Traube Drop-Weight Stalagmometer
Precision-bore borosilicate glass stalagmometer featuring an optically ground, flat, razor-beveled circular discharge tip of external radius r = 3.500 ± 0.002 mm.
Chemistry / Surface Tension Stalagmometry
FREE TO EXPLORELABORATORY 09 · NATURAL SCIENCES
Determination of Liquid Surface Tension via Drop-Weight Stalagmometry and Harkins-Jordan Correction
Determine the absolute liquid surface tension of ultra-pure water at 20.0 °C via precision drop-weight stalagmometry, applying Tate's law and Harkins-Jordan hydrodynamic detachment corrections across systematic drop count series, and extracting surface tension using ordinary least-squares regression. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
CUMULATIVE DETACHED DROPLET MASS M_TOTAL—
MEASUREMENT STATUS
Ready to dispense 30 drops of liquid.
Adjust drop count 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 surface tension via drop-weight stalagmometry is subject to specific experimental constraints: (1) Capillary Edge Boundary Pinning: Wetting fluids must pin cleanly to the sharp external circumference of the ground-glass tip; if the glass is contaminated, the liquid film can creep up the outer cylindrical wall, increasing the effective radius r. (2) Dynamic Surface Age and Adsorption Kinetics: For pure water, surface tension equilibrates in milliseconds; however, for surfactant solutions, slow diffusion to the dilating interface produces dynamic surface tension effects requiring long bubble-pressure or drop-shape analysis. (3) Satellite Droplet Recoil: During Rayleigh-Plateau neck rupture, microscopic satellite droplets (<1% of mass) can recoil or mist into ambient air. (4) Evaporative Vapor Deficit: Over a 60-drop run lasting ~10 minutes, minute evaporation through the needle-valve vent must be controlled with vapor-saturated pre-chambers. The drop-weight stalagmometry physical model embodies the relation m_total = m_drop · N + m₀, where m_drop = (2π · r · γ · φ) / g. Calibrated apparatus constants: stalagmometer external tip radius r = 0.003500 m (3.500 mm), pure water surface tension γ = 0.07280 N/m (72.80 mN/m) at 20.0 °C, water density ρ = 998.2 kg/m³, standard acceleration of gravity g = 9.80665 m/s². The single-drop volume is V = 0.10058 cm³ = 1.0058 × 10⁻⁷ m³, giving the dimensionless shape parameter r / V^{1/3} = 0.00350 / (1.0058 × 10⁻⁷)^{1/3} = 0.7526. The corresponding Harkins-Jordan correction factor is exactly φ = 0.6150. Under these parameters, the theoretical single-drop mass is m_drop = (2π · 0.00350 · 0.07280 · 0.6150) / 9.80665 = 0.00010040 kg = 0.10040 g/drop. Multi-point linear regression across N = 10 to 60 drops yields an empirical slope of m_slope = 0.10040 g/drop with R² = 1.00000. Any constant weighing bottle tare offset or initial wetting residue is absorbed into m₀ = 0.0000 g, guaranteeing that the slope serves as an unbiased estimator of single-drop mass.
Analytical chemistry apparatus & tools.
Thermostated Circulating Glass Mantle
Double-walled optical glass jacket enclosing the stalagmometer, connected to a circulating bath maintaining the test liquid at 20.0 ± 0.05 °C.
Fine PTFE Micro-Metering Needle Valve
Micro-flow control valve attached to the top aspiration port to throttle droplet detachment to a slow, quasi-static rate of 1 drop every 8 to 10 seconds.
Tared Ground-Glass Weighing Bottle
Lightweight borosilicate weighing bottle with ground-glass stopper to collect detached droplets and prevent volatile evaporative loss during multi-drop collection.
Four-Decimal Analytical Balance & Draft Shield
0.1 mg electronic electromagnetic force restoration balance to measure cumulative droplet masses up to 6.0000 g with ±0.0001 g resolution.
Chromic-Sulfuric Acid Cleaning Station & Ethanol Wash
Glassware degreasing apparatus to strip organic surfactants and grease from the stalagmometer tip, guaranteeing perfect wetting (zero contact angle θ = 0°).
FOLLOW THE METHOD
A reason behind every step.
Determine the absolute liquid surface tension of ultra-pure water at 20.0 °C via precision drop-weight stalagmometry, applying Tate's law and Harkins-Jordan hydrodynamic detachment corrections across systematic drop count series, and extracting surface tension using ordinary least-squares regression. Suggested independent volumetric settings: 10, 20, 30, 40, 50, 60 drops.
01
Stalagmometer Cleaning and Tip Degreasing
Clean the stalagmometer with warm chromic-sulfuric acid cleaning mixture, rinse thoroughly with 500 mL of boiling deionized water, wash with absolute ethanol, and dry under filtered nitrogen to ensure the flat tip is perfectly hydrophilic and free of organic surfactant films.
02
Thermostatic Temperature Equilibration
Mount the stalagmometer inside the circulating glass water jacket set to 20.0 °C. Charge the upper reservoir with ultra-pure deionized water and allow 15 minutes for thermal equilibrium.
03
Droplet Detachment Rate Calibration
Adjust the micro-needle valve at the top of the stalagmometer until pendent droplets form smoothly and detach at a rate of exactly one drop every 8 to 10 seconds, ensuring quasi-static detachment without inertial jetting.
04
Tared Vessel Placement and Drop Collection
Tare a clean, dry, stoppered weighing bottle on the analytical balance to ±0.0001 g. Position the bottle directly beneath the stalagmometer tip inside the draft-shielded enclosure.
05
Multi-Drop Gravimetric Run
Uncap the weighing bottle, count exactly 10 drops as they detach from the tip into the bottle, immediately replace the stopper to prevent evaporation, and record the mass on the analytical balance.
06
Systematic Drop Count Series and Regression
Repeat the procedure for 20, 30, 40, 50, and 60 drops. Regress total collected mass against drop count to obtain the single drop mass m_drop, compute the Harkins-Jordan factor φ(r/V^{1/3}), and calculate absolute surface tension γ.
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
m_total = m_drop · N + m₀ ==> m = 0.1004 · N
| # | Detached droplet count N (drops) (drops) | Cumulative detached droplet mass m_total (g) | Detached droplet count N (drops) | Cumulative droplet mass m_total (g) | Remove |
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