High-Precision AC Conductivity Bridge
Digital impedance bridge operating at 1.0 kHz with auto-ranging resolution of 0.001 μS·cm⁻¹, 0.05% basic accuracy, and automatic phase-quadrature nulling to eliminate reactive impedance.
Chemistry / Debye-Hückel-Onsager Electrolyte Conduction
FREE TO EXPLORELABORATORY 33 · NATURAL SCIENCES
Molar Conductivity of Strong Electrolytes and the Debye-Hückel-Onsager Limiting Law
Determine the limiting molar conductivity (Λ_m°) of potassium chloride (KCl) and test the validity of the Debye-Hückel-Onsager limiting law across a series of dilute strong electrolyte solutions. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
SPECIFIC ELECTROLYTIC CONDUCTIVITY Κ—
MEASUREMENT STATUS
Ready to dispense 1.0 mM of liquid.
Adjust c(KCl) 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 Debye-Hückel-Onsager limiting law is strictly valid only at infinite dilution and low concentrations (c < 0.015 M for 1:1 salts); at higher concentrations, finite ion size and ion association cause deviations.', 'Dissolved atmospheric carbon dioxide (CO₂) forms carbonic acid which can elevate solvent background conductivity if water is not degassed or protected under nitrogen.', 'For multi-valent electrolytes (e.g., 2:2 salts like MgSO₄), strong electrostatic ion pairing requires extended Fuoss-Onsager association models rather than the simple linear square-root law.'] The Debye-Hückel-Onsager limiting law is expressed as Λ_m = Λ_m° - (A_rel · Λ_m° + B_el) · √c = Λ_m° - S · √c, where Λ_m° is the limiting molar conductivity at infinite dilution and S is the theoretical Onsager slope. For a 1:1 univalent electrolyte in water at 25.00 °C, the theoretical coefficients derived from first principles are A_rel = 0.2289 (mol/L)⁻¹/² and B_el = 60.20 S·cm²·mol⁻¹·(mol/L)⁻¹/². For potassium chloride (Λ_m° = 149.85 S·cm²·mol⁻¹), the theoretical slope is S = 94.50 S·cm²·mol⁻¹·(mol/L)⁻¹/². By plotting molar conductivity Λ_m against √c, linear least-squares regression yields an empirical intercept confirming Λ_m° = 149.9 S·cm²·mol⁻¹ and an empirical slope confirming S = 94.5 S·cm²·mol⁻¹·M⁻¹/² with R² > 0.99999, providing authoritative experimental confirmation of electrolyte conduction theory.
Analytical chemistry apparatus & tools.
Platinized Platinum Dip Cell
Rigid glass dip cell housing two parallel platinum plates (1.0 cm × 1.0 cm, separation 1.0 cm, cell constant K_cell = 1.000 cm⁻¹) electrolytically platinized with colloidal platinum black to suppress electrode polarization.
Thermostatic Double-Walled Conduction Vessel
Water-jacketed cylindrical borosilicate glass cell coupled to a constant-temperature refrigerated circulator maintaining solution temperature at 25.00 ± 0.02 °C.
Class A Volumetric Glassware & Dispensers
Calibrated 100.0 mL, 250.0 mL, and 500.0 mL Class A volumetric flasks and electronic micropipettes (tolerance ±0.2%) for precision serial dilution of KCl standard solutions.
Analytical Dual-Range Microbalance
Five-decimal electronic balance (±0.01 mg precision) used for primary gravimetric preparation of 0.1000 M stock KCl from fused, oven-dried analytical grade salt.
Triple-Distilled Ultrapure Water Source
Polished Milli-Q deionized water system delivering solvent with resistivity ρ > 18.2 MΩ·cm (solvent background conductivity κ_w < 0.055 μS·cm⁻¹ at 25 °C).
FOLLOW THE METHOD
A reason behind every step.
Determine the limiting molar conductivity (Λ_m°) of potassium chloride (KCl) and test the validity of the Debye-Hückel-Onsager limiting law across a series of dilute strong electrolyte solutions. Suggested independent volumetric settings: 0.5, 1.0, 2.0, 4.0, 8.0, 12.0 mM.
01
Solvent Background Conductivity Determination
Rinse the platinized platinum cell four times with freshly drawn ultrapure water. Fill the thermostatic vessel with 80.0 mL of ultrapure water equilibrated at 25.00 ± 0.02 °C. Record the solvent background conductivity κ_w (typically 0.04 to 0.06 μS·cm⁻¹), which must be subtracted from all subsequent electrolyte measurements.
02
Cell Constant Verification with Primary KCl Standard
Prepare a 0.0100 M KCl calibration standard from desiccated primary-standard salt. Equilibrate at 25.00 °C in the thermostatic bath and measure conductivity κ_std = 1408.7 μS·cm⁻¹ to confirm the cell constant K_cell = 1.000 ± 0.004 cm⁻¹.
03
Serial Dilution of Strong Electrolyte Series
Using calibrated Class A volumetric flasks, prepare six precision test solutions of KCl spanning the dilute Debye-Hückel regime: 0.50 mM, 1.00 mM, 2.00 mM, 4.00 mM, 8.00 mM, and 12.00 mM (concentrations c from 0.0005 M to 0.0120 M).
04
Thermostatic Equilibration of Analyte Samples
Transfer the lowest concentration test solution (0.50 mM KCl) into the double-walled conduction cell. Allow 10 minutes of closed-loop thermal equilibration at 25.00 ± 0.02 °C under gentle magnetic stirring, pausing stirring prior to logging.
05
Conductance Acquisition & Frequency Independence Check
Measure specific electrolytic conductivity κ on the 1.0 kHz bridge. Verify frequency independence by switching briefly to 2.0 kHz to confirm that capacitive electrode reactance is negligible (< 0.02%). Repeat sequentially for all six concentrations from lowest to highest.
06
Molar Conductivity Computation & Onsager Linearization
Subtract solvent background conductivity (κ_corr = κ - κ_w). Compute molar conductivity Λ_m = 1000 × κ_corr / c_M (S·cm²·mol⁻¹). Calculate the square root of molarity √c_M, construct the Kohlrausch plot (Λ_m vs √c), and perform least-squares linear regression to extract limiting molar conductivity Λ_m° and the empirical Onsager slope S.
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
\Lambda_m = -S \cdot \sqrt{c} + \Lambda_m^\circ \implies \Lambda_m = -94.54 \cdot \sqrt{c} + 149.85 \implies \Lambda_m^\circ = 149.9\text{ S}\cdot\text{cm}^2\cdot\text{mol}^{-1}
| # | Potassium Chloride Concentration c (mM) | Specific Electrolytic Conductivity κ (μS·cm⁻¹) | Square Root of Concentration √c (M¹/²) | Molar Conductivity Λ_m (S·cm²·mol⁻¹) | Remove |
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