Microprocessor AC Conductivity Bridge
Alternating-current impedance bridge operating at 1.0 kHz with 0.001 μS·cm⁻¹ sensitivity, automatic phase-angle balance, and 0.05% basic conductance accuracy.
Chemistry / Conductometric Solubility Product K_sp
FREE TO EXPLORELABORATORY 34 · NATURAL SCIENCES
Determination of Solubility Product of Sparingly Soluble Salts by Conductometry
Determine the solubility product constant (K_sp) and standard enthalpy of dissolution (ΔH°_sol) of silver chloride (AgCl) across a range of temperatures using high-precision electrolytic conductometry. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
SATURATED SOLUTION CONDUCTIVITY Κ_SAT—
MEASUREMENT STATUS
Ready to dispense 25.0 °C of liquid.
Adjust T(cell) 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
['Conductometric solubility determination is limited to salts with solubilities between 10⁻³ M and 10⁻⁶ M; salts more soluble than 10⁻³ M require extended Debye-Hückel activity corrections, while salts less soluble than 10⁻⁶ M (such as AgI) produce signals below the solvent water baseline.', 'Trace ionic contamination in glassware or reagents produces large relative errors due to the extremely low ionic strength of the analyte solution.', 'Dissolution kinetics can become slow at lower temperatures (< 15 °C), requiring extended equilibration times to avoid undersaturation artifacts.'] The thermodynamics of sparingly soluble salt dissolution is governed by the van 't Hoff relationship: ln(K_sp) = -(ΔH°_sol / R)(1/T) + ΔS°_sol / R. For silver chloride, dissolution is endothermic (ΔH°_sol = +65.50 kJ·mol⁻¹) due to the high crystal lattice enthalpy (916 kJ/mol) relative to ion hydration enthalpies (-850 kJ/mol). Because the saturated solution is at virtually infinite dilution (ionic strength I ≈ 1.3 × 10⁻⁵ M, activity coefficient γ_± > 0.995), molar conductivity equals the limiting molar conductivity Λ_m°(T) = 138.25 [1 + 0.0220(T - 25.0)] S·cm²·mol⁻¹. Saturated solution conductivity κ_sat increases from 1.352 μS/cm at 20 °C to 6.148 μS/cm at 45 °C. After subtracting the ultrapure water background κ_w, solubility product values track the van 't Hoff equation with R² > 0.99999, yielding an experimental enthalpy of dissolution agreeing within 0.01% of the certified literature benchmark.
Analytical chemistry apparatus & tools.
Platinized Platinum Dip Cell
Rigid glass electrode assembly housing parallel platinum plates (1.0 cm × 1.0 cm, separation 1.0 cm, K_cell = 1.000 cm⁻¹) platinized with platinum black to eliminate Faradaic polarization.
Thermostatic Double-Walled Dissolution Cell
Water-jacketed cylindrical reaction vessel connected to an external programmable heating/cooling circulator regulated from 20.00 °C to 45.00 ± 0.02 °C.
High-Purity Precipitated AgCl Slurry
Freshly synthesized silver chloride precipitate prepared from analytical grade AgNO₃ and KCl, washed six times by decantation with boiling ultrapure water to eliminate ionic impurities.
Submersible Magnetic Stirrer with PTFE Bar
Teflon-coated magnetic stir bar maintaining 300 RPM hydrodynamic agitation to ensure solid-liquid dissolution equilibrium without entraining air bubbles.
Polished Ultrapure Deionized Water Supply
Milli-Q deionized water source delivering solvent with specific resistivity ρ > 18.2 MΩ·cm (background specific conductivity κ_w < 0.055 μS·cm⁻¹ at 25 °C).
FOLLOW THE METHOD
A reason behind every step.
Determine the solubility product constant (K_sp) and standard enthalpy of dissolution (ΔH°_sol) of silver chloride (AgCl) across a range of temperatures using high-precision electrolytic conductometry. Suggested independent volumetric settings: 20.0, 25.0, 30.0, 35.0, 40.0, 45.0 °C.
01
Precipitation & Extensive Washing of Silver Chloride
Precipitate silver chloride by slowly mixing stoichiometric amounts of 0.100 M AgNO₃ and 0.100 M KCl under dim red safety lighting to prevent photolytic decomposition. Wash the precipitate six consecutive times by centrifugation and decantation with boiling ultrapure water until the supernatant exhibits zero chloride conductivity.
02
Solvent Background Conductivity Calibration
Rinse the clean platinized conductivity cell thoroughly with ultrapure water. Fill the thermostatic reaction vessel with 100.0 mL of pure water and record the solvent background conductivity κ_w across the temperature range 20.0 °C to 45.0 °C (0.045 μS/cm to 0.070 μS/cm).
03
Saturated Slurry Preparation & Cell Assembly
Transfer the washed AgCl precipitate into the double-walled conduction cell containing 100.0 mL of ultrapure water. Insert the dip-type conductivity cell and calibrated thermistor probe, ensuring the electrode plates are completely submerged.
04
Thermostatic Equilibration at Each Temperature
Set the circulating water bath to the lowest test temperature (20.00 ± 0.02 °C). Engage magnetic stirring at 300 RPM for 20 minutes to achieve complete heterogeneous dissolution equilibrium. Stop stirring for 15 seconds to allow solid particles to settle.
05
Specific Conductivity Acquisition Across Series
Log the steady-state specific conductivity κ_sat on the 1.0 kHz bridge. Increment the bath temperature in steps of 5.0 °C (25.0 °C, 30.0 °C, 35.0 °C, 40.0 °C, 45.0 °C). At each plateau, equilibrate for 15 minutes and record the steady-state conductivity.
06
Solubility Product & Enthalpy Extraction
Subtract the water background (κ_AgCl = κ_sat - κ_w). Calculate molar solubility s = (1000 × κ_AgCl) / Λ_m°(T) and solubility product K_sp = s². Plot ln(K_sp) versus 1000/T, perform linear least-squares regression, and extract ΔH°_sol from the slope (-ΔH°_sol / 1000 R).
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
\ln(K_{\text{sp}}) = -\left(\frac{\Delta H^\circ_{\text{sol}}}{1000 R}\right) \left(\frac{1000}{T}\right) + \frac{\Delta S^\circ_{\text{sol}}}{R} \implies \ln(K_{\text{sp}}) = -7.877 \cdot \left(\frac{1000}{T}\right) + 3.966 \implies \Delta H^\circ_{\text{sol}} = 65.50\text{ kJ}\cdot\text{mol}^{-1}
| # | Equilibration Temperature T (°C) | Saturated Solution Conductivity κ_sat (μS·cm⁻¹) | Inverse Temperature 1000/T (K⁻¹) | Logarithmic Solubility Product ln(K_sp) | Remove |
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