Quantitatively verify the law of limiting reactants and stoichiometric mole ratios by precipitating insoluble barium sulfate from standardized aqueous solutions of barium chloride and sodium sulfate, determining the experimental molar mass of BaSO₄ via ordinary least-squares linear regression, and evaluating gravimetric percentage yields and coprecipitation equilibria. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
Ready to dispense 16.0 mL of liquid.
Adjust sulfate volume 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.
The gravimetric determination of barium sulfate stoichiometry is subject to fundamental thermodynamic and mechanical boundary conditions: (1) Intrinsic Solubility Loss: Although barium sulfate is sparingly soluble (K_sp = 1.08 × 10⁻¹⁰ at 25 °C), approximately 0.24 mg of BaSO₄ dissolves per 100 mL of aqueous wash water, setting an asymptotic thermodynamic limit on quantitative recovery. (2) Coprecipitation and Occlusion: Barium sulfate exhibits a pronounced propensity to occlude alkali nitrates, alkali chlorates, and foreign multivalent cations within its crystal lattice; because our system utilizes pure BaCl₂ and Na₂SO₄ in dilute HCl, occlusion is minimized but can still account for ±0.1% mass variance. (3) Creeping and Colloidal Penetration: Sub-micron crystallites that escape Ostwald ripening can occasionally creep up crucible walls or penetrate pores larger than 1.6 µm, causing slight negative yield errors if filtration vacuum is applied too aggressively. (4) Balance Sensitivity to Ambient Static: Sintered glass crucibles can accumulate electrostatic surface charges in low-humidity environments, necessitating antistatic ionizers or balance grounding. The gravimetric stoichiometric model assumes complete precipitation of the limiting sulfate anion according to the 1:1 net ionic equilibrium Ba²⁺ (aq) + SO₄²⁻ (aq) <===> BaSO₄ (s). Because the thermodynamic solubility product of barium sulfate is K_sp = 1.08 × 10⁻¹⁰ at 25 °C, residual dissolved sulfate in a 100 mL reaction mixture with an excess barium concentration of [Ba²⁺] ≈ 0.01 M is suppressed by the common ion effect to [SO₄²⁻] = K_sp / [Ba²⁺] = 1.08 × 10⁻⁸ M, representing an unprecipitated fraction <0.0003%. Thermal digestion at 85 °C promotes Ostwald ripening, shifting the crystallite size distribution from sub-micron colloids to coarse aggregates readily captured by 1.0–1.6 µm Gooch crucibles. Dilute hydrochloric acid (1 mL of 6 M HCl) is added to maintain pH ≈ 1, effectively protonating carbonate (CO₃²⁻) and phosphate (PO₄³⁻) impurities into soluble species and preventing the coprecipitation of BaCO₃ and Ba₃(PO₄)₂.
50.00 mL Class A calibrated volumetric burettes (tolerance ±0.05 mL) with PTFE stopcocks and 25.00/30.00 mL volumetric transfer pipettes (tolerance ±0.02 mL) for precision dispensing of standardized 0.1000 M BaCl₂ and Na₂SO₄ solutions without transfer parallax error.
250 mL heavy-duty Pyrex borosilicate digestion beakers positioned on digital ceramic hotplate magnetic stirrers equipped with external PT100 temperature sensors, maintaining constant solution temperature at 85.0 ± 1.0 °C and providing controllable vortex agitation.
Porous borosilicate filtering crucibles with fused Grade 4 sintered glass fritted discs (nominal pore diameter 1.0–1.6 µm) providing quantitative retention of microcrystalline barium sulfate without the ash-reduction artifacts associated with burning filter paper.
Heavy-walled 500 mL borosilicate filtration flasks connected to a water aspirator vacuum manifold via thick-walled gum-rubber vacuum tubing, fitted with conical neoprene adapter collars to form hermetic vacuum seals with the Gooch crucibles.
Thermostatically regulated laboratory forced-air drying oven operating at 110.0 ± 1.0 °C for calcining isolated precipitates to constant mass, paired with a heavy ground-glass vacuum desiccator charged with activated cobalt-chloride-indicating silica gel desiccant.
High-precision electromagnetic force restoration balance with 0.1 mg (0.0001 g) resolution, internal calibration motor, and anti-draft glass shielding to record empty crucible tares and gross dry precipitate masses.
Quantitatively verify the law of limiting reactants and stoichiometric mole ratios by precipitating insoluble barium sulfate from standardized aqueous solutions of barium chloride and sodium sulfate, determining the experimental molar mass of BaSO₄ via ordinary least-squares linear regression, and evaluating gravimetric percentage yields and coprecipitation equilibria. Suggested independent volumetric settings: 4.0, 8.0, 12.0, 16.0, 20.0, 24.0 mL.
Using a calibrated 30.00 mL Class A volumetric transfer pipette, quantitatively dispense 30.00 mL of standardized 0.1000 M BaCl₂ solution (3.000 mmol Ba²⁺) into a clean, labeled 250 mL borosilicate digestion beaker. Dilute the aliquot with approximately 50 mL of deionized water (18.2 MΩ·cm) and deliver 1.0 mL of 6.0 M HCl using a graduated cylinder. The hydrochloric acid suppresses hydroxide, carbonate, and phosphate ion activities, preventing the coprecipitation of insoluble BaCO₃ and Ba₃(PO₄)₂ while optimizing the ionic strength.
Place the reaction beaker onto the ceramic hotplate stirrer, insert a PTFE-coated magnetic stir bar, and heat the acidified barium solution to 80–85 °C under gentle continuous stirring (300 rpm). Fill a clean 50.00 mL Class A burette with standardized 0.1000 M Na₂SO₄ solution. Slowly dispense the designated aliquot (4.00, 8.00, 12.00, 16.00, 20.00, or 24.00 mL) dropwise into the vortex of the heated barium solution over a period of 4 to 5 minutes. The dropwise addition at elevated temperature minimizes local supersaturation (von Weimarn ratio (Q - S)/S), suppressing explosive spontaneous nucleation and promoting ordered crystal growth.
Following complete sulfate addition, cover the beaker with a ribbed watch glass and maintain the suspension at 85–90 °C just below boiling for a minimum of 45 minutes on the hotplate with gentle stirring. During this digestion phase, Ostwald ripening occurs: small, high-energy, sub-micron BaSO₄ crystallites with high surface curvature and increased solubility dissolve back into solution and recrystallize onto the faces of larger crystals, coarsening the precipitate from a colloidal haze into dense, rapidly settling, easily filterable microcrystalline aggregates.
Clean a Grade 4 sintered glass Gooch crucible (1.0–1.6 µm pore size), dry it in the laboratory convection oven at 110 °C for 60 minutes, cool it inside a sealed desiccator for 25 minutes, and record its tare mass (m_tare) on the four-decimal analytical balance to ±0.0001 g. Repeat heating and cooling cycles until constant mass (agreement within ±0.0002 g) is verified. Seat the tared crucible into the neoprene adapter ring of the vacuum filtration flask and activate the water aspirator vacuum to establish a steady differential pressure of ~20 kPa.
Decant the warm supernatant liquid through the Gooch crucible under vacuum. Quantitatively transfer the digested barium sulfate precipitate into the crucible using a fine stream of boiling deionized water from a wash bottle and a PTFE rubber policeman to dislodge adhering crystals from beaker walls. Wash the precipitate with six successive 10 mL portions of boiling deionized water. Collect drops of filtrate passing through the crucible stem into a test tube and test with 3 drops of 0.1 M AgNO₃ reagent acidified with HNO₃. Continue washing until no white opalescence or AgCl cloudiness is detected, proving complete removal of adsorbed chloride and sodium ions.
Place the crucible containing washed BaSO₄ precipitate into the drying oven at 110 °C for 60 minutes. Transfer immediately to the vacuum desiccator, cool to ambient room temperature for 25 minutes, and record the gross mass on the analytical balance. Repeat the 30-minute drying and desiccation cycle until consecutive readings match within ±0.0002 g. Subtract m_tare to isolate dry precipitate mass m. Perform spot tests on the original filtrate by adding 3 drops of 0.1 M Na₂SO₄ to verify residual excess Ba²⁺ ions. Tabulate mass data across all sulfate aliquots, plot m versus V, and apply ordinary least-squares regression to extract the empirical molar mass of BaSO₄ and verify theoretical percentage yield.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | Added 0.1000 M Na₂SO₄ volume V (mL) (mL) | Isolated dry BaSO₄ precipitate mass m (g) | Volume of 0.1000 M Na₂SO₄ added V (mL) | Mass of dry BaSO₄ precipitate m (g) | Remove |
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