Jacketed Beckmann Freezing-Point Cell
Heavy-walled borosilicate inner boiling tube with side arm, fitted inside an outer air jacket to provide an insulating annular air layer preventing rapid freezing.
Chemistry / Cryoscopic Molar Mass
FREE TO EXPLORELABORATORY 10 · NATURAL SCIENCES
Determination of Molar Mass via Cryoscopic Freezing-Point Depression and Beckmann Thermometry
Determine the molecular weight and molar mass of an unknown non-electrolyte organic solute (biphenyl) via cryoscopic freezing-point depression in cyclohexane, utilizing precision Beckmann thermometry to resolve supercooling cooling curves, and extracting molar mass via ordinary least-squares regression. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
FREEZING-POINT DEPRESSION ΔT_F—
MEASUREMENT STATUS
Ready to dispense 0.6 g of liquid.
Adjust solute mass 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.
Physical chemistry assumptions and metrological limits
The determination of molar mass via cryoscopy is subject to specific experimental constraints: (1) Supercooling Latent Heat Distortion: When extensive supercooling (>1.0 °C) occurs, the rapid crystallization that follows precipitates a substantial fraction of solid solvent, concentrating the residual solution and artificially depressing the plateau temperature. (2) Solid Solution Formation: The thermodynamic derivation assumes that pure solid solvent crystallizes out; if the solute co-crystallizes as a solid solution, the freezing-point depression is reduced. (3) Solute Association and Non-Ideality: Non-polar solvents promote hydrogen-bonded association (dimers/trimers) for polar solutes like alcohols and acids, requiring concentration extrapolation to zero molality. (4) Solvent Volatility: Cyclohexane has a significant vapor pressure at 6 °C (~40 mmHg); headspace evaporation during solute additions slightly concentrates the solution if transfers are prolonged. The cryoscopic physical model incorporates the colligative freezing relation ΔT_f = [ K_f / (w_solvent · M_solute) ] · w_solute + ΔT₀. Experimental parameters: cryoscopic solvent mass w_solvent = 0.02500 kg (25.00 g cyclohexane), cryoscopic constant K_f = 20.00 K·kg/mol (20.00 °C·kg/mol), theoretical solute molar mass M = 154.21 g/mol. The theoretical regression slope is m_slope = K_f / (w_solvent · M) = 20.00 / (0.02500 · 154.21) = 5.18773 °C/g. Freezing-point depressions range from 1.038 °C at w = 0.20 g to 6.225 °C at w = 1.20 g. Motorized stirring at 60 strokes/min ensures that supercooling is restricted to ~0.5 °C before crystallization triggers latent heat release and temperature rebound to the true thermodynamic equilibrium freezing plateau. Multi-point linear regression absorbs any constant Beckmann mercury setting zero-datum offset into the intercept ΔT₀ = 0.000 °C, guaranteeing that the regression slope serves as an unbiased estimator of solute molar mass.
Analytical chemistry apparatus & tools.
Beckmann Differential Thermometer
Precision 5-degree adjustable differential mercury thermometer with 0.01 °C graduations, readable with a magnifying lens to ±0.005 °C.
Motorized Reciprocating Loop Stirrer
Platinum/nichrome wire ring stirrer operated at a constant rate of 60 strokes/min to maintain uniform temperature without introducing excess frictional heat.
Thermostated Ice-Water Cryostat Bath
Insulated 2000 mL glass vessel filled with an equilibrated slurry of crushed ice and deionized water maintained at 2.0 ± 0.5 °C.
Four-Decimal Analytical Balance
Electromagnetic force restoration balance with 0.1 mg precision to weigh both solvent (25.000 g) and solute increments (0.2000 to 1.2000 g).
Solvent Syringe & Calcium Chloride Guard Tube
30 mL airtight gas-tight syringe to deliver cyclohexane without vapor loss, protected by an anhydrous CaCl₂ guard tube to exclude atmospheric moisture.
FOLLOW THE METHOD
A reason behind every step.
Determine the molecular weight and molar mass of an unknown non-electrolyte organic solute (biphenyl) via cryoscopic freezing-point depression in cyclohexane, utilizing precision Beckmann thermometry to resolve supercooling cooling curves, and extracting molar mass via ordinary least-squares regression. Suggested independent volumetric settings: 0.2, 0.4, 0.6, 0.8, 1.0, 1.2 g.
01
Freezing Point of Pure Solvent
Charge 25.00 g of pure anhydrous cyclohexane into the inner tube, assemble the Beckmann thermometer and stirrer, seat inside the air jacket, and immerse in the ice bath. Stir smoothly while recording temperature every 15 seconds. After slight supercooling (~0.5 °C), temperature rebounds to a plateau: record T_f° to ±0.005 °C.
02
Solute Preparation and Weighing
Accurately weigh an analytical aliquot of 0.2000 g of the unknown organic solute on glazed glassine paper using the four-decimal analytical balance.
03
Quantitative Dissolution
Remove the inner tube from the cooling bath, warm it slightly in hand to remelt the cyclohexane crystals, introduce the weighed solute through the side arm, and agitate until completely dissolved.
04
Cooling Curve Determination for Solution
Reseat the tube in the air jacket, immerse in the ice bath, and record temperature every 15 seconds with steady stirring. Identify the supercooling trough, the crystallization rebound, and extrapolate the true equilibrium freezing point T_f.
05
Depression Calculation
Compute the freezing-point depression ΔT_f = T_f° - T_f for the first concentration level.
06
Cumulative Multi-Point Titration Series
Add successive increments of solute to achieve 0.40, 0.60, 0.80, 1.00, and 1.20 g total solute, recording the freezing-point depression at each stage. Regress ΔT_f against w_solute to extract the slope and determine the solute molar mass.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into quantitative chemical insight.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
ORDINARY LEAST-SQUARES FIT · m = ρ·V + m₀
ΔT_f = [K_f / (w_solvent · M)] · w_solute + ΔT₀ ==> ΔT = 5.187 · w
| # | Solute mass w_solute (g) (g) | Freezing-point depression ΔT_f (°C) | Solute mass w_solute (g) | Freezing-point depression ΔT_f (°C) | Remove |
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