We present a metrological technique to characterize the thermodynamic state (temperature, pressure, and density) of gaseous molecules in a single spectroscopic measurement. We demonstrate the accuracy and precision of our approach by using a low-pressure (number density approximately $1.76\times {10}^{18}\mathrm{molecules}/{\mathrm{cm}}^3$) acetylene gas in a sealed glass cell over a temperature range of $-70{}^{\circ }\mathrm{C}$ up to $+60{}^{\circ }\mathrm{C}$. Under these experimental conditions the sample is in the gaseous state, displaying a behavior very close to that of an ideal gas. This allows us to predict the thermodynamic state with high accuracy, and thus rigorously test the performance of our approach. Our spectroscopic measurement uses a tunable wide-band optical frequency comb to acquire the full ro-vibrationally broadened acetylene spectrum between 1512 and 1538 nm with approximately $80$-kHz spectral resolution. Through nonlinear fitting of this entire spectrum we obtain high accuracy ($<1\mathrm{\%}$) and high-precision (approximately $0.1\mathrm{\%}$) estimates of the temperature, pressure, and density of the gas across the full examined temperature range. This combination of broadband probing and ultra-high-resolution spectrum ensures that we obtain reliable and precise measurements on the thermodynamic state.

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• Analytical chemistry
• Atomic & molecular collisions
• Frequency combs & self-phase locking
• Metrology
• Molecular spectra
• Molecules
• Infrared spectroscopy
• Optical absorption spectroscopy