4°. The middle temperature for No. 6 would be 92.95°, and the distillate from this would begin to boil at about 87.0° or 5.95° lower. In this case none of the distillate would be collected in No. 4, and receiver No. 5 might be (and actually was) left in position when No. 6 fraction was added to the residue in the still and the mixture was redistilled.

In the thirteenth fractionation the range of No. 6 had been increased to 14°, from 81.4° to 95.4°. The middle temperature would be 88.4°, and the boiling point of the distillate would be, roughly, 88.4°-4-2° = 84.2°, so that no distillate would be collected in No. 5, and there would be no object in continuing the fractionation in the same way as before. This was, in fact, found to be the case, the temperature rising at once above 81°. The fractions above and below 95.4° were therefore treated separately as described on p. 104.

Application To Distillation Of Pentanes

Let us now consider the behaviour of a mixture of isopentane and normal pentane (Table 46). The difference between the boiling points is 8.35° and the middle temperature is 32.6°. If the distillate were collected in the same number of fractions as in the case of benzene and toluene, the range of the middle ones would be about 0.84°, say, 0.8°. We should then have for the corresponding fractions - No. 5, 31.0° to 31.8° ; No. 6, 31.8° to 32.6°.

The middle temperature for No. 6 would be 32.2°, and the boiling point of the distillate from this would be 32.2°-0.6 = 31.6°. Very little would therefore be collected even in No. 5. The temperature range would have to be reduced to 0.4° [No. 5, 31.8° to 32.2° ; No. 6, 32.2° to 32.6°] in order that the distillate from No. 6 might begin to boil at the initial temperature of No. 5, and that would mean that the number of fractions would have to be doubled to begin with, and that it would not be possible to increase the temperature range of the middle fractions beyond a very small amount.

It will thus be seen that, even without considering the excessive loss by evaporation of such volatile liquids, the separation of isopentane from normal pentane with an ordinary still-head would be practically impossible. It is only by using a greatly improved still-head that such a difficult separation is rendered possible.