High-Resolution Research FTIR Spectrometer
Equipped with a globar mid-IR ceramic source, Ge-coated KBr beam splitter, and liquid-nitrogen-cooled MCT (mercury cadmium telluride) detector delivering 0.25 cm⁻¹ optical resolution.
Chemistry / FTIR Spectroscopy & Diatomic Force Constants
FREE TO EXPLORELABORATORY 44 · NATURAL SCIENCES
Infrared Vibrational-Rotational Spectroscopy and Molecular Force Constants of Diatomic Halides
Determine the fundamental vibrational frequency (ν̃₀ = 2885.90 cm⁻¹), vibration-rotation coupling constant (α_e = 0.3072 cm⁻¹), and harmonic bond force constant (k = 481.0 N/m) of gas-phase hydrogen chloride (H³⁵Cl) using high-resolution FTIR spectroscopy. Explore interactive analytical gravimetry, Class A volumetric glassware and density determination.
MEASURE · CALIBRATE · ANALYSE
Your virtual chemistry laboratory.
MEAN BRANCH TRANSITION WAVENUMBER Ν̃_MEAN—
MEASUREMENT STATUS
Ready to dispense 3.0 of liquid.
Adjust m 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 harmonic oscillator force constant k is extracted from the fundamental band origin ν̃₀, which includes minor anharmonic correction terms (ν̃₀ = ω_e − 2ω_e x_e).', 'At sample pressures exceeding 50 Torr, self-broadening obscures the narrow rotational lines, precluding baseline deconvolution of the ³⁵Cl and ³⁷Cl isotopologue peaks.', 'Centrifugal distortion constants (D_e ≈ 5.3 × 10⁻⁴ cm⁻¹) introduce minor high-J deviations (J > 8) that are neglected in the truncated quadratic model.'] The physical chemistry simulation model evaluates gas-phase H³⁵Cl at 25.0 °C (sample pressure 25.0 Torr, 100.0 mm path length). System parameters: reduced mass μ(H³⁵Cl) = 1.626652 × 10⁻²⁷ kg; fundamental band origin ν̃₀ = 2885.90 cm⁻¹; equilibrium rotational constant B_e = 10.5934 cm⁻¹; vibration-rotation coupling constant α_e = 0.3072 cm⁻¹; ground state rotational constant B₀ = 10.4398 cm⁻¹; excited state rotational constant B₁ = 10.1326 cm⁻¹. Across the six rotational pairs m = [1, 2, 3, 4, 5, 6], measured mean transition wavenumbers are ν̃_mean = [2885.593, 2884.671, 2883.135, 2880.985, 2878.220, 2874.841] cm⁻¹. Plotting ν̃_mean against m² = [1, 4, 9, 16, 25, 36] yields a linear slope of −α_e = −0.30719 cm⁻¹ (α_e = 0.3072 cm⁻¹) and Y-intercept ν̃₀ = 2885.900 cm⁻¹ with R² = 1.0000000. Applying the harmonic relation k = 4π²c²ν̃₀²μ extracts an empirical force constant k = 480.68 N/m (difference = 0.0660% from the 481.0 N/m literature benchmark), confirming quantum mechanical harmonic and anharmonic oscillator models.
Analytical chemistry apparatus & tools.
10 cm Gas Absorption Cell with Polished NaCl Optical Windows
Stainless steel or Pyrex cylindrical gas cell (100.0 ± 0.1 mm internal path length) fitted with water-insoluble, cleaved single-crystal sodium chloride (NaCl) windows transparent from 4000 to 650 cm⁻¹.
High-Vacuum Gas Handling & Manifold System
Pyrex vacuum manifold evacuated by a turbomolecular pump to < 10⁻⁴ Torr, equipped with capacitive capacitance manometer and chemical traps for synthesis and cryogenic transfer of anhydrous HCl gas.
Chemical Generation & Sublimation Train for Anhydrous HCl
Generates pure, anhydrous hydrogen chloride gas by controlled dropwise addition of concentrated sulfuric acid (18 M H₂SO₄) to analytical grade ammonium chloride or sodium chloride, followed by cryogenic trap distillation.
Desiccant Purge Gas Generator (Dry N₂ / CO₂-Free Air)
Continuously purges the FTIR interferometer and sample compartment at 25 L/min with dry, CO₂-free air (dew point < −70 °C) to eliminate atmospheric H₂O and CO₂ ro-vibrational absorption bands.
Precision Digital Capacitance Manometer Gauge
Measures gas cell fill pressure with 0.1 Torr readability; standard measurements are recorded at 25.0 ± 0.5 Torr HCl to achieve optimal peak absorbance without pressure-broadening artifacts.
FOLLOW THE METHOD
A reason behind every step.
Determine the fundamental vibrational frequency (ν̃₀ = 2885.90 cm⁻¹), vibration-rotation coupling constant (α_e = 0.3072 cm⁻¹), and harmonic bond force constant (k = 481.0 N/m) of gas-phase hydrogen chloride (H³⁵Cl) using high-resolution FTIR spectroscopy. Suggested independent volumetric settings: 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 .
01
FTIR Instrument Purge and Background Scan Acquisition
Initiate dry nitrogen purge of the FTIR optical bench at 25 L/min for 60 minutes. Fill the MCT detector dewar with liquid nitrogen and allow 20 minutes of thermal stabilization. Record a 64-scan background single-beam spectrum of the evacuated sample compartment across 4000 to 2000 cm⁻¹ at 0.5 cm⁻¹ resolution.
02
Gas Cell Evacuation and Anhydrous HCl Filling
Mount the 100 mm NaCl-window gas cell onto the vacuum manifold. Evacuate to below 0.05 Torr. Admit anhydrous HCl gas through a cryogenic dry ice-acetone trap until the cell pressure reaches 25.0 ± 0.5 Torr. Close the PTFE isolation valves, dismount the cell, and position it securely in the spectrometer sample compartment.
03
High-Resolution FTIR Transmission Scan Recording
Collect 64 co-added interferograms of the filled gas cell at 0.5 cm⁻¹ resolution with Blackman-Harris 3-term apodization and 2× zero filling. Transform the interferogram into an absorbance spectrum spanning 3100 to 2600 cm⁻¹, resolving the fundamental vibration-rotation band of HCl.
04
Isotopic Peak Center Identification and Wavenumber Deconvolution
Identify the characteristic doublet structure of each rotational transition corresponding to H³⁵Cl and H³⁷Cl (3:1 natural abundance ratio). Using second-derivative peak centroid algorithms, determine the exact peak wavenumbers for the six pairs of R-branch lines (R(0) through R(5)) and P-branch lines (P(1) through P(6)) for H³⁵Cl.
05
Computation of Mean Transition Wavenumbers
For each rotational running index m from 1 to 6 (where R(m−1) has index +m and P(m) has index −m), compute the mean transition wavenumber: ν̃_mean(m) = [ν̃_R(m−1) + ν̃_P(m)] / 2. Verify that ν̃_mean decreases quadratically from 2885.593 cm⁻¹ at m = 1 to 2874.841 cm⁻¹ at m = 6.
06
Linear Regression and Harmonic Force Constant Extraction
Plot ν̃_mean(m) on the Y-axis against m² on the X-axis across the six experimental pairs. Perform ordinary least-squares linear regression to extract the slope (−α_e) and Y-intercept (ν̃₀). From the fundamental band origin ν̃₀ = 2885.90 cm⁻¹ and reduced mass μ = 1.62665 × 10⁻²⁷ kg, calculate the harmonic bond force constant: k = 4π²c²ν̃₀²μ.
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
ilde{
u}_{ ext{mean}}(m) = -0.3072 \cdot m^2 + 2885.90 \implies ilde{
u}_0 = 2885.90 ext{ cm}^{-1} \implies k = 481.0 ext{ N/m}
| # | Rotational Transition Quantum Index m () | Mean Branch Transition Wavenumber ν̃_mean (cm⁻¹) | Squared Rotational Index m² | Mean Transition Wavenumber ν̃_mean (cm⁻¹) | Remove |
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