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An azeotrope has equal coexisting liquid and vapor compositions: $y=x$. Ordinary fractional distillation cannot cross this composition boundary at fixed pressure; more packing does not remove it. A constant head temperature therefore does not establish a pure chemical substance.^[ref] The stipulated $\alpha =2$ model has $y>x$ throughout $0<x<1$, so it has no interior azeotrope and cannot represent this limit.

The Mixture measurements and the Gibbs-Duhem constraint article describes the inspected acetone–chloroform preparation, apparatus, paired readouts, controls and sampling limits.^[ref]

That existing apparatus account supplies the experimental controls and limitations. Its refractive index calibration yields mass fractions, which must be converted to mole fractions. For a measured component-A mass fraction $w_A$ and component molar masses $M_A,M_B$,Apply this conversion separately to the flask sample and to completely condensed vapor to obtain $x_A$ and $y_A$. Comparing $y_{i}P$ with $x_i{p}_i^{\ast }(T)$ tests Raoult's law at the measured temperature; using the changing temperature at each composition is essential. The chosen A/B values above are unrelated to the protocol's substances.

The more general diagnostic, retaining an ideal gas vapor and negligible pure-liquid pressure correction, isThis follows by replacing $\ln x_i$ with $\ln (x_i{\gamma }_i)$ in the chemical potential subtraction used for Raoult's law. A reproducible discrepancy from ${\gamma }_i=1$ can expose failure of the ideal solution approximation, but interpreting it requires checking measurement uncertainty, representative paired sampling and the ideal gas approximation. Apparent agreement within uncertainty supports an approximation over the tested conditions; it cannot establish exact ideality at every composition.

Positive or negative deviations of component partial pressures require activity coefficients different from one under these assumptions. An azeotrope is also absent from the chosen unequal-vapor pressure model: the explicit inequality in ideal binary vapor composition gives $y_A>x_A$ throughout $0<x_A<1$. An interior equality would require $p_A^{\ast }=p_B^{\ast }$; in that degenerate case every composition has $y_A=x_A$, rather than an isolated enrichment reversal. Neither an azeotrope nor liquid phase separation should be inferred from the ideal curves.

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]