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Distillation separates a mixture by producing vapor from a liquid and collecting the condensed liquid, called the distillate. The more volatile component can have a higher mole fraction in the vapor. Simple distillation collects this condensate directly; fractional distillation adds repeated contact in a fractionating column.^[ref]

Two questions must be kept separate. Vapor-liquid equilibrium describes which compositions can coexist. A distillation material balance accounts for how much of each component leaves in each product. A product can be enriched without containing all the original component, and even a feasible distillation material balance does not establish that an apparatus can make those products.

A laboratory condenser removes heat from vapor so that it becomes liquid. In distillation, the downstream laboratory condenser makes collectable distillate. Complete condensation, without loss or reaction, preserves the entering vapor's overall component mole fractions; cooling alone does not give another enrichment step. Partial condensation can instead leave two streams of different composition, requiring both vapor-liquid equilibrium and a distillation material balance.

A concrete motivating experiment is the acetone–chloroform mixture in Truman State University's Liquid-Vapor Equilibrium of a Binary System, Procedure and Figure 1. A two-neck flask feeds a distillation head with a water-cooled laboratory condenser, condensate sampling arm and temperature probe. Starting with one pure liquid, the procedure adds the other component successively and waits for stable temperature with returning condensate. Small paired samples from the flask and condensate are read on an Abbé refractometer; a tabulated refractive index–composition relation gives the two compositions. Controls include three-point thermometer calibration, corrected atmospheric pressure readings, and agreement of the initial pure-liquid and condensate refractive indices with the reference value. Small withdrawals and little retained condensate reduce disturbance of composition. Sample evaporation can bias the readout. The inferred paired mole fractions, temperature and pressure describe vapor-liquid equilibrium, subject to the conversion from mass fraction to mole fraction and to representative sampling. This teaching protocol reports no measured results of a particular student run.^[ref]

How does such a measurement expose activity coefficients? Let $x_i$ and $y_i$ be the mole fractions in the liquid and gas thermodynamic phases, respectively, and let $p_i^{\ast }(T)$ be the pure-component vapor pressure. Assume the gas thermodynamic phase is an ideal gas mixture and neglect the change of the pure-liquid reference chemical potential between its saturation pressure and the experimental pressure. Equality of each component's chemical potential between the two thermodynamic phases then givesThis turns the paired composition readings into estimates of the activity coefficients. The approximation needs refinement when the gas departs appreciably from ideal gas behavior or the neglected liquid pressure effect matters.

The apparatus measures a boiling-composition series in which temperature changes as the mixture changes. Its readings therefore cannot be inserted directly into the fixed-temperature, fixed-pressure activity coefficient constraint. They motivate the more general task: test whether the measured mixture properties can arise from a common Gibbs free energy while accounting for changing state variables. A failure can reveal incompatible property fits or experimental bias; a pass supplies a consistency check, not proof that every reading is correct.

McMaster University's 1997/98 laboratory manual compares simple distillation and fractional distillation using charges of $25\mathrm{mL}$ each of cyclohexane and p-xylene. Part B uses a $100\mathrm{mL}$ round-bottom flask and a fractionating column. The protocol specifies a boiling chip, a heating mantle on a ring support, and the top of the thermometer bulb midway in the opening toward the laboratory condenser. Heating is adjusted for roughly one drop per second. Students record head temperature every $2\mathrm{mL}$ collected, up to $45\mathrm{mL}$, and plot both runs against collected volume on the same axes.^[ref]

Charge, atmospheric operation, and collection rate provide comparison conditions; the fractionating column is changed. A sharper separation of temperature regions would support improved fractionation. It would not directly measure product mole fractions or prove purity. The manual distinguishes collected volume from composition and states that this pair forms no azeotrope. No student dataset is supplied here, and the constant-relative volatility example is not assigned to these liquids.^[ref]

In simple distillation, pot vapor passes directly to the laboratory condenser. An initial small condensate sample can approximate vapor-liquid equilibrium with the current pot liquid. Removing enriched distillate depletes the pot's more volatile component. A collected fraction averages the changing condensate composition, rather than preserving the first-drop mole fraction.^[ref]