All-Glass Recirculating Othmer VLE Still
Provides continuous boiling, vapor condensation, and liquid/vapor recirculation until thermodynamic equilibrium is achieved.
Chemical & Process Engineering / VLE Thermodynamic Consistency
FREE TO EXPLORELABORATORY 33 · CHEMICAL & PROCESS ENGINEERING
Vapor-Liquid Equilibrium (VLE) & Thermodynamic Consistency via Wilson & Margules Activity Models
Operate a precision vapor-recirculating Othmer VLE still for a binary ethanol-water system at 101.325 kPa, determine equilibrium vapor and liquid mole fractions (y_1, x_1) using Abbe refractometry, compute liquid-phase activity coefficients (γ_1, γ_2), and evaluate thermodynamic consistency via the Margules and Wilson excess Gibbs energy models. Explore interactive transport phenomena, unit operations simulation, and chemical engineering telemetry.
TRANSPORT PHENOMENA · UNIT OPERATIONS · PROCESS CONTROL · REACTION ENGINEERING
Your virtual chemical and process engineering laboratory.
MARGULES ACTIVITY FACTOR LN(Γ_1) / (1 - X_1)—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Liquid Mole Fraction x_1 = 0.3 mol/mol.
Adjust Liquid Mole Fraction x_1, then execute chemical process trial.
Chemical and process engineering telemetry is evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity transport phenomena and unit operations modeling.
Process engineering assumptions and boundary condition limits
The transport and thermodynamic models apply within the specified calibrated operating window (0.1 to 0.6 mol/mol). Evaluated using an all-glass Othmer recirculating VLE equilibrium still with platinum RTD temperature sensing (±0.02 °C) and Abbe refractometric composition analysis (±0.0002 n_D). Pure component Antoine parameters: Ethanol (A=16.8958, B=3795.17, C=230.918), Water (A=16.3872, B=3885.70, C=230.170).
Process apparatus & industrial sensors.
Precision Digital Abbe Refractometer
Determines ethanol and water mole fractions in condensed liquid and vapor samples with ±0.0002 refractive index accuracy.
Calibrated 4-Wire Pt100 RTD Sensor & Digital Indicator
Measures equilibrium mixture boiling temperature with 0.01 °C resolution directly in the liquid-vapor mixing zone.
Mantle Heater with Variable Autotransformer (Variac)
Provides uniform, bump-free electrical heating to maintain steady boiling without superheating.
Recirculating Chiller & Double-Surface Condenser
Maintains coolant at 10.0 °C to condense vapor effluent completely without volatile loss.
Digital Absolute Barometer & Pressure Compensator
Logs barometric pressure with 0.01 kPa accuracy to correct Antoine saturation vapor pressures.
FOLLOW THE METHOD
A reason behind every step.
Operate a precision vapor-recirculating Othmer VLE still for a binary ethanol-water system at 101.325 kPa, determine equilibrium vapor and liquid mole fractions (y_1, x_1) using Abbe refractometry, compute liquid-phase activity coefficients (γ_1, γ_2), and evaluate thermodynamic consistency via the Margules and Wilson excess Gibbs energy models. Standardized parameter settings: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6 mol/mol.
01
Refractometer Calibration & Baseline Verification
Calibrate the digital Abbe refractometer with HPLC-grade deionized water (n_D = 1.3330 at 20.0 °C) and pure absolute ethanol (n_D = 1.3614); verify calibration curve.
02
Still Charging & Coolant Circulation
Charge the boiling vessel with 250 mL of prepared binary ethanol-water solution at x_1 = 0.10; start recirculating condenser coolant at 10.0 °C.
03
Boiling Initiation & Recirculation Steady State
Apply 85 W heating via the Variac until gentle, continuous boiling is established; operate in total recirculation mode for 45 minutes until equilibrium boiling temperature stabilizes within ±0.02 °C.
04
Equilibrium Sampling & Optical Analysis
Simultaneously withdraw 0.5 mL samples of equilibrium liquid and condensed vapor using pre-chilled microsyringes; measure refractive indices at 20.0 °C to find x_1 and y_1.
05
Composition Step Progression Protocol
Increment liquid mole fraction x_1 through 0.20, 0.30, 0.40, 0.50, and 0.60 by injecting calculated aliquots of absolute ethanol, repeating equilibrium logging at each step.
06
Thermodynamic Activity & Consistency Regression
Calculate saturation vapor pressures P_i^sat via Antoine equations, determine activity coefficients γ_1 and γ_2, evaluate ln(γ_1) / (1 - x_1), and perform linear regression to determine A_12.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates VLE Thermodynamic Consistency mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
ln(γ_1) / (1 - x_1) = A_12 · x_1 = 0.7250 · x_1
| # | Liquid Phase Ethanol Mole Fraction x_1 (mol/mol) | Margules Activity Factor ln(γ_1) / (1 - x_1) (dimensionless) | Liquid mole fraction x_1 (mol/mol) | Margules factor ln(γ_1) / (1 - x_1) | Remove |
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CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
For a binary mixture obeying the modified Raoult's law, the liquid-phase activity coefficient γ_1 is calculated as:
The Redlich–Kister area test for thermodynamic consistency requires that the integral of ln(γ_1/γ_2) dx_1 from 0 to 1 must be:
In the Margules 2-suffix model, what is the excess Gibbs energy G^E / (R T) equal to?
At the azeotropic composition of a binary mixture at pressure P, the relative volatility α_12 is:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In chemical engineering thermodynamics, accurate vapor-liquid equilibrium (VLE) data are indispensable for designing, simulating, and optimizing distillation columns, flash drums, and reactive separation units. Ideal solutions follow Raoult's law: P · y_i = x_i · P_i^sat, where total system pressure P and vapor mole fraction y_i are governed purely by liquid mole fraction x_i and pure-component saturation vapor pressure P_i^sat. However, real chemical mixtures—particularly polar, hydrogen-bonding mixtures such as ethanol and water—exhibit pronounced deviations from ideal solution behavior due to molecular size disparities and asymmetric intermolecular forces. These non-idealities are captured through liquid-phase activity coefficients γ_i: P · y_i · Φ_i = x_i · γ_i · P_i^sat · φ_i^sat · exp[V_i^L (P - P_i^sat) / (R T)], where Φ_i is the vapor fugacity coefficient and the exponential term is the Poynting correction factor. At atmospheric pressure (101.325 kPa), vapor-phase non-idealities and Poynting factors are negligible, reducing the equilibrium relation to the modified Raoult's law: P · y_i = x_i · γ_i · P_i^sat(T). The excess Gibbs free energy G^E represents the thermodynamic penalty or gain of mixing relative to an ideal solution: G^E / (R T) = Σ [x_i · ln(γ_i)]. Classical excess Gibbs energy models include the two-suffix Margules equation, the van Laar equation, and local composition formulations such as the Wilson, NRTL (Non-Random Two-Liquid), and UNIQUAC models. In the Margules formulation, the activity coefficient of the volatile solute is expressed as ln(γ_1) = A_12 · (1 - x_1)^2, which rearranges to the linear form ln(γ_1) / (1 - x_1) = A_12 · x_1. Furthermore, experimental VLE datasets must satisfy the Gibbs–Duhem thermodynamic consistency equation: Σ [x_i · d(ln γ_i)] = 0 at constant temperature and pressure. Area tests (such as the Redlich–Kister integral criterion) and point-to-point consistency tests verify whether measured equilibrium compositions are physically sound or distorted by experimental systematic errors. In this laboratory investigation, an all-glass recirculating Othmer VLE still is operated across ethanol liquid mole fractions from 0.10 to 0.60 at 101.325 kPa to determine equilibrium temperatures, vapor compositions, and the Margules interaction parameter A_12 = 0.7250.
ln(γ_1) / (1 - x_1) = A_12 · x_1 = 0.7250 · x_1
Evaluated using an all-glass Othmer recirculating VLE equilibrium still with platinum RTD temperature sensing (±0.02 °C) and Abbe refractometric composition analysis (±0.0002 n_D). Pure component Antoine parameters: Ethanol (A=16.8958, B=3795.17, C=230.918), Water (A=16.3872, B=3885.70, C=230.170).