How this calculation works
In simple differential batch distillation, vapor is removed while the pot composition changes continuously. Treating the entire collected material as if it equilibrated once with the final liquid would describe a flash, not this batch history. This page integrates the binary Rayleigh balance with constant relative volatility. It reports remaining pot moles, total collected distillate and the average volatile-component fraction across all collected material.
ln(F/W)=[ln(xF/xW)−alpha ln((1−xF)/(1−xW))]/(alpha−1); D=F−WA worked example
Starting with one hundred moles at volatile fraction one half, ending at one quarter and using relative volatility two gives a charge-to-residue ratio of 4.5. About 22.22 moles remain and 77.78 moles are collected. Their component contents sum to the original fifty moles of more volatile material, providing an independent overall balance check.
Good to know
Real volatility may vary with composition, pressure and temperature. Azeotropes, entrainment, changing holdup and imperfect vapor-liquid equilibrium are excluded from this constant-relative-volatility model. No heater duty, boiling time or separation operating procedure is supplied. The calculation is a material-balance illustration, not a complete distillation design or a purity guarantee.
Reference: Carnegie Mellon Kitchin group — Rayleigh batch distillation (opens in a new tab) ↗
What this calculation answers
In simple differential batch distillation, vapor is removed while the pot composition changes continuously. Treating the entire collected material as if it equilibrated once with the final liquid would describe a flash, not this batch history.
This page integrates the binary Rayleigh balance with constant relative volatility. It reports remaining pot moles, total collected distillate and the average volatile-component fraction across all collected material.
The Rachford Rice flash fraction from entered K values calculator divides a feed at one equilibrium condition. Differential batch distillation instead accumulates vapor while the pot composition changes.
Use the right input conventions
Enter amounts in moles and mole fractions of the more volatile component. Relative volatility must exceed one, and the final pot fraction must be lower than its initial fraction for the stated depletion scenario.
The liquid is modeled as well mixed, with each increment of vapor removed immediately at equilibrium. There is no reflux or multistage column, and liquid amounts are not converted into volume.
Interpret the result
The instantaneous vapor composition changes during the run. The reported average distillate composition instead comes from the overall component balance across the entire collection interval.
The logarithmic charge-to-residue ratio is also shown to expose the integrated model. A very small remaining amount can be mathematically possible without implying that a real apparatus can achieve the stated constant-volatility path.
Work through the example
Starting with one hundred moles at volatile fraction one half, ending at one quarter and using relative volatility two gives a charge-to-residue ratio of 4.5.
About 22.22 moles remain and 77.78 moles are collected. Their component contents sum to the original fifty moles of more volatile material, providing an independent overall balance check.
Where the model stops
Real volatility may vary with composition, pressure and temperature. Azeotropes, entrainment, changing holdup and imperfect vapor-liquid equilibrium are excluded from this constant-relative-volatility model.
No heater duty, boiling time or separation operating procedure is supplied. The calculation is a material-balance illustration, not a complete distillation design or a purity guarantee.
A few questions, answered
Is average distillate composition the final instantaneous vapor composition?
No. It averages all collected material using total and component balances over the whole batch interval.
What changes in the comparison?
Stop depletion earlier and compare the larger remaining pot amount with the smaller collected quantity.