= HCl and DCl vibrational isotope experiment
{c}
An actual <infrared spectroscopy> route is to compare gaseous <hydrogen chloride> containing ordinary <hydrogen> with its <deuterium> counterpart. A documented teaching experiment uses a stopcock-equipped gas cell with potassium bromide windows and a Nicolet Avatar instrument for <Fourier transform spectroscopy>. A nitrogen-purged flask and drying tube supply the mixture; the sample also contains sulfur dioxide. An empty sample-chamber background precedes the filled-cell scan. The <absorbance> trace and peak-picked <spectroscopic wavenumbers> are the readout. The analysis assigns and indexes $^{1}\mathrm H^{35}\mathrm{Cl}$ and $^{2}\mathrm H^{35}\mathrm{Cl}$ transitions separately and propagates transition uncertainties. The instructions distinguish resolvable <chlorine> <isotope> peaks from adequate precision for the intended parameter analysis. <Vibrational-Rotational Spectroscopy of HCl by James M. McCormick>[McCormick, Introduction; Experimental, Laboratory Component, Figures 1–2 and background/peak-picking paragraphs; Analysis and Discussion, first three paragraphs]{ref}
A separate published teaching dataset reports a Nicolet Nexus 670 instrument, a $10\,\mathrm{cm}$ gas cell at $20\,\mathrm{Torr}$, and <chlorine> <isotope> peaks resolved to baseline. These apparatus details describe that dataset, not the preceding experiment. <HCl and DCl IR absorption spectra by Jonathan Gutow>[Gutow, HCl and DCl IR absorption spectra, dataset description: instrument, path length, pressure and resolved chlorine isotope peaks]{ref}
The inference connects several models. Fit correctly assigned transitions to separate <molecular rotation> from <molecular vibration>, then compare the inferred vibrational scales using <isotope scaling of diatomic vibration>. Agreement supports the approximate separation between a nearly unchanged <chemical bond> stiffness and a changed nuclear <mass>. It does not make a real <molecule> an exact classical <spring>: <anharmonicity> shifts the fundamental transition away from the local <harmonic oscillator> scale, and coupling to <molecular rotation> shifts individual lines.
For an independent test, calculate the <reduced masses> from the specified <isotopes> and compare the inferred values $k=\mu(2\pi c\widetilde\nu_{\rm harm})^2$. Agreement within uncertainty tests the common-curvature assumption; choosing separate $k$ values just to fit each <frequency> would not test it. The documented background addresses instrument and ambient contributions, but does not by itself subtract window absorption, identify contaminating species, or calibrate the <spectroscopic wavenumber> scale. Those require separate controls. Finite spectral resolution, blended peaks, incorrect <isotope> assignments, and departure from the <harmonic approximation near a potential minimum> limit the comparison. No numerical measured line positions are assumed here.
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