A Method for the Determination of Rate Coefficients\nfor the Formation of Protonated Monomers and Proton Bound Dimers of\nVolatile Organic Compounds in Air at Ambient Pressure by Ion Mobility\nSpectrometry

Rate coefficients\n(<i>k</i>) for the reactions of hydrated\nprotons and a sample vapor (M) to form protonated monomers (MH<sup>+</sup>(H<sub>2</sub>O)<sub><i>n</i></sub>) and proton\nbound dimers (M<sub>2</sub>H<sup>+</sup>) were determined simultaneously\nby using ion mobility spectrometry with a tandem drift tube at ambient\npressure. In this method, sample vapors were introduced to a first\ndrift region with stepwise reactions: M + H<sup>+</sup>(H<sub>2</sub>O)<i>n</i>→k1 <sub>MH</sub><sup>+</sup> (H<sub>2</sub>O)<sub><i>y</i></sub> + (<i>n</i> – <i>y</i>) H<sub>2</sub>O and M + MH<sup>+</sup> (H<sub>2</sub>O)<i>y</i>→k2 M<sub>2</sub>H<sup>+</sup> + <i>y</i>H<sub>2</sub>O. Ions with a drift time between\n9 and 18 ms in the\nfirst drift region were subsequently mobility analyzed in purified\nair with the second drift region using a synchronized second ion gate\nwith boxcar averaging. Slope for plots of ion abundance against drift\ntime was fitted by successive approximation between peaks of H<sup>+</sup>(H<sub>2</sub>O)<sub><i>n</i></sub> and MH<sup>+</sup>(H<sub>2</sub>O)<sub><i>y</i></sub> to obtain <i>k</i><sub>2</sub> until computed and experimental slopes matched within\na maximal deviation of 0.01. Values for <i>k</i><sub>1</sub> were obtained from the experimental baseline slope when adjusted\nfor <i>k</i><sub>2</sub>. Rate coefficients for triethyl\nphosphate and phenylacetate were determined using this method with <i>k</i><sub>1</sub> values of 1.14 × 10<sup>–9</sup> ± 1.87 × 10<sup>–10</sup> cm<sup>3</sup>/s and\n0.81 × 10<sup>–9</sup> ± 9.26 × 10<sup>–11</sup> cm<sup>3</sup>/s and <i>k</i><sub>2</sub> values of 1.05\n× 10<sup>–9</sup> ± 4.13 × 10<sup>–10</sup> cm<sup>3</sup>/s and 1.07 × 10<sup>–9</sup> ± 1.86\n× 10<sup>–10</sup> cm<sup>3</sup>/s, respectively. Relative\nerror for this method was determined using mobility spectra generated\nwith a COMSOL model and artificial rate coefficients. Rate coefficients\nwere then extracted from the modeled mobility spectra and compared\nto the original artificial values. Relative error of this method was\n10% and should be generally applicable for individual substances with\nreactions forming protonated monomers and proton bound dimers.