Calibrated 25.000 mL Gay-Lussac Quartz Pycnometer
Measures solution liquid density with ±0.00005 g/cm^3 precision via capillary ground stopper.
Chemical & Process Engineering / Partial Molar Volume Dilatometry
FREE TO EXPLORELABORATORY 36 · CHEMICAL & PROCESS ENGINEERING
Partial Molar Volume & Excess Volume in Binary Solutions via Precision Pycnometry & Dilatometry
Determine the densities of ethanol-water mixtures across ethanol mole fractions x_EtOH from 0.05 to 0.30 at 25.00 °C using Gay-Lussac pycnometry and capillary dilatometry, evaluate the apparent molar volume phi_V, and extract the infinite-dilution partial molar volume and volumetric concentration slope. 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.
APPARENT MOLAR VOLUME PHI_V—
PROCESS & PILOT PLANT TELEMETRY
Ready to sample with Ethanol Mole Fraction = 0.15 mol/mol.
Adjust Ethanol Mole Fraction, 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 (0.05 to 0.3 mol/mol). Evaluated using calibrated 25.000 mL Gay-Lussac quartz pycnometers and a constant-temperature immersion bath at 25.000 ± 0.005 °C. Density of pure deionized water at 25.00 °C = 0.997048 g/cm^3; pure ethanol = 0.78506 g/cm^3.
Process apparatus & industrial sensors.
Ultra-Stable Thermostatic Water Bath
Controls temperature at 25.000 ± 0.005 °C to eliminate thermal expansion density drift.
High-Precision Analytical Balance (0.0001 g)
Weighs empty, dry, and liquid-filled pycnometer vessels with 0.1 mg accuracy.
Capillary Dilatometer Cell
Measures continuous volume contraction upon mixing with 0.001 cm^3 sensitivity.
Degassed HPLC-Grade Reagents (Water & Absolute Ethanol)
Eliminates dissolved microbubbles that skew volumetric pycnometric measurements.
Digital Quartz Density Meter (Verification Standard)
Provides secondary oscillating U-tube density validation at 25.000 °C.
FOLLOW THE METHOD
A reason behind every step.
Determine the densities of ethanol-water mixtures across ethanol mole fractions x_EtOH from 0.05 to 0.30 at 25.00 °C using Gay-Lussac pycnometry and capillary dilatometry, evaluate the apparent molar volume phi_V, and extract the infinite-dilution partial molar volume and volumetric concentration slope. Standardized parameter settings: 0.05, 0.1, 0.15, 0.2, 0.25, 0.3 mol/mol.
01
Pycnometer Tare & Volume Calibration
Thoroughly clean, rinse with acetone, and vacuum-dry the pycnometer; record empty dry weight W_0; fill with degassed DI water at 25.000 °C to find calibrated volume V_pyc.
02
Binary Solution Preparation
Prepare binary ethanol-water solutions at mole fractions x_EtOH = 0.05, 0.10, 0.15, 0.20, 0.25, and 0.30 by gravimetric dispensing on the analytical balance.
03
Thermal Equilibration in Constant Bath
Fill pycnometer with x_EtOH = 0.05 solution; immerse in 25.000 °C bath for 30 minutes; seat capillary stopper and wipe exterior dry.
04
Precision Density Determination
Weigh filled pycnometer W_1; compute solution density ρ = (W_1 - W_0) / V_pyc corrected for air buoyancy.
05
Apparent Molar Volume Calculation
Compute apparent molar volume phi_V = (M_2 / ρ) - [(ρ - ρ_1^*) / (m · ρ · ρ_1^*)] for each composition.
06
Composition Step & Infinite Dilution Regression
Repeat density measurements for remaining mixtures; plot phi_V versus x_EtOH to determine infinite-dilution volume phi_V0 and slope S.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into chemical process engineering insight.
Points are your recorded observations. The solid regression line validates Partial Molar Volume Dilatometry mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
phi_V = S · x_EtOH + phi_V0 = 14.5000 · x_EtOH + 54.2000
| # | Ethanol Mole Fraction x_EtOH (mol/mol) | Apparent Molar Volume phi_V (cm^3/mol) | Ethanol mole fraction x_EtOH (mol/mol) | Apparent molar volume phi_V (cm^3/mol) | Remove |
|---|
No readings yet. Execute a process trial and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING
Explain what the process engineering metrics mean.
The apparent molar volume phi_V of a solute in binary solution is defined as:
At infinite dilution (x_2 -> 0), the apparent molar volume phi_V0 is equal to:
For ethanol-water mixtures at 25 °C, the excess molar volume V^E is:
Euler's theorem for extensive properties dictates that total solution volume V is:
THEORY AND UNIT OPERATIONS CONTEXT
Process engineering background & physical principles.
In chemical solution thermodynamics, extensive thermodynamic properties—including total volume V, enthalpy H, entropy S, and Gibbs free energy G—depend not only on temperature and pressure but also on mixture composition. For a non-ideal binary mixture, the total volume is not simply the sum of the pure component volumes due to differences in molecular packing, interstitial cavity filling, and intermolecular hydrogen bonding. The partial molar volume of component i, defined as V_bar_i = (∂V / ∂n_i)_{T, P, n_j≠i}, represents the change in total mixture volume per mole of component i added at constant temperature, pressure, and remaining component amounts. By Euler's theorem for homogeneous functions of degree 1, the total volume of a binary solution containing n_1 moles of solvent (water) and n_2 moles of solute (ethanol) is given by: V = n_1 · V_bar_1 + n_2 · V_bar_2. Dividing by total moles yields the mean molar volume: V_m = x_1 · V_bar_1 + x_2 · V_bar_2. In dilute and moderately concentrated solutions, experimental data are analyzed through the apparent molar volume phi_V: phi_V = (V - n_1 · V_1^*) / n_2 = (M_2 / ρ) - [(ρ - ρ_1^*) / (m · ρ · ρ_1^*)], where M_2 is solute molar mass, m is molality, and ρ and ρ_1^* are solution and pure solvent densities. In the dilute alcohol concentration regime (x_EtOH = 0.05 to 0.30), the apparent molar volume increases linearly with mole fraction according to the Redlich–Meyer and Mason relations: phi_V = phi_V0 + S · x_EtOH, where phi_V0 is the infinite-dilution partial molar volume of ethanol in water (representing an isolated ethanol molecule surrounded purely by a cage of hydrogen-bonded water molecules, often exhibiting hydrophobic hydration) and S is the volumetric interaction slope. In this laboratory investigation, precision Gay-Lussac pycnometers and capillary dilatometers are operated at 25.000 ± 0.005 °C to measure densities across x_EtOH from 0.05 to 0.30, evaluate phi_V, and determine the infinite-dilution volume phi_V0 = 54.2000 cm^3/mol and slope S = 14.5000 cm^3/mol.
phi_V = S · x_EtOH + phi_V0 = 14.5000 · x_EtOH + 54.2000
Evaluated using calibrated 25.000 mL Gay-Lussac quartz pycnometers and a constant-temperature immersion bath at 25.000 ± 0.005 °C. Density of pure deionized water at 25.00 °C = 0.997048 g/cm^3; pure ethanol = 0.78506 g/cm^3.