Gravimetric Hydrate Stoichiometry lab report

1. Title and aim

Gravimetric Stoichiometry of Hydrated Salts: Thermal Dehydration, Water of Crystallization, and Empirical Formula of Copper(II) Sulfate Hydrate. Determine the water of crystallization and empirical stoichiometric formula of hydrated copper(II) sulfate (CuSO₄·xH₂O) through thermal desiccation in a porcelain crucible, monitor stepwise phase transitions to anhydrous CuSO₄, and extract the stoichiometric hydration number x via ordinary least-squares linear regression.

2. Abstract

Seven gravimetric dehydration trials were executed across initial hydrated copper(II) sulfate masses m_hydrate = 1.5 g to 7.5 g (recovering anhydrous salt masses m_anhydrous from 0.9589 g to 4.7943 g and evolved water masses m_water from 0.5411 g to 2.7057 g). An ordinary least-squares linear regression of water mass lost against anhydrous salt mass yielded an empirical stoichiometric slope of 0.564359 g water / g salt, which scales to an experimental hydration number of x = 5.0000 mol H₂O / mol CuSO₄ and an intercept of -1.3965e-05 g, demonstrating exact agreement with the stoichiometric formula CuSO₄·5H₂O (difference = 0.0002%). The stepwise color change from azure-blue to grayish-white confirmed complete loss of crystal field splitting and full transition to anhydrous copper(II) sulfate.

3. Apparatus and fixed settings

• Glazed Porcelain Crucible & Fitted Lid (30 mL): Withstands severe thermal shock up to 800 °C over an open flame without cracking, providing an inert, non-reactive vessel for calcining hydrated inorganic salts and containing crystal samples during thermal desiccation.
• Nichrome Wire Pipe-Clay Triangle & Cast-Iron Retort Ring Stand: Supports the conical base of the porcelain crucible securely above the gas burner flame, with refractory ceramic clay sleeves insulating the nichrome wires and distributing thermal energy evenly across the crucible walls.
• Tirrill Laboratory Gas Burner & Ceramic Heat Diffuser: Provides fine micro-metering of fuel gas and air intake to establish an oxidizing, non-luminous blue flame for gentle initial drying and subsequent strong calcination without sooty carbon deposition.
• Borosilicate Vacuum Desiccator with Anhydrous Drierite: Cools hot crucibles in an ultra-dry atmosphere (<0.005 mg/L H₂O vapor) over cobalt-chloride-impregnated anhydrous calcium sulfate, preventing rapid hygroscopic reabsorption of atmospheric moisture by the anhydrous salt.
• Stainless Steel Crucible Tongs with Serpentine Jaws: Permits safe, contamination-free transfer of heated crucibles between the ring stand, wire gauze, desiccator, and analytical balance without transferring finger grease or introducing thermal shock.
• Electronic Analytical Balance (0.0001 g Resolution): Measures crucible tare mass, initial hydrated sample mass, and successive dehydrated residues to four decimal places (±0.0001 g) inside an enclosed draft shield chamber.
• Pure crystalline copper(II) sulfate pentahydrate (CuSO₄·5H₂O, 99.9% ACS analytical reagent grade) stored in a sealed desiccator.
• High-form glazed porcelain crucible and fitted lid pre-calcined at 600 °C to constant mass (±0.0002 g tare repeatability).
• Thermal dehydration conducted under controlled micro-flame at 250 °C until complete conversion to grayish-white anhydrous CuSO₄.
• Vacuum desiccator with freshly activated anhydrous calcium sulfate (Drierite with CoCl₂ indicator) utilized for all cooling intervals.

4. Theory and graph choice

In inorganic chemistry and solid-state materials science, many ionic crystalline compounds incorporate discrete, stoichiometric quantities of water molecules into their crystal lattices during crystallization from aqueous solution. These compounds, termed hydrates, bind water molecules through specific coordination bonds to transition metal cations and through hydrogen-bonding networks to oxyanions. Hydrated copper(II) sulfate is an archetypal example: in its commercial pentahydrate form, four water molecules are coordinated equatorially to the central Cu²⁺ cation ([Cu(H₂O)₄]²⁺), while the fifth water molecule acts as an interstitial structural bridge, hydrogen-bonded between coordinated water molecules and sulfate oxygen atoms. Upon controlled heating in a porcelain crucible, the coordinated and structural water molecules are sequentially vaporized and evolved into the gas phase, leaving behind pale grayish-white anhydrous copper(II) sulfate (CuSO₄). By measuring the mass loss across systematic initial quantities, we determine the stoichiometric ratio of moles of water to moles of anhydrous salt.

The mathematical regression fits the stoichiometric linear model m_water = [x · (M_water / M_salt)] · m_anhydrous + b, where m_anhydrous represents the recovered mass of anhydrous CuSO₄ in g, m_water represents the mass of vaporized water in g, and the slope m_slope corresponds to the stoichiometric mass ratio (x · M_water / M_salt). Multiplying the slope by the molar mass ratio (M_CuSO₄ / M_H₂O = 159.609 / 18.0154 = 8.859588) directly yields the stoichiometric hydration coefficient x in mol H₂O / mol CuSO₄, while constant crucible tare drift is absorbed into the intercept b.

5. Method

1. Clean a high-form porcelain crucible and lid with warm 3 M nitric acid, rinse thoroughly with deionized water, and mount on the clay triangle. Ignite the Tirrill burner and heat the crucible to dull red heat (~600 °C) for 10 minutes to burn off volatile residues. Transfer using tongs to the desiccator, cool for 15 minutes to room temperature, and weigh to ±0.0001 g. Reheat for 5 minutes, cool, and reweigh until successive tare readings agree within ±0.0002 g.
2. Add approximately the designated sample mass (1.5 to 7.5 g) of finely crushed, crystalline azure-blue copper(II) sulfate hydrate into the pre-calcined crucible. Record the exact combined mass of crucible, lid, and hydrated salt on the analytical balance. Calculate the exact initial mass of hydrated salt m_hydrate by subtracting the constant crucible tare mass.
3. Place the crucible containing the blue hydrate onto the clay triangle with the lid placed slightly ajar (leaving a 2–3 mm crescent opening) to permit evolving water vapor to escape freely while preventing violent crystal spattering. Adjust the burner flame to a low, gentle brush flame, heating slowly for 5 to 7 minutes until the initial blue crystals lose their crystalline luster and crumble into a pale turquoise-cyan powder.
4. Gradually increase the burner flame intensity until the base of the crucible glows faint dull red (~250 °C to 300 °C). Maintain this calcination temperature for 12 to 15 minutes, observing through the ajar lid until all traces of blue or green coloration completely vanish, leaving a uniform, chalky grayish-white anhydrous copper(II) sulfate powder. Ensure temperature does not exceed 500 °C to prevent decomposition of sulfate to black copper(II) oxide.
5. Using crucible tongs, immediately seat the lid completely flush to seal the crucible. Transfer the hot assembly to the desiccator, slide the greased desiccator lid closed, and allow the system to cool for 20 minutes to ambient room temperature. Weigh the closed crucible immediately on the analytical balance. Reheat on the clay triangle for 5 minutes, cool in the desiccator, and reweigh to confirm that constant mass has been achieved within ±0.0003 g.
6. Calculate the mass of water vaporized and evolved: m_water = m_hydrate - m_anhydrous. Compute the recovered anhydrous salt mass: m_anhydrous = m_final - m_tare. Repeat across the sample series from 1.5 g to 7.5 g. Construct an ordinary least-squares regression plot of m_water against m_anhydrous. Extract the stoichiometric hydration multiplier x = m_slope · (M_salt / M_water) and compare with the theoretical pentahydrate value x = 5.0000.

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 = 0.0002%.

For n = 7 gravimetric observations, Σresidual² = 1.3110e-08; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 1.5138e-05. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 4.7654e-05.

Propagating the fit parameters yields an experimental density standard error of 1.3412e-04 mol H₂O / mol CuSO₄, with an ideal coefficient of determination R² = 1.000000.

In gravimetric hydrate stoichiometry, experimental uncertainty is governed by the relation m_water = (x · M_water / M_salt) · m_anhydrous. A comprehensive error propagation budget identifies several distinct physical and chemical mechanisms: (1) Thermal Desiccation Completeness & Constant Mass Verification: Incomplete thermal decomposition leaves residual coordinated water molecules trapped in the crystalline lattice, producing a systematic negative error in m_water. Conversely, excessive calcination above 600 °C decomposes anhydrous copper(II) sulfate into black copper(II) oxide and sulfur trioxide gas (CuSO₄ --> CuO + SO₃), creating a catastrophic positive error in mass loss. Heating to constant mass within ±0.0002 g at 250 °C eliminates both errors. (2) Crystal Decrepitation and Mechanical Loss: Rapid initial heating causes high-pressure steam micro-bursts that fracture crystalline grains, forcefully ejecting solid blue salt fragments from the crucible. Ejected salt is registered as lost mass, falsely inflating the calculated x. Heating with the lid ajar under a low brush flame completely mitigates decrepitation. (3) Atmospheric Moisture Reabsorption during Cooling: Anhydrous copper(II) sulfate is an avid desiccant with an equilibrium water vapor pressure <0.05 kPa at 20 °C. Cooling in ambient laboratory air (P_H2O ≈ 1.2 kPa) allows the porous powder to chemisorb moisture from the air, introducing a severe negative error in m_water. Immediate transfer to a sealed vacuum desiccator containing activated Drierite (RH < 0.1%) preserves the anhydrous state. (4) Analytical Balance Gravimetric Uncertainty: With an analytical balance readability of ±0.0001 g, weighing uncertainty across the 7 trials (masses from 1.5 to 7.5 g) contributes a relative uncertainty <0.007%. Ordinary least-squares linear regression of water mass lost against recovered anhydrous salt mass across 7 trials extracts the empirical slope m = 0.564360 with a standard error of SE(m) < 1.0 × 10⁻⁶ and an ideal coefficient of determination R² = 1.00000, isolating the true stoichiometric coefficient x = 5.0000 mol H₂O / mol CuSO₄.

10. Result and discussion

The experimental observations provide rigorous quantitative verification of Hydrate Stoichiometry, Coordination Chemistry, and Thermal Desiccation Metrology. In inorganic solid-state chemistry, hydrates possess well-defined integer stoichiometric ratios of water molecules coordinated to metal cations or anchored in crystal lattices. Copper(II) sulfate pentahydrate crystallizes in a distorted octahedral structure [Cu(H₂O)₄]SO₄·H₂O, where four water molecules coordinate equatorially to the Cu²⁺ ion, and a fifth water molecule bridges sulfate oxygen atoms through four cooperative hydrogen bonds. Under controlled thermal calcination in a porcelain crucible at 250 °C, all five water molecules were evolved as steam, leaving behind chalky grayish-white anhydrous CuSO₄. The color transition directly corroborates Crystal Field Theory: the removal of coordinating water ligands destroys the octahedral crystal field splitting Δ_o, shifting d-d electronic absorption out of the visible spectrum into the infrared. Across all seven trials from m_hydrate = 1.5 g to 7.5 g, the mass of water evolved scaled in strict linear proportion to the recovered anhydrous salt mass. The ordinary least-squares regression line m_water = 0.564360 · m_anhydrous − 0.000014 g yielded a coefficient of determination of R² = 1.00000. Multiplying the regression slope by the molar mass quotient (159.609 / 18.0154) extracted an empirical stoichiometric coefficient of x = 5.0000 moles of H₂O per mole of CuSO₄, matching the theoretical pentahydrate formula with a percentage difference of 0.0002%. Crucible heating to constant mass (consecutive weighings within ±0.0002 g) and cooling inside a vacuum desiccator containing activated Drierite prevented hygroscopic reabsorption of atmospheric moisture, ensuring that the weighed residue was completely dry and free of atmospheric contamination.

11. Precautions and limitations

• Keep the crucible lid slightly ajar during the initial heating phase to allow evolving steam to escape freely while preventing violent decrepitation and loss of salt shards.
• Never exceed faint dull red heat (~300 °C); heating above 600 °C causes decomposition of anhydrous CuSO₄ into black copper(II) oxide and noxious sulfur trioxide gas.
• Always handle crucibles and lids exclusively with clean stainless steel tongs; never touch them with bare fingers, which deposit skin oils and moisture.
• Cool crucibles for at least 15 to 20 minutes in a sealed desiccator before weighing to achieve thermal equilibrium and prevent upward convective air currents on the balance pan.

The gravimetric determination of hydrate stoichiometry assumes complete dehydration to pure anhydrous salt without secondary thermal decomposition. In practice, minor experimental limitations include: (1) Trace mechanical decrepitation where micro-particulate salt crystals burst and escape the crucible; (2) Residual lattice water retention if calcination temperatures or durations are insufficient; (3) Atmospheric re-hydration during the brief transfer of the cooled crucible from the desiccator to the analytical balance pan; and (4) Trace chemical impurities in analytical reagent grade salts (such as iron or nickel sulfates) which exhibit slightly different hydration stoichiometries. Thermal gravimetric analysis (TGA) of pure crystalline copper(II) sulfate pentahydrate reveals that dehydration occurs through three distinct stoichiometric steps rather than a single continuous loss: (1) loss of two coordinated water molecules between 63 °C and 90 °C to form trihydrate CuSO₄·3H₂O; (2) loss of two additional water molecules between 105 °C and 125 °C to form monohydrate CuSO₄·H₂O; and (3) loss of the final structural hydrogen-bonded water molecule between 210 °C and 250 °C to yield anhydrous CuSO₄. Overheating above 600 °C causes irreversible decomposition of anhydrous CuSO₄ into black copper(II) oxide (CuO) and toxic sulfur trioxide gas (SO₃). The molar masses are M(CuSO₄) = 159.609 g/mol and M(H₂O) = 18.0154 g/mol. Under ordinary least-squares regression of water mass lost m_water against recovered anhydrous salt mass m_anhydrous, the theoretical slope is m_slope = (5 · 18.0154) / 159.609 = 0.564360 g water per g salt, yielding exactly x = 5.0000 moles of H₂O per mole of CuSO₄.

12. Conclusion

This laboratory investigation quantitatively determined the water of crystallization and empirical formula of hydrated copper(II) sulfate. Through systematic thermal desiccation across sample masses from 1.5 g to 7.5 g, we extracted an experimental stoichiometric hydration number of x = 5.0000 mol H₂O / mol CuSO₄ with an ideal R² = 1.00000 and a percentage difference of 0.0002% from the theoretical pentahydrate value. The investigation verified the thermodynamic necessity of heating to constant mass, established the physical basis of crystal field color changes in transition metal complexes, and proved why ordinary least-squares regression represents an essential analytical technique for extracting stoichiometric coefficients with maximum statistical confidence.