Constant-Temperature Circulating Water Bath (±0.05 °C)
Maintains a constant thermal plateau for the borax saturation flask with continuous magnetic stirring to establish true thermodynamic solid-liquid equilibrium.
Chemistry / van 't Hoff Thermodynamic Solubility
FREE TO EXPLORELABORATORY 16 · NATURAL SCIENCES
Thermodynamic Determination of Gibbs Free Energy, Enthalpy, and Entropy of Dissolution via van 't Hoff Solubility Analysis
Determine the standard molar Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) of dissolution for borax (disodium tetraborate decahydrate) by measuring its temperature-dependent solubility product via titrimetric analysis with standard hydrochloric acid, linearizing the thermodynamic equilibrium with the van 't Hoff equation, and extracting the state functions using ordinary least-squares regression. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
TITRANT VOLUME V_HCL—
MEASUREMENT STATUS
Ready to dispense 40.0 °C of liquid.
Adjust equilibration temperature 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 standard van 't Hoff linear model assumes that the molar enthalpy of dissolution ΔH° and entropy ΔS° remain constant over the 30–55 °C interval, and that the activity coefficient product γ_±³ remains close to unity. In reality, ionic strength increases from 0.17 M to 0.51 M across this temperature range, which causes a modest ~1.5% suppression of activity that is effectively averaged out by ordinary least-squares regression. The physical simulation model calculates the temperature-dependent solubility product K_sp and titrant volume V_HCl using the integrated van 't Hoff relation ln K_sp = −(ΔH° / R) · (1/T) + (ΔS° / R). Thermodynamic benchmark constants for borax dissolution: standard molar enthalpy of dissolution ΔH° = 110.00 kJ/mol (110000 J/mol); standard molar entropy of dissolution ΔS° = 330.00 J/(mol·K); universal gas constant R = 8.31446 J/(mol·K). Solubility relation: s = (K_sp / 4.0)^(1/3) in mol/L. Titrimetric calculation: a 5.00 mL (0.00500 L) aliquot contains n_borax = s · 0.00500 mol. Stoichiometric reaction with standardized 0.500 M HCl: 1 mol tetraborate consumes 2 mol HCl, so n_HCl = 2 · s · 0.00500 = 0.0100 · s mol. Required titrant volume: V_HCl = n_HCl / M_HCl = (0.0100 · s) / 0.500 L = 0.0200 · s L = 20.0 · s mL. Across equilibration temperatures from 30.0 °C to 55.0 °C (303.15 K to 328.15 K), V_HCl spans 3.37 mL to 10.22 mL. Scaled regression coordinates: x = 1000.0 / T (in K⁻¹), y = ln(K_sp). Theoretical regression slope: m_slope = −ΔH° / (1000 · R) = −110000 / 8314.46 = −13.230 K. Theoretical intercept: b = ΔS° / R = 330.0 / 8.31446 = 39.690. Ordinary least-squares linear regression isolates ΔH° = −m_slope · (1000 · R) with R² = 1.00000; pre-warmed filtering pipettes prevent premature crystallization in the pipette barrel.
Analytical chemistry apparatus & tools.
Borax Saturation Flask and Magnetic Stirrer
Contains an aqueous slurry of disodium tetraborate decahydrate with substantial excess solid phase present, ensuring 100% saturation at all temperatures.
Pre-Warmed Volumetric Transfer Pipettes (5.00 ± 0.01 mL)
Equilibrated in a drying oven at the bath temperature and fitted with a cotton wool filter plug to sample clear saturated solution without drawing in solid crystals or inducing thermal shock precipitation.
Precision 50 mL Class-A Glass Burette (±0.05 mL)
Dispenses standardized 0.5000 M hydrochloric acid titrant dropwise to determine the exact neutralization volume of dissolved tetraborate ions.
NIST-Calibrated Digital Thermometer (±0.01 °C)
Directly measures the temperature of the saturated borax slurry inside the flask at the instant of aliquot extraction.
Bromocresol Green pH Indicator Solution
Provides a sharp, highly visible color transition from blue (basic borate) to yellow (acidic boric acid) at pH 4.0, signalling the stoichiometric titration endpoint.
FOLLOW THE METHOD
A reason behind every step.
Determine the standard molar Gibbs free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) of dissolution for borax (disodium tetraborate decahydrate) by measuring its temperature-dependent solubility product via titrimetric analysis with standard hydrochloric acid, linearizing the thermodynamic equilibrium with the van 't Hoff equation, and extracting the state functions using ordinary least-squares regression. Suggested independent volumetric settings: 30.0, 35.0, 40.0, 45.0, 50.0, 55.0 °C.
01
Slurry Preparation and Thermal Equilibration
Prepare a saturated slurry by adding approximately 25 g of pure borax to 100 mL of deionized water in an Erlenmeyer flask. Immerse in the water bath set to the assigned temperature (30.0 °C). Stir vigorously for at least 15 minutes to establish solid-liquid phase equilibrium, verifying that excess solid remains at the bottom.
02
Stirring Interruption and Sediment Settling
Turn off the magnetic stirrer and allow the suspension to stand quietly for 2 minutes to permit dense undissolved borax crystals to settle to the bottom, leaving a clear supernatant liquid.
03
Filter Plugged Pipetting of Saturated Aliquot
Insert a small wad of clean surgical cotton wool into the tip of a clean 5.00 mL volumetric pipette that has been pre-warmed in a water bath to avoid premature crystallization. Rapidly draw up exactly 5.00 mL of clear supernatant liquid. Remove the cotton plug, wipe the exterior tip, and transfer into a 125 mL titration flask containing 25 mL deionized water.
04
Titration with Standardized Hydrochloric Acid
Add 3 drops of bromocresol green indicator to the aliquot, producing a distinct blue color. Fill the Class-A burette with standardized 0.5000 M HCl. Titrate dropwise under continuous swirling until the solution transitions through green to a permanent bright yellow endpoint (pH 4.0). Record the titrant volume V_HCl to ±0.01 mL.
05
Multi-Temperature Series Execution
Increase the water bath temperature to 35.0, 40.0, 45.0, 50.0, and 55.0 °C. At each plateau, equilibrate for 15 minutes, allow crystals to settle, filter a fresh 5.00 mL aliquot, and titrate in duplicate with standardized HCl.
06
van 't Hoff Regression and State Function Derivation
Compute molar solubility s = (0.500 · V_HCl) / (2 · 5.00) = 0.050 · V_HCl, and solubility product K_sp = 4 s³. Calculate 1000/T (K⁻¹) and ln(K_sp). Perform ordinary least-squares regression of ln(K_sp) vs 1000/T. Extract ΔH° = −m_slope · (1000·R), ΔS° = b · R, and compute ΔG° = ΔH° − T ΔS° at 298.15 K.
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_sp) = −[ΔH° / (1000·R)] · (1000/T) + (ΔS° / R) ==> ln(K_sp) = −13.241 · (1000/T) + 39.723
| # | Equilibration temperature t (°C) (°C) | Titrant volume V_HCl (mL) | Inverse absolute temperature 1000/T (K⁻¹) | Natural logarithm of solubility product ln(K_sp) | Remove |
|---|
No readings yet. Dispense and weigh a volumetric aliquot to record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING