Fractional distillation

Each component's boiling point at the still pressure comes from its Antoine constants (NIST WebBook sets in our database) or, where there are none, from the estimate described on the pressure–temperature nomograph, which is marked as such. Antoine constants that contradict a measured boiling point are not used.

A column with enough plates takes off the lowest-boiling species first. At 1 atm a minimum-boiling azeotrope from our table counts as a species of its own: it distils first at its temperature and composition until one of its partners runs out, and the partner left over comes over later at its own boiling point. For each change-over the table gives the best purity the column reaches at total reflux, the Fenske equation solved for the purity with the stages you have; the curve rises gradually where that purity is low and steps where it is high. For a cut that is an azeotrope, the column is judged by treating the azeotrope as one liquid that boils at its azeotropic temperature, with the vapour pressure estimate of the nomograph.

The pot temperature at the start is the bubble point of the charge by Raoult's law, Σ x_iP_i(T) = P. Real mixtures that form azeotropes deviate from it; the value is marked as ideal.

For two neighbours in the boiling order, α is the ratio of their vapour pressures, taken as the geometric mean of the ratio at the two boiling points. The Fenske equation gives the minimum number of equilibrium stages at total reflux for a purity x in both cuts: N_min = ln[(x/(1 − x))²] / ln α. The pot is one stage, so the column itself needs N_min − 1 theoretical plates.

No distillate is taken at total reflux. At a working reflux ratio a column delivers far fewer plates: a column with 30 plates at total reflux gives about 14 at a reflux ratio of 10:1 and 8 at 4:1 (Murov). A pair is shown as separating when the column has at least twice the Fenske minimum, and as needing a high reflux ratio between one and two times the minimum. The length to plan for uses the same factor of two.

Typical heights equivalent to a theoretical plate, all very approximate: empty tube 40 cm, Vigreux column 10 cm, 3 mm glass helices 4 cm (Murov). A 76 cm spinning band column of 10 mm bore was reported with 28 plates, 2.7 cm per plate, and a 1 m Podbielniak Heli-Grid column with 200 to 400 plates, 0.25 to 0.5 cm per plate (Armarego and Perrin). We have no reliable typical value for glass beads or Raschig rings in laboratory columns; enter the HETP you measured.

HETP depends on the bore, the boil-up rate and the pressure. Under vacuum a Vigreux column loses about a quarter of its efficiency going from 1 atm to 1 mmHg, a spinning band column about 70 % going down to 10 mmHg (Chem. Eng. Sci. 1952).

The prediction assumes ideal behaviour apart from the azeotropes in our table, which holds 26 binary pairs measured at 1 atm. Ternary azeotropes, column hold-up and the change of composition in the pot during a cut are not modelled. Use it to plan the column and the cuts, then follow the head temperature.

• Antoine constants: NIST Chemistry WebBook, as stored in our database with their fitted temperature ranges.
• Azeotropes: Horsley-type tables as cited per row (Suzuki 1979; CRC Handbook with the Dortmund Data Bank).
• S. Murov, Experiments in Organic Chemistry, Experiment 8, Distillation: HETP of lab columns, plates needed per boiling point gap, effect of the reflux ratio.
• W. L. F. Armarego and D. D. Perrin, Purification of Laboratory Chemicals, 4th ed., Butterworth-Heinemann 1996, chapter 1: spinning band and Podbielniak columns.
• Vacuum distillation II: performance of a Vigreux column and a spinning band column over a wide range of pressures, Chem. Eng. Sci. 1 (1952) 174.
• M. R. Fenske, Ind. Eng. Chem. 24 (1932) 482: minimum stages at total reflux.