The occurrence of chemical reactions in supersonic expansions of a gas into a vacuum and its relation to mass spectrometric sampling

Chemical reactions in gas phase systems such as flames are often studied by pumping a small sample of the gas through an orifice, after which the sample expands down a conical duct into one or more vacuum chambers, where finally it is analysed mass spectrometrically. One purpose of the expansion is to reduce suddenly the temperature and pressure of the gas to prevent chemical change in it. The extent to which chemical reactions in fact proceed during such an expansion is computed here using, as an example, the hydration of H3O+ (the most commonly occurring ion in flames) in H3O + + H2O + M ⇌H5O2+ + M. (I) Here M represents any molecule acting as a chaperon. For this purpose it is necessary to calculate the temperature, pressure and density of the gas in a conical expansion duct. This has been done in two ways, namely, with a simple one-dimensional model and also with a more realistic two-dimensional treatment employing the method of characteristics. This information on the flow field has been used together with thermodynamic and kinetic data on reaction (I) to compute the extent to which H3O+ hydrates everywhere in the expansion and also the final levels of hydration attained when (I) finally freezes. Considerable hydration is predicted with final compositions corresponding to conditions roughly three or four orifice diameters inside the duct. Differences between the results of the one- and two-dimensional models are obtained, but it is established that both approaches give the same final extent of hydration, when averaged over all mass, for conical nozzles with total angles as large as 90°. The one-dimensional model, having been shown to be adequate, is used to determine the effect of the following parameters on the extent of reaction in the nozzle: initial temperature and composition, throat diameter, angle of the nozzle, mean molecular weight and ratio of the principal specific heats of the gas, and velocity constants for reaction (I). The results are compared with experimental determinations of [H5O2+]/[H3O+] in a hydrogen flame at 2000 K. Such a comparison indicates first that the majority of the H5O2+ ion observed in practice is produced during the sampling process, rather than in a flame, and secondly that the velocity constant for the three-body hydration process in (I) is 7 x 10-28 molecule-2 ml2 s-1 at 300 K. Criteria are given for ascertaining whether any particular chemical reaction is likely to proceed in these expansions and thereby falsify measurements of chemical composition. The implications of this work for sampling gas phase systems in general are illustrated by computations on the hydration of alkali metal ions.