The equilibrium constant of NO2 with N2O4 and the temperature dependence of the visible spectrum of NO2: A critical review and the implications for measurements of NO2 in the polar stratosphere

Measurements of stratospheric NO₂ by ground-based visible spectrometers rely on laboratory measurements of absorption cross-sections. We review low-temperature laboratory measurements, which disagree by amounts claimed to be significant. Our recalculation of their errors shows that in general disagreements are not significant and that errors in the ratios of cross-sections at low to room temperature are between ±3% and ±8.8%. Of these errors, up to ±3.5% was contributed by errors in the equilibrium constant,K _p, in those measurements where the pressure was above 0.1 mbar.We review measurements and calculations ofK _p, which were accurate to ±5% from 300 to 233 K. Each method was potentially flawed. For example, infrared measurements of the partial pressure of NO₂ ignored the dependence of absorption on total pressure. From thermodynamic theory, formulae forK _pcan be derived from expressions for the variation of heat capacity with temperature. Contrary to common belief, coefficients in the formulae used by spectroscopists were not derived from the thermodynamic quantities. Rather, they were fitted to measurements or to calculations. Hence, they are empirical and it is dangerous to extrapolate below 233 K, the lowest temperature of the measurements.There are no measurements of NO₂ cross-sections below 230 K. Extrapolation of these cross-sections to analysis of measurements of NO₂ at the low temperatures of the Arctic and Antarctic stratosphere is also dangerous. For satisfactory analysis of polar spectra, the NO₂ cross-sections should be measured at temperatures down to 190 K with a relative accuracy of ±1%. This difficult experiment would need a cell of minimum length 32 m whose length can be adjusted. Because their effects are circular, many errors cannot be removed simply. Although circular errors also arise in the measurements ofK _pand of the infrared spectrum, their weights differ from those in the visible spectrum. The optimum experiment might therefore simultaneously measure the visible and infrared spectra andK _p.