To determine the isobaric liquid-vapor equilibrium (VLE) boiling point diagram of binary ethanol-water mixtures at 101.325 kPa using an Othmer-type dynamic recirculating equilibrium still with Cottrell thermo-lift pumping, measure coexisting liquid and vapor compositions via Abbe refractometry, compute non-ideal liquid activity coefficients (γ₁), evaluate the Margules interchange energy parameter (A), and identify the minimum-boiling azeotropic composition and thermodynamic limits of fractional distillation. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
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Adjust liquid mole fraction V, then weigh the dispensed aliquot.
Mass observations are determined by the high-precision thermodynamic equation of state for pure liquid water. Readings reflect thermal equilibrium and analytical balance force restoration.
The 1-parameter symmetric Margules model assumes that the excess Gibbs free energy is symmetric with respect to mole fraction (g^E = A·x₁·x₂). In reality, the ethanol-water system displays slight asymmetry (A₁₂ ≠ A₂₁), which can be modeled with higher-order 2-parameter Margules, van Laar, Wilson, or NRTL equations for industrial design. Furthermore, non-ideal vapor phase fugacity corrections (virial equation) become relevant at pressures significantly above 1 atm. The physical simulation model computes vapor-liquid equilibrium (VLE) at 101.325 kPa using the 1-parameter Margules excess Gibbs energy formulation: g^E / (RT) = A·x₁·x₂, giving activity coefficients ln(γ₁) = A·x₂² and ln(γ₂) = A·x₁² with interchange parameter A = 1.4000. Pure component saturation vapor pressures are calculated via empirical Antoine equations: log₁₀(P₁*/mmHg) = 8.20417 − 1642.89 / (T/°C + 230.300) for ethanol (normal boiling point 78.37 °C) and log₁₀(P₂*/mmHg) = 8.07131 − 1730.63 / (T/°C + 233.426) for water (normal boiling point 100.00 °C). At each liquid mole fraction x₁ ∈ [0.10, 0.60], bubble point temperatures T_b are solved using a high-precision bisection algorithm enforcing P_tot = P₁*(T_b)·x₁·γ₁ + P₂*(T_b)·x₂·γ₂ = 101.325 kPa. Coexisting equilibrium vapor mole fractions span y₁ = 0.4360 (T_b = 87.09 °C) at x₁ = 0.10 to y₁ = 0.7227 (T_b = 77.37 °C) at x₁ = 0.60. Linear regression of ln(γ₁) against (1 − x₁)² isolates slope A = 1.400 with R² = 1.00000; the Gibbs-Konovalov condition locates the minimum-boiling azeotrope at x_azeo = 0.894, establishing the theoretical ceiling for conventional distillation.
Precision borosilicate distillation apparatus equipped with Cottrell vapor-lift pump, vacuum thermal jacket, and separate liquid and condensed vapor sampling receivers operating under continuous reflux steady state.
High-accuracy dual-prism refractometer with water-jacketed thermal control (20.00 ± 0.02 °C) measuring optical refractive index n_D to ±0.0001 for rapid non-destructive determination of ethanol mole fractions.
Four-wire platinum resistance temperature detector (RTD) positioned directly in the liquid-vapor spray from the Cottrell tube to record true boiling point equilibrium without superheating.
Digital barometric transducer reading atmospheric ambient pressure to ±0.01 kPa to correct vapor pressures to the standard 101.325 kPa reference state.
Electrically insulated spherical heating mantle with electronic thyristor regulator providing uniform thermal power to sustain stable boiling without bumping or decomposition.
Spectroscopic grade anhydrous ethanol (≥ 99.8%, n_D²⁰ = 1.3614) and vacuum-degassed Type 1 Millipore water (n_D²⁰ = 1.3330) used for refractive index calibration and mixture synthesis.
To determine the isobaric liquid-vapor equilibrium (VLE) boiling point diagram of binary ethanol-water mixtures at 101.325 kPa using an Othmer-type dynamic recirculating equilibrium still with Cottrell thermo-lift pumping, measure coexisting liquid and vapor compositions via Abbe refractometry, compute non-ideal liquid activity coefficients (γ₁), evaluate the Margules interchange energy parameter (A), and identify the minimum-boiling azeotropic composition and thermodynamic limits of fractional distillation. Suggested independent volumetric settings: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 mole frac.
Circulate 20.00 °C water through the Abbe refractometer prisms, calibrate zero with pure degassed water (n_D = 1.3330), measure refractive indices for known ethanol standards across 0.0 to 1.0 mole fraction, and construct the calibration polynomial.
Clean and dry the Othmer still, charge the boiling chamber with 150 mL of prepared binary ethanol-water solution (starting at x₁ = 0.10), add Teflon boiling stones, seat the Cottrell pump assembly, and inspect all ground glass joints.
Energize heating mantle to achieve vigorous boiling, observe the Cottrell thermo-lift pumping an intimate mixture of boiling liquid and vapor over the PT100 sensor, and allow the system to reflux for 30 minutes until boiling temperature stabilizes to ±0.02 °C.
Using chilled airtight syringes through septum ports, withdraw 0.5 mL samples of circulating liquid and condensed vapor simultaneously to freeze equilibrium composition and prevent preferential volatile evaporation.
Apply two drops of each sample to the Abbe refractometer prisms at 20.00 °C, record refractive index n_D, convert to equilibrium mole fractions x₁ and y₁, and log the stabilized boiling temperature T_b and ambient barometric pressure P.
Spike the still with absolute ethanol to advance liquid composition sequentially through x₁ = 0.20, 0.30, 0.40, 0.50, and 0.60, repeat reflux equilibration, compute activity coefficients γ₁, and perform linear Margules regression.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | Liquid ethanol mole fraction x_liquid (mole frac) | Equilibrium vapor mole fraction y_vapor (mole frac) | Squared water mole fraction (1 − x_liquid)² | Logarithmic activity coefficient ln(γ_EtOH) | Remove |
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