Determine the mass and molar magnetic susceptibility, effective magnetic moment μ_eff, and number of unpaired d-electrons in hexaaquairon(II) ammonium sulfate (Mohr's salt) using a calibrated Gouy magnetic balance. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
Ready to dispense 1.0 T² of liquid.
Adjust B² 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 elementary Gouy formulation assumes an ideal infinite cylinder with B_0 = 0 at the upper boundary; in practice, residual fringe fields (B_0 ≈ 0.015 B) introduce a minor systematic truncation error of ~0.02%.', 'Radial packing inhomogeneities within the 4.00 mm diameter bore produce localized magnetic susceptibility variations that are averaged over the bulk volume.', 'Orbital angular momentum quenching is assumed to be complete in the spin-only approximation; minor spin-orbit coupling (λ ≈ −100 cm⁻¹ for Fe²⁺) introduces a slight temperature-dependent orbital contribution (typically μ_eff ≈ 5.1–5.3 μ_B in single-crystal studies).'] The physical chemistry simulation model evaluates analytically pure Mohr's salt, [Fe(H2O)6](NH4)2(SO4)2·6H2O (M = 392.14 g/mol), at 25.0 °C (298.15 K). Experimental parameters: sample mass m_s = 2.500 g (0.00250 kg), tube inner diameter d = 4.00 mm, powder packing height h = 50.00 mm (0.0500 m), gravitational acceleration g = 9.80665 m/s², magnetic permeability μ_0 = 4π × 10⁻⁷ N/A². Across the six magnetic flux density settings B = [0.40, 0.60, 0.80, 1.00, 1.20, 1.40] T (B² = [0.16, 0.36, 0.64, 1.00, 1.44, 1.96] T²), the measured apparent mass gains are Δm = [102.312, 230.203, 409.249, 639.452, 920.811, 1253.326] mg. Ordinary least-squares regression yields an empirical slope S = 639.4521 mg/T² (6.39452 × 10⁻⁴ kg/T²) and intercept b = −0.0001 mg with Pearson correlation coefficient R² = 0.9999999999998. Applying the Gouy force relation extracts a gram magnetic susceptibility χ_g(SI) = 3.15209 × 10⁻⁷ m³/kg (χ_g(cgs) = 2.50834 × 10⁻⁵ emu/g). Multiplying by molar mass gives raw molar susceptibility χ_M = 0.009836 emu/mol. Applying Pascal's diamagnetic correction for [Fe(H2O)6](NH4)2(SO4)2 (|χ_dia| = 230 × 10⁻⁶ emu/mol) yields the corrected paramagnetic molar susceptibility χ_M,corr = 0.010066 emu/mol. Applying the Curie relation μ_eff = √[8 · T · χ_M,corr] extracts an effective magnetic moment μ_eff = 4.90 μ_B (difference = 0.00007% from the 4.90 μ_B theoretical spin-only benchmark for high-spin d⁶ Fe²⁺), rigorously confirming four unpaired d-electrons.
Precision microbalance (readability ±0.01 mg) suspended above a heavy-duty water-cooled electromagnet with 50 mm flat-tapered pole pieces generating stable homogeneous magnetic fields from 0.0 to 1.5 T.
Digital Hall-effect gaussmeter (resolution ±0.001 T) with an optical micro-positioning stage to map the magnetic flux density B(z) along the vertical coordinate between pole caps.
Calibrated cylindrical Pyrex tube (inner diameter 4.00 ± 0.02 mm, outer diameter 6.00 mm, length 120.0 mm) suspended from the balance beam by a fine non-magnetic phosphor-bronze wire.
Crystalline ammonium iron(II) sulfate hexahydrate, (NH4)2Fe(SO4)2·6H2O (purity ≥ 99.9%, M = 392.14 g/mol), finely pulverized in an agate mortar and packed to h = 50.00 mm (net mass m_s = 2.500 g).
Certified primary magnetic standard Hg[Co(NCS)4] (gram susceptibility χ_g = 16.44 × 10⁻⁶ cm³/g at 20.0 °C) used to calibrate the Gouy tube constant and verify field gradient linearity.
Bipolar DC current-regulated power supply (0–20.00 A, stability ±0.01%) with reverse-polarity switching and digital current/voltage telemetry to suppress residual ferromagnetic pole hysteresis.
Determine the mass and molar magnetic susceptibility, effective magnetic moment μ_eff, and number of unpaired d-electrons in hexaaquairon(II) ammonium sulfate (Mohr's salt) using a calibrated Gouy magnetic balance. Suggested independent volumetric settings: 0.16, 0.36, 0.64, 1.0, 1.44, 1.96 T².
Finely pulverize high-purity Mohr's salt crystals in an agate mortar to produce a uniform microcrystalline powder (< 100 mesh). Carefully transfer the powder into the clean, dry Gouy tube in small increments of ~5 mm, tapping the tube firmly on a rubber mat after each addition to eliminate air voids and establish uniform packing density up to a height of h = 50.00 ± 0.05 mm. Record net sample mass m_s = 2.500 g.
Suspend the empty Pyrex Gouy tube between the electromagnet pole faces using the phosphor-bronze wire. With the magnet power switched off (B = 0 T), tare the microbalance to 0.0000 g. Energize the electromagnet across field settings (0.40 to 1.40 T) and record the small diamagnetic mass change of the empty tube (Δm_tube) to serve as a baseline blank correction.
Position the calibrated transverse Hall probe at the central horizontal axis between the pole caps where the lower tip of the Gouy tube will hang. Increment the regulated DC current from 2.0 A to 15.0 A to establish target magnetic flux densities B = 0.40, 0.60, 0.80, 1.00, 1.20, and 1.40 T (B² = 0.16, 0.36, 0.64, 1.00, 1.44, and 1.96 T²). Confirm field stability and linearity.
Suspend the packed Mohr's salt tube from the balance arm so that its lower flat base coincides with the central horizontal plane of the pole caps (maximum field B) while its upper powder meniscus resides in the near-zero fringe field (B₀ ≈ 0). Ensure the tube hangs freely without touching the pole faces or draft shield walls. Record the unperturbed initial mass m₀ at B = 0 T.
Apply magnetic fields B = 0.40, 0.60, 0.80, 1.00, 1.20, and 1.40 T sequentially. At each field setting, allow the balance to mechanically damp and equilibrate for 60 seconds, recording the apparent mass m_field. Calculate the net downward paramagnetic mass change Δm = (m_field − m₀) − Δm_tube in milligrams.
Plot Δm (mg) against B² (T²). Execute ordinary least-squares linear regression to determine the empirical slope S = (m_s · χ_g) / (2 μ₀ g h). Convert the mass susceptibility χ_g to molar susceptibility χ_M, apply Pascal's diamagnetic corrections (χ_dia = −230 × 10⁻⁶ cm³/mol) to isolate paramagnetic molar susceptibility χ_M,corr, and compute the effective magnetic moment μ_eff = 2.828 √(χ_M,corr · T), establishing the number of unpaired d-electrons via the spin-only formula.
Points are your recorded gravimetric observations. The regression line validates the linear mass-volume proportionality and extracts density.
| # | Squared Magnetic Flux Density B² (T²) | Apparent Mass Change Δm (mg) | Squared Magnetic Field B² (T²) | Apparent Mass Change Δm (mg) | Remove |
|---|
No readings yet. Dispense and weigh a volumetric aliquot to record it.