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The infrared spectrum of HCl gas: a bond length

Record the fundamental band of HCl gas on an FTIR, number every line of the P and R branches, obtain the rotational constants of both vibrational levels from combination differences, and finish with the H–Cl bond length — a classic of the physical chemistry laboratory.

Difficulty ●●● ≈ 40 min

Aim Resolve the rotational structure of the HCl fundamental, determine B₀, B₁, αₑ and the equilibrium bond length rₑ, and compare H³⁵Cl with H³⁷Cl.
FTIR · lines computed from molecular constants

Gas-phase infrared: a rotation–vibration band

Resolution
ν̃₀, no line R(2) R branch (ΔJ = +1) P branch (ΔJ = −1)260027002800290030003100Wavenumber / cm⁻¹Absorbance (relative)
Levels of v = 0 and v = 1 (rotational spacing magnified); the arrow is the selected transition, and the bars show how many molecules sit in each J.
R(2)

R(2) · H³⁵Cl · J = 2 → 3 · 2944.91 cm⁻¹

18.4 % of the molecules are in the lower level J = 2; relative intensity 1.00. At 296 K the most populated level is J = 3.

B₀ = 10.440 cm⁻¹, B₁ = 10.136 cm⁻¹, ν̃₀ = 2885.98 cm⁻¹.

The H³⁷Cl line beside it is 2.19 cm⁻¹ away: resolved at 0.5 cm⁻¹.

Line positions are computed from the Huber–Herzberg molecular constants (NIST Chemistry WebBook), with G(v), B_v and D_v taken to higher order; other isotopologues follow from the Dunham isotope relations (ρ = √(μ/μ′)). The same constants predict the radioactive H³⁶Cl lines measured in 2021 to within 0.02 cm⁻¹. Intensity ∝ isotopic fraction × ν̃ × Hönl–London factor (J+1 in R, J in P) × Boltzmann factor, without the Herman–Wallis correction; each line is broadened to the instrument resolution as a Gaussian. DCl is taken as fully deuterated.

Procedure

  1. In a fume hood, add concentrated sulfuric acid dropwise to dry NaCl; dry the HCl gas by bubbling it through concentrated sulfuric acid and admit it to an evacuated 10 cm gas cell at about 5–10 kPa.
  2. Record a background with the empty cell, then the sample from 2600 to 3100 cm⁻¹ at 0.5 cm⁻¹ resolution.
  3. Number the lines: the gap in the middle marks the band origin ν̃₀; count R(0), R(1)… towards higher wavenumber and P(1), P(2)… towards lower. The stronger line of each doublet belongs to H³⁵Cl.
  4. Tabulate R(J−1) − P(J+1) and R(J) − P(J), plot them against J + ½ and fit straight lines; then divide the differences by (J + ½), plot against (J + ½)² + ¾, and obtain B₀, B₁ and the centrifugal distortion constant D.
  5. Calculate αₑ = B₀ − B₁, Bₑ = B₀ + αₑ/2 and rₑ; repeat with the weaker H³⁷Cl lines and compare the two values of rₑ.

What to notice

  • At room temperature each branch shows about ten lines that rise and then fall in strength; there is no line at the band origin, 2886 cm⁻¹, and R(0) and P(1) are about 41 cm⁻¹ apart.
  • Every line is a doublet about 2 cm⁻¹ apart with heights close to 3 : 1, the abundance ratio of ³⁵Cl to ³⁷Cl; at 4 cm⁻¹ resolution each doublet merges into one peak.
  • The R branch crowds together further out and the P branch spreads apart: the rotational constant is smaller in v = 1.
  • The combination differences give B₀ ≈ 10.44 cm⁻¹, B₁ ≈ 10.14 cm⁻¹ and rₑ ≈ 1.275 Å; H³⁷Cl has slightly smaller B values and the same rₑ.

In a real lab

  • HCl gas is toxic and corrosive, and concentrated sulfuric acid causes severe burns: generate and handle the gas in a fume hood, with goggles and acid-resistant gloves.
  • NaCl and KBr windows dissolve in water: keep the cell dry, flush it after use and store it in a desiccator.
  • Water vapour and CO₂ in the beam path have rotation–vibration lines of their own; a background spectrum and a purge with dry air or nitrogen remove them.
  • Lines broaden as the pressure rises (pressure broadening); to separate isotope doublets 2 cm⁻¹ apart you need enough resolution and not too much gas.

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