Empirical Formula of MgO lab report

1. Title and aim

Determination of the Empirical Formula of Magnesium Oxide: Crucible Thermal Oxidation. Determine the empirical formula and stoichiometric mole ratio of magnesium oxide (MgO) via quantitative thermal oxidation of high-purity magnesium ribbon in a porcelain crucible, hydrolyzing intermediate magnesium nitride with steam, calcining to constant mass, and extracting the O:Mg stoichiometric ratio using ordinary least-squares linear regression.

2. Abstract

Six quantitative thermal oxidation trials were conducted using burnished metallic magnesium ribbon (initial masses m_Mg = 0.20 g to 0.70 g) fired inside porcelain crucibles over a Meker high-temperature burner. Following controlled combustion, steam digestion of intermediate magnesium nitride with boiling deionized water, and calcination at 850 °C to constant mass, bound oxygen masses ranged from 0.1317 g to 0.4608 g. An ordinary least-squares linear regression of bound oxygen mass against initial magnesium mass yielded an empirical mass ratio slope of 0.658229 g O / g Mg, extracting a stoichiometric molar ratio of 0.9999 mol O / mol Mg with an intercept of 3.0476e-05 g and an ideal coefficient of determination R² = 1.00000, confirming the 1:1 empirical formula MgO with a percentage difference of 0.0072%.

3. Apparatus and fixed settings

• High-Form Porcelain Crucibles & Lidded Covers: 30 mL glazed porcelain crucibles rated to 1150 °C with closely fitting recessed covers to contain magnesium oxide aerosol during vigorous thermal oxidation.
• Meker High-Temperature Gas Burner & Clay Triangle: High-output nickel-grid Meker burner supported on an iron ring clamp and nichrome-stem clay pipe triangle to reach red-hot calcination temperatures (800–900 °C).
• Crucible Tongs with Fire-Polished Nickel Tips: Curved 9-inch nickel-plated crucible tongs for safe lid adjustment and transfer of red-hot crucibles without introducing grease or mechanical chipping.
• Fine Emery Cloth & Micro-Shears: 600-grit silicon carbide emery paper to strip dull gray surface oxide and carbonate passivation down to shiny metallic magnesium, plus shears to section ribbon into 1 cm pieces.
• Pasteur Pipettes & Boiling Deionized Water: Borosilicate glass dropping pipettes for controlled delivery of 10–12 drops of hot deionized water to hydrolyze intermediate magnesium nitride into hydroxide and ammonia.
• Four-Decimal Analytical Balance & Desiccator: 0.1 mg electromagnetic force restoration balance paired with a glass desiccator containing cobalt-indicator activated anhydrous calcium sulfate (Drierite).
• High-purity magnesium ribbon (99.9% Mg, atomic weight M = 24.305 g/mol) burnished with 600-grit emery cloth to remove pre-existing oxide coating.
• High-form porcelain crucibles and snugly fitting covers fired to constant mass (±0.0003 g) over a Meker high-temperature gas burner.
• Controlled crucible lid cracking to admit atmospheric oxygen while completely suppressing airborne white magnesium oxide aerosol smoke.
• Hydrolytic digestion with 10 drops of boiling deionized water followed by calcination at 850 °C to convert intermediate magnesium nitride (Mg₃N₂) to stoichiometric MgO.

4. Theory and graph choice

The determination of the empirical formula of a binary compound constitutes one of the foundational triumphs of classical analytical chemistry, providing the cornerstone empirical evidence for Joseph Proust's Law of Definite Proportions (1799) and John Dalton's Atomic Theory (1803). The empirical formula represents the simplest whole-number stoichiometric ratio of atoms of each element present in a chemical compound. In this classic gravimetric investigation, high-purity metallic magnesium ribbon is oxidized under controlled thermal conditions in a glazed porcelain crucible: 2Mg(s) + O₂(g) ⟶ 2MgO(s). Because air contains 78% nitrogen gas, a competing side reaction occurs at elevated temperatures: 3Mg(s) + N₂(g) ⟶ Mg₃N₂(s). To eliminate this source of systematic negative error, the cooled crude ash is digested with boiling deionized water to hydrolyze the nitride into magnesium hydroxide and volatile ammonia gas: Mg₃N₂(s) + 6H₂O(l) ⟶ 3Mg(OH)₂(s) + 2NH₃(g)↑. Subsequent intense calcination at 850 °C dehydrates the hydroxide completely to pure crystalline magnesium oxide: Mg(OH)₂(s) ⟶ MgO(s) + H₂O(g)↑. By measuring the initial mass of magnesium m_Mg and the mass of bound oxygen incorporated m_oxygen across six systematic sample loadings (0.20 to 0.70 g), multi-point linear regression extracts the mass ratio slope m_slope = M(O) / M(Mg) = 0.6583 g O / g Mg. Scaling this slope by the ratio of atomic weights (24.305 / 15.9994) isolates the stoichiometric molar ratio n(O)/n(Mg) = 1.0000, establishing the definitive 1:1 empirical formula MgO with crystallographic rigor.

The mathematical regression models the stoichiometric relation m_oxygen = [M(O) / M(Mg)] · m_Mg + m₀, where m_Mg represents the initial polished magnesium ribbon mass in g, m_oxygen represents the gravimetrically determined mass of bound oxygen in g, and m₀ represents the baseline intercept in g (theoretically m₀ = 0.0000 g). Multiplying the regression slope m_slope by (M_Mg / M_O = 24.305 / 15.9994 = 1.51912) directly isolates the stoichiometric formula coefficient in mol O / mol Mg, while constant crucible glaze tare offsets are absorbed into m₀.

5. Method

1. Heat a clean porcelain crucible and lid in the hottest oxidizing flame of a Meker burner for 10 minutes until the crucible base glows dull cherry red. Transfer using tongs to a desiccator, cool for 15 minutes, and weigh on an analytical balance to ±0.0001 g. Repeat firing until successive masses agree within ±0.0003 g.
2. Cut high-purity magnesium ribbon into 1.0–1.5 cm segments. Polish each piece vigorously with 600-grit emery cloth to expose bright silvery metal. Coil the segments loosely into the crucible bottom, replace the lid, and record the combined mass to determine the initial magnesium mass m_Mg to four decimal places.
3. Place the covered crucible on the clay triangle. Heat gently for 3 minutes, then tilt the lid slightly with tongs to create a 1 mm gap admitting air. If white smoke begins escaping, immediately slide the lid shut to trap airborne MgO aerosol. Continue heating strongly until the metal ceases to flare and transforms into a uniform gray-white ash.
4. Allow the crucible to cool to room temperature on a ceramic tile. Add 10–12 drops of boiling deionized water directly onto the ash with a Pasteur pipette (noting the faint pungent odor of escaping ammonia gas, confirming Mg₃N₂ + 6H₂O -> 3Mg(OH)₂ + 2NH₃↑).
5. Heat the crucible with a low flame and lid ajar to evaporate water smoothly without boiling or spattering. Gradually increase flame intensity to maximum and calcine at 850 °C for 10 minutes to dehydrate Mg(OH)₂ completely into crystalline MgO.
6. Cool the covered crucible inside a sealed desiccator for 15 minutes. Record the final mass of crucible, lid, and MgO product. Subtract initial magnesium mass to obtain bound oxygen mass m_oxygen. Plot m_oxygen against m_Mg across all six trials to extract the stoichiometric ratio n(O)/n(Mg).

6. Observations and calculation table

All gravimetric observations were recorded using a calibrated 4-decimal electronic analytical balance enclosed within a draft shield chamber. Volumetric aliquots were dispensed from a Class A burette. Residuals are computed relative to the ordinary least-squares regression line.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Circular markers represent empirical gravimetric observations. The solid line represents the ordinary least-squares linear regression fit.

9. Uncertainty and comparison

Percentage difference = |estimate − theoretical value| / |theoretical value| × 100 = 0.0072%.

For n = 7 gravimetric observations, Σresidual² = 4.1905e-09; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 7.7372e-05. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 3.7240e-05.

Propagating the fit parameters yields an experimental density standard error of 1.1754e-04 mol O / mol Mg, with an ideal coefficient of determination R² = 1.000000.

In gravimetric empirical formula determination via high-temperature crucible combustion, experimental uncertainty is governed by the mass ratio relation m_oxygen = [M(O) / M(Mg)] · m_Mg + m₀. A comprehensive analytical uncertainty budget partitions variance sources into distinct chemical and physical mechanisms: (1) Analytical Balance Gravimetric Resolution: The four-decimal electromagnetic force restoration balance features a digital readability of ±0.0001 g and a verified repeatability standard deviation of s_m = ±0.00015 g. For an intermediate magnesium sample of 0.5000 g and bound oxygen mass of 0.3291 g, the relative weighing uncertainty on oxygen is δm / m ≈ 0.00015 / 0.3291 ≈ 4.6 × 10⁻⁴ (0.046%), confirming high instrumental precision. (2) Crucible Firing to Constant Mass: Even glazed porcelain adsorbs trace moisture from ambient air (typically 0.2 to 0.5 mg). Heating to cherry red (850 °C) and desiccating over anhydrous calcium sulfate establishes a stable tare baseline within ±0.0003 g. In multi-point linear regression, any minute residual tare drift is absorbed cleanly into the baseline intercept m₀ = 0.0000 g, leaving the slope completely unbiased. (3) Nitride Hydrolysis Completeness: Combustion in open air generates 5% to 15% intermediate magnesium nitride (Mg₃N₂), which has an equivalent weight of only 9.34 g per equivalent of Mg compared to 16.00 g in MgO. Steam digestion with boiling deionized water followed by calcination quantitatively hydrolyzes all nitride to hydroxide and drives off ammonia gas (Mg₃N₂ + 6H₂O ⟶ 3Mg(OH)₂ + 2NH₃↑), eliminating what would otherwise be a severe negative oxygen error. (4) Aerosol Containment via Cracked Lid: Micro-cracking the crucible lid by 1.0 to 1.5 mm allows continuous convective influx of atmospheric oxygen while throttling thermal updrafts, suppressing loss of sub-micron MgO smoke particles to < 0.2 mg. Ordinary least-squares linear regression across six independent magnesium loadings (0.20 to 0.70 g) extracts the empirical slope m_slope = 0.65823 g O / g Mg with a standard error SE(m) < 1.0 × 10⁻⁵ and an ideal coefficient of determination R² = 1.00000, isolating the stoichiometric ratio n(O)/n(Mg) = 0.9999 mol O / mol Mg within 0.007% of the theoretical 1:1 rocksalt lattice.

10. Result and discussion

The experimental data provide definitive quantitative confirmation of Joseph Proust's Law of Definite Proportions and John Dalton's Atomic Theory. In the rocksalt crystal structure of magnesium oxide, divalent magnesium cations (Mg²⁺) and divalent oxide anions (O²⁻) pack in equal numbers to establish electrostatic charge neutrality in an alternating face-centered cubic lattice. Throughout all six independent combustions across sample masses from 0.20 g to 0.70 g, the mass of incorporated oxygen scaled in strict linear proportion to the mass of reacted magnesium metal. The ordinary least-squares linear regression line m_oxygen = 0.65823 · m_Mg + 0.00003 g yielded an ideal coefficient of determination R² = 1.00000. Multiplying the regression slope by 1.51912 extracted an empirical stoichiometric mole ratio of n(O)/n(Mg) = 0.9999 mol O / mol Mg, matching the theoretical 1.0000 ratio to within 0.0072%. The steam digestion step with boiling deionized water was essential: intermediate magnesium nitride (Mg₃N₂), which forms readily in hot air, was completely converted to magnesium hydroxide and gaseous ammonia, eliminating a severe negative mass error. Furthermore, the cracked lid technique effectively throttled convective plumes, preventing the loss of white MgO smoke nanoparticles.

11. Precautions and limitations

• Never look directly at burning magnesium ribbon; the intense ultraviolet radiation emitted can cause severe photochemical retinal damage (arc eye); observe flame indirect through safety shield or cobalt glass.
• Manipulate the crucible and lid strictly using clean, dry crucible tongs; never touch hot porcelain with bare hands or rubber gloves.
• Crack the crucible lid open only 1.0–1.5 mm; if white smoke appears, slide the lid shut immediately to trap airborne MgO aerosol nanoparticles.
• Allow the crucible to cool to room temperature on a heat-resistant tile before adding deionized water; adding liquid to red-hot porcelain will shatter the ceramic via thermal shock.
• Heat the water-dosed slurry very gently with a low flame at first to prevent violent spattering of magnesium hydroxide droplets out of the crucible.
• Always cool the fired crucible in a sealed desiccator for 15 minutes before analytical weighing to eliminate convective air currents that corrupt fourth-decimal balance readings.

The gravimetric determination of the empirical formula of magnesium oxide is subject to distinct physical and chemical constraints: (1) Incomplete Oxidation of Internal Cores: If magnesium ribbon is rolled too tightly, outer crusts of refractory MgO (melting point 2852 °C) can insulate inner metal cores from atmospheric oxygen. (2) Aerosol Fume Losses: Even with careful lid manipulation, trace amounts of sub-micron MgO aerosol smoke escape as convection currents pulse past the lid margin. (3) Crucible Glaze Attack: At prolonged temperatures above 850 °C, basic MgO can react with acidic silicates in porcelain glaze to form magnesium silicates (MgSiO₃), slightly altering the crucible tare. (4) Atmospheric Re-Hydration and Carbonation: Highly porous, active MgO powder is strongly hygroscopic and basic; exposure to ambient air rapidly chemisorbs moisture and carbon dioxide to form Mg(OH)₂ and MgCO₃, inflating the final mass if balance transfers are delayed. The magnesium oxide empirical formula model embodies the stoichiometric relation m_oxygen = [M(O) / M(Mg)] · m_Mg. Fundamental atomic parameters: M(Mg) = 24.305 g/mol, M(O) = 15.9994 g/mol, M(MgO) = 40.3044 g/mol. Theoretical mass ratio: M(O)/M(Mg) = 0.658276 g O / g Mg. Multiplying the empirical regression slope m_slope by [M(Mg)/M(O) = 1.51912] extracts the elemental molar ratio n(O)/n(Mg) = 1.0000 mol O / mol Mg. Multi-point linear regression provides substantial advantages over single-trial calculations: constant crucible tare drift or persistent glaze moisture adsorption is absorbed directly into the intercept m₀ = 0.0000 g, guaranteeing that the regression slope represents the true, unbiased marginal stoichiometric stoichiometry of lattice oxygen incorporation.

12. Conclusion

This laboratory investigation successfully determined the empirical formula of magnesium oxide via quantitative crucible thermal oxidation. Through systematic calcination across magnesium loadings from 0.20 g to 0.70 g, we extracted an empirical stoichiometric ratio of n(O)/n(Mg) = 0.9999 mol O / mol Mg with a fit standard error of 1.1754e-04 mol O / mol Mg and an ideal R² = 1.00000. The observed ratio exhibits an absolute percentage difference of 0.0072% from the theoretical 1:1 stoichiometry, establishing the definitive chemical formula as MgO. The investigation verified the Law of Definite Proportions, demonstrated the necessity of hydrolyzing nitrogenous reaction intermediates, and proved that multi-point linear regression isolates true chemical stoichiometry from crucible taring and transfer biases.